Opening
Transcriber's Note:
Text:
Words surrounded by a tilde such as ~this~ means the word is in bold face.
Letters in brackets with an = sign before it means that the letters have a macron over them, e.g. H[=A=c] signifies that the Ac has a macron over it.
Numbers and equations:
Parentheses have been added to clarify fractions.
Underscores before bracketed numbers in equations denote a subscript.
Superscripts are designated with a caret and brackets, e.g. 11.1^{3} is 11.1 to the third power.
The symbol .'. designates the symbol usually used for therefore (three periods in a triangle shape).
A down arrow is represented by a vertical line over a capital V. Like this: | V
Minor typographical errors have been corrected. Footnotes have been moved to the end of the chapter, and all advertisements have been moved to the end of the book.
A TEXT-BOOK OF ASSAYING: FOR THE USE OF THOSE CONNECTED WITH MINES.
by
C. AND J. J. BERINGER.
Revised by
J. J. BERINGER,
Assoc. of the Royal School of Mines; Fellow of the Chemical Society and of the Inst. of Chemistry; Principal of the Camborne Mining School; and Late Public Analyst for the County of Cornwall.
With numerous Diagrams and Tables.
Ninth Edition.
London: Charles Griffin and Company, Limited, Exeter Street, Strand. 1904. [All rights reserved.]
PUBLISHER'S NOTE TO THE NINTH EDITION
The continued popularity of the present work, the last edition of which was published only a little over a year ago, continues to be a source of gratification to the publishers, who have much pleasure in issuing the present edition.
January 1904.
PREFACE TO THE SIXTH EDITION
The principal changes in this edition are additions to the articles on Gold, Cyanides, and Nickel, and a much enlarged Index. The additional matter covers more than forty pages.
J. J. BERINGER.
CAMBORNE, January 1900.
Preface
The Text-book now offered to the public has been prepared to meet the existing want of a practical "handy book" for the Assayer.
To mining men the word "assaying" conveys a sufficiently clear meaning, but it is difficult to define. Some writers limit it to the determination of silver and gold, and others imagine that it has only to do with "furnace-work." These limitations are not recognised in practice. In fact, assaying is becoming wider in its scope, and the distinction between "assayers" and "analysts" will in time be difficult to detect. We have endeavoured rather to give what will be of use to the assayer than to cover the ground within the limits of a faulty definition.
At first our intention was to supply a description of those substances only which have a commercial value, but on consideration we have added short accounts of the rarer elements, since they are frequently met with, and occasionally affect the accuracy of an assay.
Under the more important methods we have given the results of a series of experiments showing the effect of varying conditions on the accuracy of the process. Such experiments are often made by assayers, but seldom recorded. Statements like those generally made--that "this or that substance interferes"--are insufficient. It is necessary to know under what conditions and to what extent.
Students learning any particular process cannot do better than repeat such a series of experiments. By this means they will, at the same time, acquire the skill necessary for performing an assay and a confidence in their results based upon work under different conditions.
The electrolytic method of copper assaying given under Copper is a modification of Luckow's; it was introduced by us into the offices of the Rio Tinto Copper Company, and has been in use for many years with success. This modification is now employed in copper-works in Spain, Germany, and England, and is used in place of the dry assay for the commercial valuation of copper ores.
We have adhered to the gram and the "c.c." as the units of weight and volume. Those who prefer working with grains and grain-measures can use the figures given, multiplied by ten. For example:--When 1 gram is mentioned, 10 grains should be used, and 10 grain-measures take the place of 1 "c.c." It is not advisable to mix the two systems, as by using gram weights and grain-measures.
We have intentionally to a large extent omitted to mention the names of those who have originated or modified the various processes. The practice of naming a process after its discoverer has developed of late years, and is becoming objectionable. It is a graceful thing to name a gas-burner after Bunsen, or a condenser after Liebig; but when the practice has developed so far that one is directed to "Finkenerise" a residue, or to use the "Reichert-Meissl-Wollny" process, it is time to stop.
We are indebted to the standard works of Allen, Crookes, Fresenius, Lunge, Michell, Percy, and Sutton, and wish to express our sense of special indebtedness to Mr. Richard Smith, of the Royal School of Mines. One or two of the illustrations are taken from Mr. Sexton's excellent little book on Qualitative Analysis. Our obligation to some others is mentioned in the text.
Finally, we have to thank for assistance in the experimental work Messrs. Bailey, Beswick, Clarke, Grant, Higgins, and Smith.
THE AUTHORS.
CAMBORNE, Nov. 1889.
Chapter I
INTRODUCTORY. Page Object of assaying 1 Sampling 1 Drying: determination of moisture 5 Calculation and statement of results 7 Laboratory books and report forms 9 Quantity to be taken for an assay 11 Exercises 14
II. METHODS OF ASSAYING.--DRY GRAVIMETRIC METHODS
Methods of assaying 15 Gravimetric methods 15 Mechanical separations 16 Dry assays 16 (a) Fluxes 16 (b) Reducing agents 21 (c) Oxidising agents 22 (c) Apparatus 24
III. WET GRAVIMETRIC METHODS
Wet gravimetric methods 27 (a) Solution 29 (b) Precipitation 30 (c) Filtration 31 (c) Drying and igniting 32
IV. VOLUMETRIC ASSAYS
Titrometric assays 35 (a) Standard solutions 36 (b) Standardising 37 (c) Methods of working 42 (c) Indirect titration 43 Colorimetric assays 44 Gasometric assays 44
V. WEIGHING AND MEASURING
Weighing 47 Measuring liquids 49 (a) Graduated flasks 49 (b) Pipettes 50 (c) Burettes 51 Measuring gases 52
VI. REAGENTS
Acids, &c. 54 Bases, salts, &c. 59
Chapter VII
Formulæ, equations, &c. 68
VIII. SPECIFIC GRAVITY
Introductory 75
Determination of specific gravity-- (a) Hydrometers 76 (b) Specific gravity bottles 78 Calculations depending on specific gravity 84
IX. SILVER, GOLD, PLATINUM, CYANIDES, MERCURY
SILVER--Detection 87 Dry assay 87 (1) Scorification 88 (2) Pot assays, average ores 90 " ores with metallic oxides 91 " ores with metallic sulphides 91 Explanatory notes on the fusion 93 The effect of charcoal, flour, &c. 94 The effect of nitre 95 The effect of mineral sulphides 95 (3) Cupellation 98 The loss of silver 101 Condition affecting the loss 102 Methods of correction 103 Lead required for cupellation 105 (4) Calculation of the results in ounces to the ton of 2240 lbs. Table 107 Ores with metallic particles 108 (5) Explanatory notes 110 (6) Examples of dry silver assays 113 Wet assays 116 Gravimetric method 117 Gay-Lussac's method 119 Volhard's method 121 A modified Gay-Lussac 123 Volhard's method applied to arsenic 124 GOLD--Detection 126 Amalgamation assay 126 Dry assay 127 (1) Size of charges 127 (2) Sampling 127 (3) Assay tons 131 (4) Small buttons, weighing 131 " " measuring 133 (5) Concentration in lead 136 Quartz ores 136 Ores with oxide of iron 138 Ores with metallic sulphides 139 (6) Cyanide charges, residues, &c. 140 (7) Cupellation 142 Cupels 142 Cupellation temperature 143 Cupellation loss 145 (8) Inquartation 146 (9) Flatting 149 (10) Parting, in flasks 151 " in test tubes 152 " in glazed crucibles 153 " Loss, &c. 154 (11) Check assays, surcharge 154 (12) Bullion assays in special apparatus 156 Silver, &c., in gold bullion 157 (13) Sampling of base bullion, &c. 157 CYANIDES--Commercial cyanides 160 Double cyanides 161 Prussic acid 162 Gold-dissolving power of cyanide liquor 162 Assay for cyanide strength 163, 165 Assay of commercial cyanide 167 Alkalinity of cyanides 167 Acidity of ores 168 Metals in cyanide liquors 169 Cyanicides 169 PLATINUM 170 IRIDIUM 171 MERCURY 171 Dry assay 172 Wet method 173
X. COPPER, LEAD, THALLIUM, BISMUTH, ANTIMONY
COPPER--Introductory 175 Dry assay 176 Valuation of copper ores 181 Wet methods 183 (1) Electrolytic assay 184 Volumetric methods 194 (1) Cyanide method 194 (2) Iodide method 199 (3) Colorimetric method 203 Examination of commercial copper 205 LEAD 211 Dry assay 211 Wet assay 213 (1) Gravimetric method 213 (2) Volumetric method 214 (3) Colorimetric method 218 THALLIUM 219 BISMUTH 220 Dry assay 221 Wet method 221 (1) Gravimetric determination 222 (2) Colorimetric assay 223 ANTIMONY 225 Dry assay 225 Wet method 227 (1) Gravimetric assay 228 (2) Volumetric method 229
XI. IRON, NICKEL, COBALT, ZINC, CADMIUM
IRON 231 Gravimetric determination 233 Permanganate and bichromate methods 234 Stannous chloride method 244 Colorimetric determination 247 NICKEL 251 Dry assay 251 Electrolytic assay 254 Titration by cyanide 255 COBALT 259 ZINC 261 Gravimetric method 262 Volumetric method 263 Gasometric method 266 CADMIUM 269
XII. TIN, TUNGSTEN, TITANIUM
TIN 271 Vanning 273 Dry assay 276 Detection, &c. 279 Gravimetric determination 281 Volumetric determination 282 Examples 284 TITANIUM 292 TUNGSTEN 295 NIOBIC AND TANTALIC OXIDES 297
XIII. MANGANESE, CHROMIUM, ETC
MANGANESE 298 Gravimetric determination 300 Volumetric determination 300 Ferrous sulphate assay 301 Iodine assay 302 Colorimetric determination 306 CHROMIUM 307 VANADIUM 310 MOLYBDENUM 311 URANIUM 312
XIV. EARTHS, ALKALINE EARTHS, ALKALIES
ALUMINA 314 THORIA 317 ZIRCONIA 317 CERIUM 318 LANTHANUM AND DIDYMIUM 319 YTTRIA 319 BERYLLIA 319 LIME 320 STRONTIA 324 BARYTA 326 MAGNESIA 328 THE ALKALIES 330 SODIUM 334 POTASSIUM 336 LITHIUM 338 CÆSIUM 339 RUBIDIUM 340 AMMONIUM 340
XV. OXYGEN AND OXIDES--THE HALOGENS
OXYGEN 344 OXIDES 345 WATER 350 THE HALOGENS 358 CHLORINE 359 BROMINE 361 IODINE 362 FLUORINE 363
XVI. SULPHUR AND SULPHATES
SULPHUR 367 Gravimetric determination 369 Volumetric determination 370 SULPHATES 377 SELENIUM 379 TELLURIUM 379
XVII. ARSENIC, PHOSPHORUS, NITROGEN
ARSENIC 381 Gravimetric determination 383 Volumetric method, "iodine" 384 " " "uranic acetate" 389 PHOSPHORUS 394 Gravimetric determination 396 Volumetric determination 397 NITROGEN AND NITRATES 400
XVIII. SILICON, CARBON, BORON
SILICON AND SILICATES 405 CARBON AND CARBONATES 414 COALS 418 SHALES 420 CARBONATES 424 BORON AND BORATES 429
APPENDIX A.
Table of atomic weights and other constants 433 Table for converting degrees of the centigrade thermometer into degrees of Fahrenheit's scale 435 Tables showing strengths of aqueous solutions of nitric and hydrochloric acids, of ammonia and of sulphuric acid 436
APPENDIX B.
Estimation of small quantities of gold 440 Practical notes on the iodide process of copper assaying 441 Method of separating cobalt and nickel 442
APPENDIX C.
A lecture on the theory of sampling 444
INDEX 450
A TEXT-BOOK OF ASSAYING.
I. INTRODUCTORY
Assaying has for its object the determination of the quantities of those constituents of a material which add to or detract from its value in the arts and manufactures. The methods of assaying are mainly those of analytical chemistry, and are limited by various practical considerations to the determination of the constituents of a small parcel, which is frequently only a few grains, and rarely more than a few ounces, in weight. From these determinations calculations are made, which have reference to a mass of material of, perhaps, hundreds of tons. But in all cases, whether the mass under consideration be large or small, whether the material be obtained by mining, grown, or manufactured, the assayer is supposed to receive a small quantity, called "the sample," which is, or ought to be, the exact counterpart of the mass of material that is being dealt with. The taking and making of this sample is termed "sampling"; and the men whose special work it is to select such samples are "the samplers."
But although "sampling" is thus distinct from "assaying," the assayer should be familiar with the principles of sampling, and rigorous in the application of these principles in the selecting, from the sample sent him, that smaller portion upon which he performs his operations.
~Sampling.~--In the case of gases, there is absolutely no trouble in mixing. The only difficulty is in drawing off a fair sample where, as in flues, the body of the gas is in motion, and varies a little in composition from time to time. In this case, care must be taken to draw off uniformly a sufficient volume of the gas during a prolonged period; any portion of this larger volume may then be taken for the analytical operation.
In the case of liquids, which mix more or less easily--and this class includes metals, &c., in the state of fusion--more or less severe agitation, followed by the immediate withdrawal of a portion, will yield a fairly representative sample.
In the case of solids, the whole mass must be crushed, and, if not already of fairly uniform quality, mixed, before sampling can take place. Most of the material which a sampler is called upon to deal with, is, however, in a more or less divided state and fairly uniform. In practice it is assumed that 5 per cent. of the whole (= 1/20th), if taken in portions of equal weight and at frequent and regular intervals, will represent the mass from which it was taken. Taking a heap of ore, A, and selecting one out of every twenty spade-, bag-, barrow-, or wagon-fuls, according to the quantity of stuff in the heap, there is obtained a second heap, B, containing one-twentieth of the stuff of the heap A. If we crush the stuff in B until this heap contains approximately the same number of stones as A did--which means, crushing every stone in B into about twenty pieces--B will become the counterpart of A. Selecting in the same manner 5 per cent. of B, there is got a third heap, C. This alternate reduction and pulverising must be carried on until a sample of suitable size is obtained. This may be expressed very clearly thus:--
A = 1000 tons of rocks and lumpy ore. B = 50 " " rough stones, 1/20th of A. C = 2.5 " " small stones, 1/20th of B. D = 0.125 " " coarse powder, 1/20th of C.
If the material to be sampled is already a dry powder, 5 per cent. of it should be heaped in a cone; each lot being added on the apex of the cone already formed, so that it may distribute itself by falling evenly in all directions. When the cone is completed, convert it into a low frustrum of a cone by drawing stuff uniformly and in a direct line from the centre to the circumference. Draw two diameters at right angles to each other, and reserving any two alternate quarters, reject the others. Mix; and form another cone, and proceed until a sample is got of the bulk required.
This is the usual plan, and all samples should be treated in this way when the stuff is fine enough to fall evenly down the sides of a cone.
Samples as they reach the assay office are seldom in a fit state for the work of the assayer; they are generally too coarse, and ought always to be more than he wants for any particular determination. The portion he requires should never be taken at hap-hazard; the sample must be reduced systematically to the quantity required.
1. If the sample is a liquid: it is sufficient to shake the bottle, and take out a measured or weighed quantity for the assay.
2. If a liquid with a solid in suspension: measure the whole of it. Filter. Make up the filtrate with the wash-water or water to the original bulk. Assay it. Dry and weigh the residue, and make a separate assay of it.
3. If of a creamy consistency, free from heavy particles: mix well; spread out evenly on a glazed tile. Take up equal portions at equal distances. Mix and assay.
4. If a mud of coarse and fine particles, or of particles of unequal density: weigh and transfer to a porcelain dish, or weigh in the dish. Dry at 100° C., weigh. Treat the residue as a solid capable of being powdered.
5. If a solid capable of being powdered, or already powdered: heap up into a cone; flatten with a spatula; divide along two diameters at right angles, and carefully reject the whole of two alternate quarters, brushing away any fine powder. Mix the other quarters, and repeat (if necessary). For small quantities a fine state of division is essential.
6. If a solid with metallic particles: powder and pass through a sieve; the metallic particles will not pass through. Weigh both portions and assay separately. Sifting should be followed by a very thorough mixing.
7. If a metal or alloy in bar or ingot: clean the upper surface of the bar, and bore through the bar. Use the borings. If the ingot or bar is small, cut it through and file the section. Filings must be freed from fragments of the file by means of a magnet; and from oil, if any be present, by washing with a suitable solvent.[1] Where practicable, metals and alloys are best sampled by melting and granulating. The student must carefully avoid any chance of mixing dirt or particles of other samples with the particular sample which he is preparing. One ore should be done at a time, and when finished, it should be labelled and wrapped up, or bottled, before starting on a fresh sample.
When an ore requires to be very finely ground in an agate mortar, it is often advisable to mix with a little pure alcohol and rub until free from grit; dry at 100° C. and mix well before weighing.
When an assay is required of a quantity of ore made up of parcels of different weight and quality, each parcel should be separately sampled and parts of each sample, bearing to each other the same proportion by weight as the original parcels, should be taken and mixed. For example, a lot of ore is made up of one parcel of A, 570 tons, one of B, 180 tons, and another of C, 50 tons; a sample representing the whole may be got by mixing 57 parts of a sample of A with 18 parts of a sample of B, and 5 parts of a sample of C.
A bruising plate, like that in fig. 2, is convenient for general office work. The slab is of cast iron, about an inch thick. It is firmly supported on a solid block of wood, and pivoted for convenience in emptying. The bruising-hammer is steel-faced, about 4 inches square, and 1-1/2 inch thick. The block is firmly fixed to a small table or tressel, so that the slab is about 2 feet 6 inches from the ground. The slab is cleaned, and the sample collected with the help of a stiff-haired brush.
~Drying: Determination of Moisture.~--In practice, the moisture is generally determined by the samplers, and the proportion is specified in grains per pound on the label attached to the sample when it reaches the assay office. The method adopted is usually to dry 1 lb. = 7000 grs. of the ore in a frying-pan heated over a gas flame, or in an ordinary oven, until a cold bright piece of metal or glass is no longer damped when held over it. The loss of weight in grains = moisture.
Properly, however, this work should be done by the assayer, if only for the following reason. It is assumed that the dry ore of the sampler and of the assayer are the same thing; according to the nature of the ore, this may or may not be the case. The assayer, however, uses the sample which he has dried for his moisture-determination, as the dry ore on which he makes his other assays, and no variation in moisture would influence the other and more important determinations. Some ores are sent to the smelter with from 5 to 15 per cent. of adherent water. In these cases it is best to spread out the sample, and taking equal portions fairly at regular intervals, weigh into a Berlin dish 20 grams. This should then be dried over a sand-bath, or if the ore is likely to be injured by excess of heat, over a water-bath until the weight is constant. The loss of weight multiplied by 5 gives the percentage of water present.
Example:--
Weight of dish + wolfram 32.67 grms. " " dish 12.67 " ----- " " wolfram 20.00 "
" " dish + wolfram 32.67 " " " " dried 30.15 " ----- " " water 2.52 "
2.52 × 5 = 12.6 ~12.6%.~
There are other ores which are not apparently wet, but in the state called "air-dried." It is easier to take fair samples of these, and, consequently, it is not necessary to use so large a quantity as 20 grams. But with a smaller quantity, extra precautions must be taken. All dry solids at ordinary temperatures absorb moisture from the air. The amount varies with the nature of the material and with the quantity of surface exposed. Light bulky powders absorb more than heavy ones, because of the greater condensing surface. It is on this account that it is well to weigh substances, which have been dried, between close-fitting watch-glasses. The method of determining moisture is to weigh out into the glasses 5 grams of ore, and dry in the water-oven until there is no further loss of weight. On taking the glasses out of the oven, they should be at once closed, the clip put on, and after cooling in a desiccator weighed. If after a second trial the loss is the same, or only increased by a milligram, the determination is finished.
Example:--
Weight of glasses + pyrites 31.0470 grms. " " glasses 26.0470 " ------- " " pyrites 5.0000 " " " glasses + pyrites, dried 1 hour 30.8965 " " " " " dried 1-1/2 " 30.8957 " " " " " 31.0470 " " " " " dried 30.8957 " ------- " " moisture 0.1513 "
0.1513 × 20 = 3.026 ~3.02%.~
Sometimes it may be advisable to dry 10 grams, in which case multiplying the loss by 10 will give the percentage. The dried ore should be transferred to a weighing-tube (fig. 3), and reserved for the subsequent determinations. The weighing-tube with the ore must be marked, and kept in a desiccator.
Most ores and inorganic substances can be dried, and their moisture determined by the loss in this way. When, however, the substance contains another somewhat volatile ingredient, it is exposed over sulphuric acid in a desiccator for two days (if in vacuo, all the better), and the loss determined. Moisture in dynamite should be determined in this way.
When water is simply mechanically mixed with a substance it presents but little difficulty. The combined water is a different matter. Slaked lime, even when perfectly dry, contains much water; and if the water of soda crystals were separated and frozen, it would occupy a volume equal to that of the original crystals. Perfectly dry substances may contain much water, and this combined water is retained by different materials with very unequal vigour. Sodium sulphate and sodium phosphate crystals lose water even when exposed under ordinary conditions to dry air. Soda crystals when heated melt, and at a moderate temperature give off their water with ebullition. The temperature at which all the water is given up varies with each particular salt; the actual determination of the water in each case will require somewhat different treatment. Such determinations, however, are seldom required; and from a practical point of view this combined water causes no trouble.
In assaying ores, we term "moisture" all water which is lost by exposure in a water-oven at 100° C., and the "dry ore" is the ore which has been dried at this temperature. No advantage, but rather endless confusion, would be caused by varying the temperature with the object of estimating the whole of the water which a hydrated salt may contain. The results of the assay of the other components should be calculated on the "dry ore." One advantage of this is obvious:--The dry ore has a constant composition, and the results of all assays of it will be the same, no matter when made; the moisture, however, may vary from day to day, and would be influenced by a passing shower of rain. It is well to limit this variability to the moisture by considering it apart, and thus avoid having the percentage, say, of copper rising and falling under the influence of the weather.
In the case of certain salts, however, such as soda crystals and hydrated sulphate of copper (when these constitute the bulk of the substance to be assayed), it is as well to perform the assay on the moist, or at any rate air-dried, substance.[2] It would be equally convenient to calculate on the substance dried at 100° C.; but in this case it would be well, in order to avoid a somewhat shallow criticism, to replace the term "moisture" by the longer but equivalent phrase "water lost at 100° C."
~Calculation and Statement of Results.~--By far the most generally convenient method of stating the results of an assay is that of the percentage or parts in a hundred, and to avoid a needlessly troublesome calculation it is well to take such a quantity of ore for each assay as by a simple multiplication will yield the percentage. In these calculations decimals are freely employed, and students should make themselves familiar with the methods of using them.
Other methods of statement are in use, and have advantages in certain special cases. With bullion the parts in a thousand are given, and in those cases in which the percentage is very small, as in water analysis, it is convenient to report on parts in 100,000, or even on parts per 1,000,000. These are easily got from the corresponding percentages by shifting the decimal point one, three, or four places to the right. Thus 92.5 per cent. is 925 per thousand; and 0.0036 per cent. is 3.6 per 100,000, or 36 per million.
With ores of tin, silver, and gold, the result is stated as so many cwts., lbs., or ozs., in the ton. With dressed tin ores as they are sent to the smelter, the produce is given in cwts. and quarters to the ton. The corresponding percentage may be obtained by multiplying by five; or, inversely, if the percentage is given, the produce may be got by dividing by five. A produce of 13-1/2 equals a percentage of 13.5×5 = 67.5; and a percentage of 70.0 equals a produce of 70/5 = 14. With tin ores as raised (in which the percentage is small) the reduction must be carried to pounds per ton. One per cent. equals 22.4 lbs. to the ton; consequently, if we multiply the percentage by 22.4, the produce will be given. Thus, if an ore contains 6.7 per cent. of oxide of tin, the produce is 6.7×22.4 = 150 lbs. (or 1 cwt., 1 quarter, and 10 lbs.) to the ton. With gold and silver ores, the proportion of precious metal is small, and it is necessary to carry the reduction to ozs. and dwts. to the ton; and since gold and silver are sold by troy weight, whilst the ton is avoirdupois, it is of importance to remember that the ounces in the two systems are not the same. A ton contains 15,680,000 grains, which equal 653,333.3 dwts. or 32,666.6 ozs. (troy). The following rules are useful:--
To get ozs. (troy) per ton, multiply parts per 100,000 by 0.327; To get dwts. per ton, multiply parts per 100,000 by 6.53; To get grains per ton, multiply parts per 100,000 by 156.8.
Where liquids are being assayed, cubic centimetres are held to be equivalent to grams, and the usual method of statement is, "so many parts by weight in so many by measure." Where the statement is made as grams per litre or grains per gallon, there can be no doubt as to what is meant; and even if it be expressed in parts per 100,000, parts by weight in a measured volume must be understood unless the contrary is expressly stated.
In some cases, where the density of the solution differs greatly from that of water, the percentage by weight may be given; and in others, mixtures of two or more liquids, the percentages may be given by volume or by weight; as so many c.c. in 100 c.c., or as so many grams in 100 grams, or even as so many grams in 100 c.c. In such cases it must be distinctly shown which method of statement is adopted.
One grain per gallon means 1 grain in 70,000 grain-measures, or one part in 70,000. Dividing by 7 and multiplying by 10 will convert grains per gallon into parts per 100,000. Inversely, dividing by 10 and multiplying by 7, will convert parts per 100,000 into grains per gallon.
Grams per litre are parts per 1000; multiplying by 100 will give parts per 100,000, and multiplying by 70 will give grains per gallon.
Among foreign systems of weights, the French is by far the best. Kilograms (2.205 lbs.) per quintal (220.5 lbs.) are parts per cent.; and grams (15.43 grs.) per quintal are parts per 100,000. From the rule already given, grams per quintal may be converted into ounces to the ton by multiplying by 0.327.
The German loths per centner (1/2 oz. (avoirdupois) to 100 lbs.) equal parts per 3200; they are converted into parts per cent. by dividing by 32, or into ounces (troy) per ton by multiplying by 10.208.
In the United States, as a sort of compromise between the avoirdupois and metric systems, a ton is taken as 2000 lbs. There, too, the custom is adopted of reporting the gold and silver contents of an ore as so many dollars and cents to the ton. In the case of gold, an ounce is considered to be worth 20.6718 dollars. With silver, the nominal value is 1.2929 dollars per ounce, but frequently in assay reports it is taken as one dollar. The practice is objectionable. The prices of metals vary with the fluctuations of the market, and if the assayer fixed the price, the date of his report would be all important; if, on the other hand, he takes a fixed price which does not at all times agree with the market one, it leaves a path open for the deception of those unacquainted with the custom. American "dollars on the ton of 2000 lbs." may be converted into "ounces in the ton of 2240 lbs." by dividing by 1.1544 in the case of silver, and by 18.457 in the case of gold.
~Laboratory Books and Report Forms.~--The record which the assayer makes of his work must be clear and neat, so that reference, even after an interval of years, should be certain and easy. One method should be adopted and adhered to. Where there are a large number of samples, three books are required.
Sample Book.--This contains particulars of the samples (marks, &c.), which are entered by the office-clerk as they arrive. He at the same time puts on each sample the distinguishing number.
EXAMPLE OF PAGE OF SAMPLE BOOK.
+----------+----------+--------------------------+----------------+ | Date. | Number. | Sample. | Remarks. | +----------+----------+--------------------------+----------------+ | Feb. 1 | 482 | Tough Copper | For Arsenic. | | " 2 | X | Piece of Metal | For Ni and Cu. | | " | 483 | Tough Copper. | | | " | 73 | Silver Precipitate, | With Letter. | | | | 4 casks, 24 cwt. 1 qr. | | | " | 494 | Purple Ore, 200 tons. | | | " | 1 J.T. | Lead Ore, 1 J.T. | From Corsica. | | " | 2 J.T. | " 2 J.T. | | +----------+----------+--------------------------+----------------+
Laboratory Book. This is the Assayer's note-book, in which he enters clearly the particulars of his work--the results obtained, as well as how these results were arrived at. The calculations should be done on scrap-paper, and should not be entered, although, of course, detail enough must be shown to enable the results to be recalculated.
EXAMPLE OF PAGE OF LABORATORY BOOK. ______________________________________________________________
Purple Ore 5 grams 19/10/89 0.0042 grm. 0.0021 " ------ Colorimetric 0.0063 × 20 = 0.13% Copper ______________________________________________________________
482 Tough Copper 10 grams Feb. 1/89 10.5 c.c. Uranium. = 0.52% Arsenic ______________________________________________________________
2082 Tough Copper 10 grams 12.7 c.c. Uranium. = 0.63% Arsenic ______________________________________________________________
491 10 grams Tough Copper 13.7 c.c. Uranium Feb. 1/89 = 0.68% Arsenic ______________________________________________________________
Standard of Uranium acetate. 0.150 gram As_{2}O_{3} = 23.3 c.c. Uranium. .'. 100 cc. Uranium = 0.5 gram As. ______________________________________________________________
10071 5 grams Tin Ore Cruc. and SnO_{2} 9.6065 grms. Feb. 3/89 Cruc. and Ash 9.4235 " ------ SnO_{2} = 0.1830 = 2.88% Tin ______________________________________________________________
The Assay Book.--This is the Official book, and is a combination of the Sample and Laboratory books. It corresponds with the report-forms. Without being loaded with detail, it should contain sufficient to characterise each sample.
Key to following example page of Assay book: DR = DATE REPORTED. Not Det. = Not detected
EXAMPLE OF PAGE OF ASSAY BOOK.
-------------------------------------------+----+-------+---------------+---- DESCRIPTION OF SAMPLE. | | Water | Assay on | ------+--------------------+---------------| |Lost at| the Dry | Date. | Material. | Weight. |No. |100° C.|Material. | DR ------+--------------------+---+---+---+---+----+-------+---------------+---- 1889 | |ton|cwt|qrs|lbs| | | | Feb. 1|Tough cake copper | | | | | 482| |Arsenic, 0.52% | 7 " |Tough cake copper | | | | |2082| |Arsenic, 0.63% | 7 " |Tough cake copper | | | | | 491| |Arsenic, 0.68% | 7 | | | | | | | | | Feb. 2|Nickel disc for C.R.| | | | | X | |Copper, 73.75 | 7 | | | | | | | |Nickel, 24.34 | | | | | | | | |Iron, 2.18 | | | | | | | | | ----- | | | | | | | | | 100.27 | | | | | | | | | ------ | " |Silver precipitate, | | 24| 1| 0| 73| Not | | | 4 casks | | | | | | det. |Silver, 4.851 | 10 | | | | | | | |Gold, 0.0215| | | | | | | | |Lead, 19.37 | | | | | | | | |Zinc, 2.00 | | | | | | | | |Silver, 1584.7 | | | | | | | | | ozs. per ton | | | | | | | | |Gold, 7.0 | | | | | | | | | ozs. per ton | " |Purple ore |200| | | | 494| Not |Copper, 0.13% | 11 | | | | | | | det. |Sulphur 0.15% | ------+--------------------+---+---+---+---+----+-------+---------------+----
When the number of samples is small, the Sample Book may be omitted, and the entries made in the Assay Book as the samples arrive.
Report-forms. These should entail as little writing as possible in making out the report. For general purposes the form given on p. 12 is useful.
~The quantity of substance~ to be taken for any particular assay depends largely upon the method of assay adopted. There are, however, some general considerations which should be remembered, and some devices for simplifying the calculations which should be discussed.
The smaller the percentage of the substance to be determined, the larger should be the amount of the ore taken. The following table will give a general idea as to this:--
Percentage of the substance Amount of ore, &c. to to be determined. be weighed. 100-10 1 gram. 10-5 2 grams. 5-1 5 " 1-0.1 10 " 0.1-0.01 20 "
The rougher the method of assay adopted, the larger should be the quantity of ore taken. If the degree of accuracy attainable with the methods and instruments at the assayer's service is known, it is easy to calculate what quantity should be taken for any particular case. If the results are good within 0.001 gram, then, taking 1 gram of ore we can report within 0.1 per cent., or if they are good within 0.0002 gram, taking 20 grams of ore, we can report within 1 part per 100,000, or very closely within 6-1/2 dwt. to the ton. If it is wished to be yet more particular in reporting, larger quantities must be taken. The difficulty of manipulating very small or very large precipitates, &c., must be borne in mind. So, too, must the fact that the greater the weight of the final product of an assay, the less, as a rule, is the percentage error. The distinction between absolute and percentage error, often overlooked, is important. If 0.5 gram of silver be cupelled with 20 grams of lead, there may be obtained a button of 0.495 gram; the absolute loss is 0.005 gram, and this equals 1 per cent. of the silver present. Similarly, cupelling 0.1 gram, the resulting button may be 0.098; the absolute loss is only 0.002 gram, but this equals 2 per cent. of the silver present. In the same way the student should see that the two results, 91.5 per cent. and 92.0 per cent., are really more concordant than the results 9.1 per cent. and 9.2 per cent.
A device often adopted in practice where a large number of assays of one kind are made, and the report is given as so many ounces or pounds to the ton, is that known as the assay ton. The assay ton may be any arbitrary and convenient weight, but its subdivisions must bear to it the same relations as pounds and ounces bear to the actual ton. On the other hand, in a laboratory where many kinds of work are performed, different sets of weights of this kind would only tend to confusion, even if they were not unnecessary. With a set of gram weights and its subdivisions anything may be done. If it is desired to report as pounds to the ton, then, since there are 2240 lbs. to the ton, a weight of 2.240 grams may be taken as the assay ton, and each 0.001 gram yielded will equal 1 lb., or 22.4 grams may represent the ton, and each 0.01 gram a pound. Similarly, since there are 32,666.6 ozs. troy to the ton; if we take 32.6667 grams as the assay ton, each 0.001 gram will equal 1 oz. to the ton. In some cases it may be convenient to have, in addition to the usual gram weights, one or other of the "assay tons" mentioned above, but generally it is better to work on a purely decimal system, and convert when required into ounces per ton, &c., either by actual calculation or by reference to a set of tables.
PRACTICAL EXERCISES.
The student should practise such calculations as the following:--
1. Calculate the percentages in the following cases:-- (a) Ore taken, 2 grams; copper found, 0.2155. (b) " 1.5 gram; iron found, 0.8340. (c) " 30 grams; lead found, 23.2.
2. Calculate the parts per thousand in the following:-- (a) Bullion taken, 1.1 gram; silver found, 1.017. (b) " 1.14 gram; silver found, 1.026. (c) " 0.6 gram; gold found, 0.5500.
3. Calculate parts per 100,000 in the following:-- (a) Ore taken, 20 grams; silver found, 0.0075. (b) " 50 grams; gold found, 0.0026. (c) Water taken, 500 c.c.; solids found, 0.1205.
4. Calculate cwts. to the ton in the following:-- (a) Ore taken, 5 grams; tin found, 2.816. (b) " 5 grams; tin found, 3.128. (c) An ore with 68.2 per cent. of tin.
5. Calculate lbs. to the ton in the following:-- (a) An ore with 3.28 per cent. oxide of tin. (b) Ore taken, 20 grams; oxide of tin found, 1.67.
6. Calculate ozs. (troy) to the ton in the following:-- (a) Ore taken, 50 grams; gold found, 0.0035. (b) " 20 grams; silver found, 0.0287. (c) " 25 grains; silver found, 0.0164.
7. Calculate in grains per gallon:-- (a) 0.51 gram per litre. (b) 24.6 parts per 100,000. (c) Solution taken, 100 c.c.; copper found, 0.0045 gram. (c) " 50 c.c.; iron found, 0.165 gram.
8. Convert into ozs. (troy) per ton:-- (a) 7 loths per centner. (b) 30 grams per quintal. (c) 15 parts per 100,000.
FOOTNOTES:
[1] Ether or carbon bisulphide.
[2] Such substances are best dried by pressing between folds of dry filter-paper.
II. METHODS OF ASSAYING.--DRY GRAVIMETRIC METHODS
The methods of assaying are best classed under two heads, Gravimetric and Volumetric, in the former of which the final results are weighed, whilst in the latter they are measured. A commoner and older division is expressed in the terms much used in practice--wet assays and dry assays. Wet assays include all those in which solvents, &c. (liquid at the ordinary temperature), are mainly used; and dry assays, those in which solid re-agents are almost exclusively employed. Dry assays form a branch of gravimetric work, and we shall include under this head all those assays requiring the help of a wind furnace. Wet assays, as generally understood, would include not only those which we class as wet gravimetric assays, but also all the volumetric processes.
~Gravimetric Methods~ aim at the separation of the substance from the other matters present in the ore, so that it may be weighed; and, therefore, they must yield the whole of the substance in a pure state. It is not necessary that a metal should be weighed as metal; it may be weighed in the form of a compound of definite and well known composition. For example, one part by weight of silver chloride contains (and, if pure, always contains) 0.7527 part of silver; and a quantity of this metal can be as exactly determined by weighing it as chloride as by weighing it in the metallic state. But in either case the metal or its chloride must be pure.
Exact purity and complete separation are not easily obtained; and methods are used which are defective in one or both of these respects. It is well to note that an impure product increases the result, whilst a loss of the substance decreases it; so that if both defects exist in a process they tend to neutralise each other. Of dry methods generally, it may be said that they neither give the whole of the substance nor give it pure; so that they are only calculated to show the amount of metal that can be extracted on a manufacturing scale, and not the actual quantity of it present. Their determinations are generally rough and always low. The gold and silver determinations, however, will compare very favourably with any of the other processes for the estimation of these metals in their ores.
The calculation of the results of a gravimetric assay has already been referred to. If the result is to be stated as percentage, it may always be done by the following rule:--Multiply the weight of the substance got by the percentage of metal it contains, and divide by the weight of ore taken.
Gravimetric methods are divided into three groups: (1) mechanical separations; (2) dry methods; and (3) wet methods.
~Mechanical Separations.~--Under this head are classed the method of assaying tin ores, known as vanning, and the amalgamation assay for gold. A set of sieves to determine the relative proportion of powders of different degrees of fineness is sometimes useful. A set with 10, 20, 40 and 80 meshes to the inch is convenient.
~Dry Assays.~--An important distinction between wet and dry methods of assaying is, that in the former the substance is got into the liquid state by solution, whilst in the latter fusion is taken advantage of.
The difference between solution and fusion is easily illustrated: a lump of sugar heated over a candle-flame melts or fuses; suspended in water it dissolves. Many substances which are insoluble or infusible of themselves, become soluble or fusible when mixed with certain others; thus, in this way, solution is got with the aid of reagents, and fusion with the help of fluxes. For example, lead is insoluble in water, but if nitric acid be added, the metal rapidly disappears. It is convenient, but somewhat inaccurate, to say that the acid dissolves the lead. If the lead be acted on by nitric acid alone, without water, it is converted into a white powder, which does not dissolve until water is added; in this case it is obvious that the water is the solvent. The function of the acid is to convert the lead into a soluble compound.
~Fluxes~ may act as true solvents. Fused carbonate of soda dissolves baric carbonate, and perhaps in many slags true solution occurs; but in the great majority of cases a flux is a solid reagent added for the purpose of forming a fusible compound with the earthy or stony minerals of the ore. Few of the minerals which occur in the gangue of an ore are fusible; and still fewer are sufficiently fusible for the purposes of the assayer, consequently the subject is one of importance, and it ought to be treated on chemical principles. An idea of the composition of some of the more frequently occurring rocks may be gathered from the following table, which represents rough averages:--
----------------------------------------------------------------- | | |Oxide|Lime and | |Silica.|Alumina.| of |Magnesia.|Alkalies. | | |iron | | ----------------------------------------------------------------- | % | % | % | % | % Sandstone, grit, | | | | | quartzite, &c. |80-100 | -- | -- | -- | -- Granite, gneiss, | | | | | quartz-porphyry, | | | | | fire-clay, &c. | 70-75 | 13-20 | 2 | 2 | 5-8 | | | | |Less in | | | | |fire-clay. Mica-schist | 65 | 18 | 5 | 3 | 3 Trachyte, syenite | 60 | 17 | 7 | 4-7 | 6-9 Clay-slate | 60 | 18 | 10 | 8 | 3 Diorite | 54 | 17 | 12 | 9 | 3-4 Horneblende-rock | 50 | 18 | 15 | 12 | 3-4 Brick-clay | 50 | 34 | 8 | 6 | -- China-clay | 47 | 39 | -- | -- | -- Basalt, dolerite, &c.| 50 | 15 | 15 | 16 | 3 Serpentine | 44 | -- | -- | 44 | -- Chalk, limestone, | | | | | dolomite, &c. | -- | -- | -- | 45-55 | -- -----------------------------------------------------------------
Silica itself, and the silicates of alumina, of lime, and of magnesia, are practically infusible; the silicates of soda, of potash, and of iron are easily fusible if the base (soda, potash, or oxide of iron) be present in sufficient quantity, and if, in the case of the iron, it is present mainly as lower oxide (ferrous silicate). The addition of lime, oxide of iron, or alkali to silicate of alumina results in the formation of a double silicate of alumina and lime, or of alumina and iron, &c., all of which are easily fusible. Similarly, if to a silicate of lime we add oxide of iron, or soda, or even alumina, a fusible double silicate will be formed. Thus lime, soda, oxide of iron, and clay, are fluxes when properly used; but since lime, clay (and oxide of iron if there be any tendency to form peroxide), are of themselves infusible, any excess of these fluxes would tend to stiffen and render pasty the resulting slag. So, too, soda, which is a very strong base, may act prejudicially if it be in sufficient excess to set free notable quantities of lime and magnesia, which but for that excess would exist in combination as complex fusible silicates. There are many minerals which with but little soda form a glass, but with more yield a lumpy scoriacious mass. There are many minerals, too, which are already basic (for example, calcite), and which, when present, demand either a less basic or an acid flux according to the proportions in which they exist. For purposes of this kind borax, or glass, or clay with more or less soda may be used, and of these borax is by far the most generally useful. An objection to too basic a slag (and a very important one) is the speed with which it corrodes ordinary crucibles. These crucibles, consisting of quartz and clay, are rapidly attacked by lime, soda and bases generally.
In considering what is and what is not a good slag, certain chemical properties are of importance. If a mixture of many substances be fused and allowed to solidify in a crucible, there will be found some or all of the following. At the bottom of the crucible (fig. 4) a button of metal, resting on this a speise; then a regulus, next a slag made up of silicates and borates and metallic oxides, and lastly, on the top another layer of slag, mainly made up of fusible chlorides and sulphates. In assaying operations the object is generally to concentrate the metal sought for in a button of metal, speise or regulus, and to leave the earthy and other impurities as far as possible in the slag; whether there be one or two layers of slag is a matter of indifference;[3] but the chemical action of the lower layer upon the speise, or regulus, or metal, is of great importance.
A regulus is a compound of one or more of the metals with sulphur; it is usually brittle, often crystalline, and of a dull somewhat greasy lustre. It is essential that the slag, when solid, shall be so much more brittle than the regulus, that it shall be easy to crumble, and remove it without breaking the latter; and it must not be basic. The effect of fusing a regulus with a basic slag is well seen when sulphide of lead is fused with carbonate of soda; the result is a button of metal (more or less pure), and a slag containing sulphides of lead and sodium; and again, if sulphide of lead be fused with an excess of oxide of lead, a button of lead will be got, and a slag which is simply oxide of lead (with whatever it may have taken up from the crucible), or if a sufficient excess has not been used, oxide of lead mixed with some sulphide. When (as is most frequently the case) the desire is to prevent the formation of regulus, these reactions may be taken advantage of, but otherwise the use of a flux having any such tendency must be avoided. A good slag (from which a regulus may be easily separated) may be obtained by fusing, say, 20 grams of ore with borax 15 grams, powdered glass 15 grams, fluor spar, 20 grams, and lime 20 grams; by quenching the slag in water as soon as it has solidified, it is rendered very brittle.
Sulphide of iron formed during an assay will remain diffused through the slag, instead of fusing into a button of regulus, if the slag contain sulphide of sodium. The same is true of other sulphides if not present in too great a quantity, and if the temperature is not too high.
Speises are compounds of a metal or metals with arsenic. They are chiefly of interest in the metallurgy of nickel, cobalt, and tin. They are formed by heating the metal or ore in covered crucibles with arsenic and, if necessary, a reducing agent. The product is fused with more arsenic under a slag, consisting mainly of borax. They are very fusible, brittle compounds. On exposure to the air at a red heat the arsenic and the metal simultaneously oxidize. When iron, cobalt, nickel, and copper are present in the same speise, they are eliminated in the order mentioned.
Slags from which metals are to be separated should not be too acid; at least, in those cases in which the metal is to be reduced from a compound, as well as separated from earthy impurities. Where the object is simply to get a button of metal from a substance in which it is already in the metallic state, but mixed with dross (made up of metallic oxides, such as those of zinc or iron), from which it is desired to separate it, an acid flux like borax is best; or, if the metal is easily fusible, and there would be danger of loss of metal by oxidation or volatilising, it may be melted under a layer of resin or fat. Common salt is sometimes used with a similar object, and is often useful. Under certain conditions, however, it has a tendency to cause the formation of volatile chlorides with a consequent loss of metal.
In the great majority of cases, the fusion of the metal is accompanied by reduction from the state of oxide; in these the slag should be basic. It is not easy to reduce the whole of a reducible oxide (say oxide of copper or of iron) from a slag in which it exists as a borate or silicate; there should be at least enough soda present to liberate it. When the object is to separate one metal, say copper, without reducing an unnecessary amount of another (iron) at the same time, a slag with a good deal of borax is a distinct advantage. The slag then will probably not be free from copper, so that it will be necessary to powder and mix the slag with some soda and a reducing agent, and to again fuse the slag in order to separate this residual metal. In all those cases in which the slag retains an oxide of a heavy metal, this cleaning of the slag is advisable, and in the case of rich ores necessary. Slags containing sulphides are especially apt to retain the more easily reducible metals.
The following are the ordinary and most useful fluxes:--
~Soda.~--The powdered bicarbonate, sold by druggists as "carbonate of soda," is generally used. It gives off its water and excess of carbonic acid readily and without fusion. Where the melting down is performed rapidly, the escaping gas is apt to cause trouble by frothing, and so causing waste of the material. Ordinary carbonate of soda, when hydrated (soda crystals), melts easily, and gives off its water with ebullition. It is unfit for use in assaying, but when dried it can be used instead of the bicarbonate. One part of the dried carbonate is equivalent to rather more than one and a half parts of the bicarbonate. From two to four parts of the flux are amply sufficient to yield a fluid slag with one part of earthy matter. This statement is also true of the fluxes which follow.
~Borax~ is a hydrated biborate of soda, containing nearly half its weight of water. When heated it swells up, loses its water, and fuses into a glass. The swelling up may become a source of loss in the assay by pushing some of the contents out of the crucible. To avoid this, fused or dried borax may be used, in which case a little more than half the amount of borax indicated will suffice. Borax will flux almost anything, but it is especially valuable in fluxing lime, &c., and metallic oxides; as also in those cases in which it is desired to keep certain of the latter in the slag and out of the button of metal.
~Oxide of Lead~, in the form of red lead or litharge, is a valuable flux; it easily dissolves those metallic oxides which are either infusible or difficultly fusible of themselves, such as oxides of iron or copper. The resulting slag is strongly basic and very corrosive; no crucible will long withstand the attack of a fused mixture of oxides of lead and copper. With silicates, also, it forms very fusible double silicates; but in the absence of silicates and borates it has no action upon lime or magnesia. Whether the lead be added as litharge or as red lead, it will exist in the slag as monoxide (litharge); the excess of oxygen of the red lead is thus available for oxidising purposes. If this oxidising power is prejudicial, it may be neutralised by mixing the red lead with 1 per cent. of charcoal.
~Glass~: broken beakers and flasks, cleaned, dried, and powdered will do. It should be free from lead.
~Fluor~: fluor-spar as free as possible from other minerals, powdered. It helps to flux phosphate of lime, &c., and infusible silicates.
~Lime~: should be fresh and powdered. It must not be slaked. Powdered white marble (carbonate of lime) will do; but nearly double the quantity must be taken. One part of lime produces the same effect as 1.8 parts of the carbonate of lime.
~Tartar~ and "black flux," are reducing agents as well as fluxes. The "black flux," which may be obtained by heating tartar, is a mixture of carbonate of potash and charcoal.
REDUCING AGENTS.--The distinction between reducing agents and fluxes (too often ignored) is an important one. Fluxes yield slags; reducing agents give buttons of regulus or of metal. The action of a reducing agent is the separation of the oxygen or sulphur from the metal with which it is combined. For example, the mineral anglesite (lead sulphate) is a compound of lead, sulphur, and oxygen; by carefully heating it with charcoal the oxygen is taken away by the charcoal, and a regulus of lead sulphide remains. If the regulus be then fused with metallic iron the sulphur is removed by the iron, and metallic lead is left. The charcoal and the iron are reducing agents. But in defining a reducing agent as one which removes oxygen, or sulphur, from a metallic compound so as to set the metal free, it must be remembered that sulphur itself will reduce metallic lead from fused litharge, and that oxygen will similarly set free the metal in fused lead sulphide. There is no impropriety in describing sulphur as a reducing agent; but it is absurd to call oxygen one. Some confusion will be avoided if these substances and those which are opposite to them in property be classed as oxidising and de-oxidising, sulphurising, and de-sulphurising agents. Most oxidising agents also act as de-sulphurisers.
The de-oxidising agents most in use are the following:--
~Charcoal.~--Powdered wood charcoal; it contains more or less hygroscopic moisture and about 3 or 4 per cent. of ash. The rest may be considered carbon. Carbon heated with metallic oxides takes the oxygen; at low temperatures it forms carbon dioxide, and at higher ones, carbon monoxide. Other conditions besides that of temperature have an influence in producing these results; and as the quantity of charcoal required to complete a definite reaction varies with these, it should be calculated from the results of immediate experience rather than from theoretical considerations.
~Flour.~--Ordinary wheat flour is convenient in use. On being heated it gives off inflammable gases which have a certain reducing effect, and a residue of finely divided carbon is left. It is likely to vary in the quantity of moisture it contains. Two parts of flour should be used where one part of charcoal would be otherwise required.
~Tartar.~--This is crude hydric potassic tartrate; the purified salt, cream of tartar, may be used. On being heated it gives off inflammable gases, and leaves a residue formed of potassic carbonate mixed with finely divided carbon. Five parts of tartar should be used in the place of one of charcoal.
~Anthracite~ or ~Culm~ is a kind of coal containing 90 per cent. or more of carbon. It gives off no inflammable gas. It is denser, and takes longer in burning, than charcoal. Its reducing effect is little inferior to that of charcoal. Almost any organic substance can be used as a reducing agent, but it is well not to select one which melts, swells up, or gives off much water and gas when heated in the furnace.
~Potassic Cyanide~ is an easily fusible and somewhat volatile salt, which, when fused, readily removes oxygen and sulphur from metallic compounds, and forms potassic cyanate or sulphocyanate as the case may be. Commercial samples vary much in purity; some contain less than 50 per cent. of the salt. For assaying, only the better qualities should be used.
~Iron~ is a de-sulphurising rather than a de-oxidising agent. Iron is used in the form of rods, 1/2-inch in diameter, or of nails, or of hoop iron. In the last case it should be thin enough to be bent without difficulty. Wrought iron crucibles are very useful in the processes required for making galena assays.
The chief oxidising agents (which are also de-sulphurisers) are the following:--
~Nitre~, or Potassic Nitrate.--This salt fuses very easily to a watery liquid. It oxidises most combustible substances with deflagration, and thereby converts sulphides into sulphates, arsenides into arsenates, and most metals into oxides. In the presence of strong bases, such as soda, the whole of the sulphur is fully oxidised; but in many cases some arsenic is apt to escape, and to give rise to a peculiar garlic-like odour. The sulphates of soda and potash are thus formed, and float as a watery liquid on the surface of the slag.
~Red lead~ is an oxide of lead. About one-quarter of its oxygen is very loosely held, and, hence, is available for oxidising purposes, without any separation of metallic lead. The rest of the oxygen is also available; but for each part of oxygen given off, about 13 parts of metallic lead are deposited. In silver assays this power of readily giving up oxygen is made use of. The residual oxide (litharge) acts as a flux.
~Hot air~ is the oxidising agent in roasting operations. The sulphur and arsenic of such minerals as mispickel and pyrites are oxidised by the hot air and pass off as sulphur dioxide and "white arsenic." The metals generally remain in the form of oxide, mixed with more or less sulphate and arsenate. The residue may remain as a powdery substance (a calx), in which case the process of roasting is termed calcination; or it may be a pasty mass or liquid. In the calcination of somewhat fusible minerals, the roasting should be done at a low temperature to avoid clotting; arsenic and sulphur being with difficulty burnt off from the clotted mineral. A low temperature, however, favours the formation of sulphates; and these (if not removed) would reappear in a subsequent reduction as sulphides. These sulphates may be decomposed by a higher temperature towards the end of the operation; their removal is rendered more certain by rubbing up the calx with some culm and re-roasting, or by strongly heating the calx after the addition of solid ammonic carbonate. In roasting operations, as large a surface of the substance as possible should be exposed to the air. If done in a crucible, the crucible should be of the Cornish type, short and open, not long and narrow. For calcinations, roasting dishes are useful: these are broad and shallow, not unlike saucers, but unglazed. In those cases in which the products of the roasting are liquid at the temperature used, a scorifier (fig. 38) is suitable if it is desired to keep the liquid; but if the liquid is best drained off as quickly as it is formed, a cupel (fig. 5) should be used.
A scorifier is essentially a roasting dish sufficiently thick to resist, for a time, the corrosive action of the fused metallic oxides it is to contain. The essential property of a cupel is, that it is sufficiently porous to allow the fused oxide to drain into it as fast as it is formed. It should be large enough to absorb the whole of the liquid; and of course must be made of a material upon which the liquid has no corrosive action. Cupels do not bear transport well; hence the assayer generally has to make them, or to supervise their making. A quantity of bone ash is carefully mixed with water so that no lumps are formed, and the mixture is then worked up by rubbing between the hands. The bone ash is sufficiently wet when its cohesion is such that it can be pressed into a lump, and yet be easily crumbled into powder. Cupel moulds should be purchased. They are generally made of turned iron or brass. They consist of three parts (1) a hollow cylinder; (2) a disc of metal; and (3) a piston for compressing the bone ash and shaping the top of the cupel. The disc forms a false bottom for the cylinder. This is put in its place, and the cylinder filled (or nearly so) with the moistened bone ash. The bone ash is then pressed into shape with the piston, and the cupel finished with the help of three or four smart blows from a mallet. Before removing the piston, turn it half-way round upon its axis so as to loosen and smooth the face of the cupel. The cupel is got out by pressing up the disc of metal forming the false bottom; the removal is more easily effected if the mould is somewhat conical, instead of cylindrical, in form. The cupels are put in a warm place to dry for two or three days. A conveniently sized cupel is 1-1/4 inches in diameter and about 3/4 inch high. The cavity of the cupel is about 1/4 inch deep, and something of the shape shown in fig. 5.
There are two kinds of furnaces required, the "wind" and "muffle" furnaces. These are built of brick, fire-brick, of course, being used for the lining. They are connected with a chimney that will provide a good draught. Figure 6 shows a section of the wind furnace, fig. 7 a section of the muffle furnace, and fig. 8 a general view of a group comprising a muffle and two wind furnaces suitable for general work. When in operation, the furnaces are covered with iron-bound tiles. The opening under the door of the muffle is closed with a loosely fitting brick. The floor of the muffle is protected with a layer of bone-ash, which absorbs any oxide of lead that may be accidentally spilt. The fire bars should be easily removable.
Few tools are wanted; the most important are some cast-iron moulds, tongs (fig. 9), stirrers for calcining (fig. 10), and light tongs of a special form for handling scorifiers and cupels (see SILVER).
The coke used should be of good quality; the formation of a fused ash (clinker), in any quantity, causes ceaseless trouble, and requires frequent removal. The coke should be broken into lumps of a uniform size (about 2 in. across) before being brought into the office. The furnace should be well packed by stirring, raising the coke and not ramming it, and it should be uniformly heated, not hot below and cold above. In lighting a furnace, a start is made with wood and charcoal, this readily ignites and sets fire to the coke, which of itself does not kindle easily.
In commencing work, add (if necessary) fresh coke, and mix well; make hollows, and into these put old crucibles; pack around with coke, so that the surface shall be concave, sloping upwards from the mouths of the crucibles to the sides of the furnace; close the furnace, and, when uniformly heated, substitute for the empty crucibles those which contain the assays. It is rarely advisable to have a very hot fire at first, because with a gradual heat the gases and steam quietly escape through the unfused mass, while with too strong a heat these might make some of the matter in the crucible overflow. Moreover, if the heat should be too strong at first, the flux might melt and run to the bottom of the crucible, leaving the quartz, &c., as a pasty mass above; with a gentler heat combination is completed, and the subsequent fiercer heat simply melts the fusible compound into homogeneous slag.
The fused material may be left in the crucible and separated from it by breaking when cold. It is generally more convenient to pour it into cast-iron moulds. These moulds should be dry and smooth. They act best when warmed and oiled or black-leaded.
Air entering through the fire-bars of a furnace and coming in contact with hot coke combines with it, forming a very hot mixture of carbonic acid and nitrogen; this ascending, comes in contact with more coke, and the carbonic acid is reduced to carbonic oxide; at the top of the furnace, or in the flue, the carbonic oxide meeting fresh air, combines with the oxygen therein and re-forms carbonic acid. In the first and third of these reactions, much heat is evolved; in the second, the furnace is cooled a little. It must always be remembered, that the carbonic oxide of the furnace gases is a reducing agent. When these gases are likely to exert a prejudicial effect, and a strongly oxidising atmosphere is required, the work is best done in a muffle.
FOOTNOTES:
[3] There is an exception to this, as when the slag is liable to be acted on when exposed to the air and to the gases of the furnace. In this case a layer of fused common salt floating on the slag, so as to protect it from the air and furnace gases, is a distinct advantage.
III. WET GRAVIMETRIC METHODS
In dry assays the metal is almost always separated and weighed as metal; in wet gravimetric assays the metal is more usually weighed in the form of a definite compound of known composition. The general methods of working resemble those of ordinary chemical analysis, and their successful working is greatly helped by a knowledge of, at any rate, those compounds of the metal which enable it to be separated, and of those which are the most convenient forms in which it can be weighed. But the work of the assayer differs from that of the analyst, inasmuch as the bulk of his estimations are made upon material of practically the same kind, varying only in richness; consequently in assaying, it is possible (and necessary) to work on such a definite plan as will involve the least amount of labour in weighing and calculating.
The assayer connected with mining has generally two classes of material to deal with: those comparatively rich and those comparatively poor. For example, silver in bullion and in ores; copper precipitates or regulus, and copper ores and slags; and "black tin" and tin ores. He is only occasionally called on to assay the intermediate products. It is indispensable that he should have an approximate knowledge of the substance to be determined. With new ores this information is best got by a qualitative testing. Knowing that only certain bodies are present, it is evident that the number of separations can be reduced, and that simple methods can be devised for arriving at the results sought for. The best method is that which involves the least number of separations. The reactions must be sharp and complete, and yet not be liable to error under varying conditions.
To bring the richer and poorer materials under the same conditions for the assay, a small weight, say 1 gram of the richer, and a larger weight (5 or 10 grams) of the poorer, substance is weighed up. A method is then adopted which will concentrate the whole of the metal (either during or after solution) in a product which need not necessarily be pure. The work on this product is comparatively easy. In separating small quantities of a substance from a large bulk of impurities, the group separations must not as a rule be too much relied on. Very large precipitates carry down small quantities of bodies not belonging to the group, more especially when there is a tendency to form weak double compounds. The re-dissolving and re-precipitating of bulky precipitates should be avoided.
When a large number of assays of the same kind have to be carried out, a plan something like the following is adopted:--The samples, after having been dried, are placed in order on a table at the left hand of the assayer. He takes the first, marks it with a number, samples and weighs up the quantity required, and transfers it to a flask, which is similarly marked. As the weighings are finished, the samples are placed in the same order on his right hand. The assistant takes the flasks in batches of four or five at a time to the fume cupboard, where he adds a measured quantity of acid. When solution has been effected, dilution with a measured volume is generally necessary. The assayer sees to this and (whilst the funnels and filters are being prepared) makes any separation that is necessary. The filters are arranged in order on a rack (fig. 11), and need not be marked unless the precipitates or residues have subsequently to be dried. The filters are washed with hot water, and if the filtrates are wanted flasks are placed beneath, if not, the solution is drained off down the sink. Precipitation or reduction (or whatever it may be) is now made; the assistant filters the prepared samples, one at a time, whilst the assayer is engaged with the others. The same style of work is continued until the assays are completed. If one should be spoiled, it is better to allow it to stand over for assaying along with the next batch. If one filters slowly or is in any way less forward than the rest, it may lessen the accuracy of the other assays, owing to oxidation, &c., it should, therefore, be put on one side. The assays are dealt with in batches of ten or twenty, so that a large quantity of work can be quickly finished.
When the assays are finished, it is the duty of the assistant to clean the apparatus (with reagents, if necessary), and to put the vessels in the place set apart for them. Flasks are best kept inverted on a rack, so that they may be dry and clean by the next morning. Berlin crucibles must be cleaned and ignited.
The amount of apparatus employed should be as little as is feasible. The assay should be carried out as much as possible in the same flask. The bench must be clean, and altogether free from apparatus not in actual use. Crucibles and dishes in which weighings are made should be marked with numbers or letters; and their weights recorded, together with the date of weighing, in a small ledger, which is kept in the drawer of the balance. By this means a record of the "wear" of each piece of apparatus is obtained, and, what is more important, much weighing is saved, and increased confidence is gained. The weight of each piece of apparatus need not be taken daily. It will be seen from the record in the book and a knowledge of the use it has been put to how often a checking of the weight is necessary. The entries are made in black lead as follows:--
Dish, A. Feb. 3 9.4210 grams. 5 9.4225 6 9.4230 7 9.4200
Platinum vessels and apparatus lose, and porcelain ones slightly gain, weight with continued use.
The special details of the work is given under each assay; certain general instructions will be given here.
~Solution.~--It is not always necessary to get the whole of the mineral in solution, provided the body sought for is either completely dissolved or altogether left in the residue. It is often only by a qualitative examination of the solution (or residue, as the case may be) that the assayer can satisfy himself that it is free from the substance sought. But previous experience with the same kind of ore will show to what extent this testing is necessary.
Solution is generally best effected in flasks; but where the resulting liquid has afterwards to be evaporated to dryness and ignited, evaporating dishes (fig. 12) are used. With them clock glasses are used as covers during solution to avoid loss through effervescence. Evaporating dishes are also best when an insoluble residue has to be collected, since it is difficult to wash out most residues from a flask. Bumping occurs less frequently in dishes than in flasks.
After the addition of the acid, and mixing by agitation, the vessel containing the substance is heated. This is best done on the "hot plate" (fig. 13). This consists of a slab of cast iron about half or three-quarters of an inch thick, supported on loose fire bricks, and heated by two or three ring burners (figs. 14 and 15). The burners are connected to the gas supply by means of lead tubing, to which they are soldered. Flasks and dishes after being put on the plate are not further handled until solution is complete or the evaporation is carried to dryness. The hot plate is contained in a cupboard so as to be out of the reach of cold draughts.
The action of the acids and other solvents is described in the chapter on Reagents.
~Precipitation.~--In precipitating add sufficient of the reagent to complete the reaction. The student must be on his guard against adding a very large excess, which is the commoner error. In some reactions the finishing point is obvious enough; either no more precipitate is formed, or a precipitate is completely dissolved, or some well-marked colour or odour is developed or removed.
In those cases in which there is no such indication, theoretical considerations should keep the use of reagents within reasonable limits. The solutions of the reagents (see REAGENTS) are generally of five or ten per cent. strength. A small excess over that demanded by theory should be sufficient.
~Filtration.~--Solutions are best filtered hot whenever the assay allows of this being so done. The precipitate should be allowed to settle, and the clear liquid decanted on the filter with the aid of a glass rod if necessary. The filter-paper must not be too large, but at the same time it must not be overloaded with the precipitate. There should be ample room for washing. For general use three sizes of filter-paper are sufficient. Common quick filtering-paper (English) is best for most work in assaying. The specially prepared paper (Swedish or Rhenish) is used for collecting those precipitates which have to be weighed. The papers are folded as shown in fig. 16, and should not project above the funnel. The filter-paper works better if damped with hot water. In special cases filtering is hastened by means of an air-pump. The apparatus used consists of a water-jet (fig. 17), which is connected with the tap, as also with a bottle fitted as shown in fig. 18. The pump draws the air out from the bottle, and atmospheric pressure forces the liquid through the filter-paper. The bottom of the funnel is provided with a platinum cone, which supports the filter-paper, and prevents its breaking. The pump is only used in exceptional cases; nearly all the filtrations required by the assayer can be made without it. The usual methods of supporting the funnel during filtration are shown in fig. 19. Where the filtrate is not wanted, pickle bottles make convenient supports. After the precipitate has been thrown on the filter, it is washed. In washing, several washings with a small quantity of water are more effective than a few with a larger quantity of that fluid. The upper edge of the filter-paper is specially liable to escape complete washing. Excessive washing must be avoided; the point at which the washing is complete is found by collecting a little of the filtrate and testing it. The precipitate is removed from the filter-paper for further treatment by opening out the paper and by washing the precipitate with a jet of water from a wash-bottle into a beaker, or back through the funnel into the flask. In some cases, when the precipitate has to be dissolved in anything in which it is readily soluble, solution is effected in the filter itself allowing the liquid to run through as it is formed.
~Drying and Igniting.~--Precipitates, as a rule, require drying before being ignited. With small precipitates the filter-paper may be opened out, and placed on a warm asbestos slab till dry; or the funnel and the filter with the precipitate is placed in a warm place, and supported by any convenient means. The heat must never be sufficient to char the paper. Some precipitates must be dried at a temperature not higher than 100° C. These are placed in the water-oven (fig. 20), and, when apparently dry, they are taken from the funnel, placed between glasses, and then left in the oven till they cease to lose weight. Such precipitates are collected on tared filters. Those precipitates which will stand a higher temperature are dried in the hot-air oven at a temperature of from 120° to 150°. The drying is continued until they appear to be free from moisture, and until the precipitate ceases to adhere to the filter. In drying sulphides the heat must not be raised to the melting point of sulphur, since, if there is any free sulphur present, it fuses and filters through.
The precipitate, having been dried, is transferred to a watch-glass. The filter-paper is opened out over a sheet of note-paper, and, with a camel-hair brush, the precipitate is gently brought into the glass. Most precipitates come away easily, and the transfer can be made without apparent loss. The watch-glass is covered by the funnel, and the filter-paper (folded into a quadrant) held by the tweezers and set fire to with the flame of a Bunsen burner. It is allowed to burn over the crucible, into which the black bulky ash is allowed to drop, and two or three drops of nitric acid are then added. The crucible is placed on a pipe-stem triangle (fig. 21), supported on a tripod. It is at first heated gently with a Bunsen burner, and afterwards more strongly, until the residue is free from carbon. It is cooled, and treated with any acid necessary to convert the small amount of precipitate into the state in which it is to be weighed; heated again, and cooled. The main precipitate is transferred to the crucible, and the heating repeated very gently at first, but more strongly towards the end of the operation. It is next placed in the muffle, and, after two or three minutes at a red heat, it is removed and allowed to cool in the desiccator before weighing. This is for bodies that will bear a red heat; for those compounds that require a lower temperature the heating in the muffle is omitted. The muffle used for this purpose must not be used at the same time for cupelling; a gas muffle (fig. 22), such as one of Fletcher's, is best. A desiccator (fig. 23) is an air-tight vessel which prevents access of moisture, &c., to the substance. Usually the air in it is kept dry by means of a basin containing sulphuric acid.
The crucible is removed from the muffle with the tongs and carried to the desiccator. It is best, in an office, to have a large desiccator permanently fixed alongside the balance, into which all substances may be put before being weighed. The substance is removed from the bench or muffle in the small hand apparatus generally sold, and carried to the balance room to be transferred to the large desiccator, where it is allowed to become thoroughly cold before being weighed. Twenty minutes is generally the time allowed after ignition before it is advisable to weigh. Bodies allowed to cool in the air after they have been ignited will absorb moisture, and hot bodies placed in the balance-pan will disturb the equilibrium and show false results. Compounds that absorb moisture must be weighed quickly; they should, therefore, be weighed in covered vessels. Such compounds are detected by their continually-increasing weight. They should be ignited and weighed again in a well-covered dish.
Substances that have been washed with alcohol, ether, or any readily volatile liquid are dried in the water oven. They quickly dry if there is no water present, and are generally fit for weighing in less than one hour. Sometimes drying for a few minutes only will be sufficient.
The weight of the crucible and precipitate having been obtained, the weight of the crucible and ash is deducted; for example--
Crucible and precipitate 10.183 grams. Crucible and ash 9.527 " ------ 0.656 "
The weight of the ash is best added to that of the crucible. The amount of ash in filter-papers must not be neglected, although papers are now made almost free from ash, and the amount to be deducted is found by taking eight or ten papers and burning them until they become white, and then weighing the ash. The amount varies from 0.004 to 0.0005 gram for different papers. Having determined the ash, place in the balance-drawer three of the filter-papers pinned together, with the weights marked on them in the way shown in fig. 24, so as to be readily seen when there is occasion to refer to them.
It must be remembered that the determination of small quantities of substances generally involves the use of reagents which are often contaminated, as an impurity, with the body sought for. Thus, in assaying silver, the oxide of lead or metallic lead used is rarely free from silver; and in the case of arsenic, the acids, zinc or ferric chloride are sure to contain arsenic. The same observation applies to the precipitation of lead by zinc, &c. The errors caused by these impurities are more marked in the determination of material having small quantities of metal than in that of ores which contain larger quantities. Errors of this kind are counteracted or neutralised by "blank" or "blind" determinations. These consist in carrying out by the side of and during the assay a duplicate experiment with the reagents only, which are thereby subjected to the same processes of solution, evaporation, filtration, &c. The final result thus obtained is deducted from that given by the assay, the difference gives the corrected result. In some cases, where it is desired or necessary to have a tangible residue or precipitate, some pure inert material is added.
IV. VOLUMETRIC ASSAYS
These have been already described as those in which the results are got by measuring, either--(1) the volume of a reagent required to complete some reaction, or (2) the volume of the resulting product. For example, if a permanganate of potash solution be added to a solution containing a weighed amount of iron, dissolved in sulphuric acid, the strong colour of the permanganate of potash will be removed until a certain quantity of it has been added. Repeating the experiment, it will be found that the same amount of iron decolorises the same volume of the permanganate solution within certain narrow limits of variation, known as "error of experiment." This error is due to variation in the method of working and to slight differences in the weighings and measurings; it is present in all experimental methods, although the limits of variation are wider in some than in others. Apart from this error of experiment, however, it is certain that a given volume of the permanganate of potash solution corresponds to a definite weight of iron, so that if either is known the other may be calculated. Similarly, if a known weight of zinc (or of carbonate of lime) be dissolved in hydrochloric acid, a gas will be given off which can be measured, and so long as the conditions of the experiment do not vary, the same weight of zinc (or of carbonate of lime) gives off the same volume of gas. The weight of the one can be determined from the volume of the other.
Or, again, the quantity of some substances may be measured by the colour of their solutions, on the principle that, other things being equal, the colour of a solution depends upon the quantity of colouring matter present. So that if two solutions of the same substance are equally coloured they are of equal strength. In this way an unknown may be compared with a known strength, and a fairly accurate determination may be made. These three illustrations serve as types of the three chief classes of volumetric assays--titrometric, gasometric, and colorimetric.
~Titrometric Assays.~--Within the limits of the error of experiment, a definite volume of a solution or gas represents a certain weight of metal or other substance, hence the exact weight may be determined by experiment. The error of experiment may be reduced to insignificant dimensions by repeating the experiment, and taking the mean of three or four determinations. This will at the same time show the amount of variation. Thus, if 0.5 gram of iron were dissolved and found to require 50.3 cubic centimetres of the solution of permanganate of potash, and if on repeating, 50.4, 50.2, and 50.3 c.c. were required, the experimenter would be justified in saying that 50.3 c.c. of the permanganate solution represent 0.5 gram of iron, and that his results were good within 0.2 c.c. of the permanganate solution. So that if in an unknown solution of iron, 50.5 c.c. of the permanganate solution were used up, he could state with confidence that it contained a little more than 0.5 gram of iron. With a larger experience the confidence would increase, and with practice the experimental error will diminish.
But supposing that the unknown solution required, say, 100.5 instead of 50.5 c.c., he would not be justified in saying that, since 50.3 c.c. are equivalent to 0.5 gram, 100.6 c.c. are equivalent to twice that amount; and that, consequently, the unknown solution contained a little less than 1 gram of iron; or, at least, he could not say it except he (or some one else) had determined it by experiment. But if on dissolving 1 gram of iron, he found it to require 100.6 c.c. of the solution, and in another experiment with 0.8 gram of iron that 80.5 c.c. of the solution were required, he would be justified in stating that the volume of solution required is proportional to the quantity of metal present. There are a large number of volumetric assays of which this is true, but that it is true in any particular case can only be proved by experiment. Even where true it is well not to rest too much weight upon it, and in all cases the quantity of metal taken, to determine the strength of the solution used, should not differ widely from that present in the assay. There are certain terms which should be explained here. When the solution of a reagent is applied under such conditions that the volume added can be correctly determined, the operation is called "titrating," the solution of the reagent used the "standard solution," and the process of determining the strength of the standard solution is "standardising." The "standard" is the quantity of metal equivalent to 100 c.c. of the standard solution.
~Standard Solutions.~--In making these the salt is accurately weighed and transferred to a litre flask, or to the graduated cylinder, and dissolved. The method of dissolving it varies in special cases, and instructions for these will be found under the respective assays. Generally it is dissolved in a small quantity of liquid, and then diluted to the mark. For those substances that require the aid of heat, the solution is made in a pint flask, cooled, and transferred; after which the flask is well washed out. After dilution, the liquids in the measuring vessel must be thoroughly mixed by shaking. This is more easily and better done in the cylinder than in the litre flask. The solution is next transferred to a dry "Winchester" bottle and labelled. The label may be rendered permanent by waxing it.
Standard solutions should not be kept in a place exposed to direct sunlight. Oxidising and reducing solutions, such as those of permanganate of potash, ferrous sulphate, iodine, hyposulphite of soda, &c., gradually weaken in strength; the solutions of other salts are more stable; while those of potassium bichromate and baric chloride are almost permanent. Solutions of potassium permanganate may be kept for a month or so without much change. The solutions of hyposulphite of soda and of iodine should be examined weekly. Ferrous sulphate solutions, if acidulated with sulphuric acid, may be depended on for two or three weeks without fresh standardising. Before filling the burette, the "Winchester" bottle should be well shaken and a portion of about 50 or 100 c.c. poured into a dry beaker or test-glass. Besides the standard solutions, which are required for titrating an assay, permanent solutions of the metal or acid of equivalent strength are very useful. When the finishing point of a titration has been overstepped (i.e., the assay has been "overdone"), a measured volume, say 5 or 10 c.c., of a solution containing the same metal may be added. The titration can then be continued, but more cautiously, and the value in "c.c." for the quantity added be deducted from the final reading.
~Standardising.~--Suppose the object is to standardise a solution of permanganate similar to that referred to above. A convenient quantity of iron (say 0.5 gram) would be weighed out, dissolved in dilute sulphuric acid, and the solution titrated. Suppose 49.6 c.c. of the permanganate solution are required, then
49.6 : 0.5 :: 100 : x x = 1.008 gram.
This result, 1.008 gram, is the "standard." When a gas is measured, the standard may be calculated in the same way. For example: with 0.224 gram of zinc, 75.8 c.c. of gas were obtained. Then the quantity of zinc equivalent to 100 c.c. of the gas is got by the proportion.
75.8 : 0.224 :: 100 : x x = 0.2955 gram.
Using the term "standard" in this sense, the following rules hold good:--
To find the weight of metal in a given substance:--Multiply the standard by the number of c.c. used and divide by 100. For example: a piece of zinc was dissolved and the gas evolved measured 73.9 c.c. Then by the rule, 0.2955×73.9/100 should give the weight of the piece of zinc. This gives 0.2184 gram.
To find the percentage of metal in a given substance:--Multiply the standard by the number of c.c. used and divide by the weight of substance taken. For example: if 2 grams of a mineral were taken, and if on titrating with the permanganate solution (standard 1.008) 60.4 c.c. were required, then (1.008×60.4)/2 = 30.44. This is the percentage.
If the standard is exactly 1 gram, and 1 gram of ore is always taken, these calculations become very simple. The "c.c." used give at once the percentage, or divided by 100 give the weight of metal.
If it is desired to have a solution with a standard exactly 1.0 gram, it is best first to make one rather stronger than this, and then to standardise carefully. Divide 1000 by the standard thus obtained and the result will be the number of c.c. which must be taken and be diluted with water to 1 litre. For example: suppose the standard is 1.008, then 1000/1.008 gives 992, and if 992 c.c. be taken and diluted with water to 1000 c.c. a solution of the desired strength will be obtained. The standard of this should be confirmed. A simpler calculation for the same purpose is to multiply the standard by 1000; this will give the number of c.c. to which 1 litre of the solution should be diluted. In the above example a litre should be diluted to 1008 c.c.
It has been assumed in these rules that the titration has yielded proportional results; but these are not always obtained. There can be no doubt that in any actual re-action the proportion between any two re-agents is a fixed one, and that if we double one of these then exactly twice as much of the other will enter into the re-action; but in the working it may very well be that no re-action at all will take place until after a certain excess of one or of both of the re-agents is present. In titrating lead with a chromate of potash solution, for example, it is possible that at the end of the titration a small quantity of the lead may remain unacted on; and it is certain that a small excess of the chromate is present in the solution. So, too, in precipitating a solution of silver with a standard solution of common salt, a point is reached at which a small quantity of each remains in solution; a further addition either of silver or of salt will cause a precipitate, and a similar phenomenon has been observed in precipitating a hydrochloric acid solution of a sulphate with baric chloride. The excess of one or other of the re-agents may be large or small; or, in some cases, they may neutralise each other. Considerations like these emphasise the necessity for uniformity in the mode of working. Whether a process yields proportional results, or not, will be seen from a series of standardisings. Having obtained these, the results should be arranged as in the table, placing the quantities of metal used in the order of weight in the first column, the volumes measured in the second, and the standards calculated in the third. If the results are proportional, these standards will vary more or less, according to the delicacy of the process, but there will be no apparent order in the variation. The average of the standards should then be taken.
+-------------+---------------+----------+ | Weight. | Volume found. | Standard | +-------------+---------------+----------+ | 0.2160 gram | 72.9 c.c. | 0.2963 | | 0.2185 " | 73.9 " | 0.2957 | | 0.2365 " | 79.9 " | 0.2959 | | 0.2440 " | 82.3 " | 0.2964 | | 0.2555 " | 85.9 " | 0.2974 | +-------------+---------------+----------+
Any inclination that may be felt for obtaining an appearance of greater accuracy by ignoring the last result must be resisted. For, although it would make no practical difference whether the mean standard is taken as 0.2961 or 0.2963, it is well not to ignore the possibility that an error of 0.4 c.c. may arise. A result should only be ignored when the cause of its variation is known.
In this series the results are proportional, but the range of weights (0.216-0.2555 gram) is small. All processes yield fairly proportional results if the quantities vary within narrow limits.
As to results which are not proportional, it is best to take some imaginary examples, and then to apply the lesson to an actual one. A series of titrations of a copper solution by means of a solution of potassic cyanide gave the following results:--
+---------------+---------------+-----------+ | Copper taken. | Cyanide used. | Standard. | +---------------+---------------+-----------+ | 0.1 gram | 11.9 c.c. | 0.8403 | | 0.2 " | 23.7 " | 0.8438 | | 0.3 " | 35.6 " | 0.8426 | | 0.4 " | 47.6 " | 0.8403 | +---------------+---------------+-----------+
These are proportional, but by using a larger quantity of acid and ammonia in the work preliminary to titration, we might have had to use 1 c.c. of cyanide solution more in each case before the finishing point was reached. The results would then have been:
+---------------+---------------+-----------+ | Copper taken. | Cyanide used. | Standard. | +---------------+---------------+-----------| | 0.1 gram | 12.9 c.c. | 0.7752 | | 0.2 " | 24.7 " | 0.8097 | | 0.3 " | 36.6 " | 0.8191 | | 0.4 " | 48.6 " | 0.8230 | +---------------+---------------+-----------+
It will be noted that the value of the standard increases with the weight of metal used; and calculations from the mean standard will be incorrect.
By subtracting the lowest standardising from the highest, a third result is got free from any error common to the other two; thus:--
0.4 gram = 48.6 c.c. "cyanide." 0.1 " = 12.9 " " --- ---- 0.3 " = 35.7 " "
And the standard calculated from this corrected result is 0.8404. Further, if 0.3 gram requires 35.7 c.c., then 0.1 gram should require 11.9 c.c., or 1.0 c.c. less than that actually found.
We may therefore use the following rules for working processes which do not yield proportional results. Make a series of two or three titrations, using very different quantities of metal in each. Subtract the lowest of these from the highest, and calculate the standard with the remainder. Calculate the volume required by this standard in any case, and find the excess or deficit, as the case may be. If an excess, subtract it from the result of each titration; if a deficit, add it; and use the standard in the usual way. The following table shows an actual example:--
+--------------+---------------+-----------+ | Chalk taken. | Gas obtained. | Standard. | +--------------+---------------+-----------+ | 0.0873 gram | 17.8 c.c. | 0.4904 | | 0.1305 " | 27.3 " | 0.4780 | | 0.1690 " | 35.8 " | 0.4721 | | 0.1905 " | 40.4 " | 0.4715 | | 0.2460 " | 52.5 " | 0.4686 | | 0.3000 " | 64.0 " | 0.4687 | +--------------+---------------+-----------+
It will be seen that the standard decreases as the quantity of chalk increases; this points to a deficiency in the quantity of gas evolved.
Then
0.3000 = 64.0 c.c. 0.0873 = 17.8 " ------ = ---- 0.2127 = 46.2 "
and 0.2127×100/46.2 = 0.4604. Then, multiplying the weight of chalk taken by 100, and dividing by 0.4604, we get the calculated results of the following table:--
+--------------+------------+-----------------+-------------+ | Chalk taken. | Gas found. | Gas calculated. | Difference. | +--------------+------------+-----------------+-------------+ | 0.0873 gram | 17.8 c.c. | 18.9 c.c. | -1.1 c.c. | | 0.1305 " | 27.3 " | 28.3 " | -1.0 " | | 0.1690 " | 35.8 " | 36.7 " | -0.9 " | | 0.1905 " | 40.4 " | 41.4 " | -1.0 " | | 0.2460 " | 52.5 " | 53.4 " | -0.9 " | | 0.3000 " | 64.0 " | 65.1 " | -1.1 " | +--------------+------------+-----------------+-------------+
By adding 1 c.c. to the quantity of gas obtained, and taking 0.4604 as the standard, the calculated results will agree with those found with a variation of 0.1 c.c. When a large number of assays of the same kind are being made, this method of calculation is convenient; when, however, only one or two determinations are in question, it is easier to make a couple of standardisings, taking quantities as nearly as possible the same as those present in the assays.
Sometimes it is necessary to draw up a table which will show, without calculation, the weight of substance equivalent to a given volume of gas or of solution. The substance used for standardising should be, whenever possible, a pure sample of the substance to be determined--that is, for copper assays pure copper should be used, for iron assays pure iron, and so on; but when this cannot be got an impure substance may be used, provided it contains a known percentage of the metal, and that the impurities present are not such as will interfere with the accuracy of the assay. Including compounds with these, the standard may be calculated by multiplying the standard got in the usual way, by the percentage of metal in the compound or impure substance, and dividing by 100. If, for example, the standard 1.008 gram was obtained by using a sample of iron containing 99.7 per cent. of metal, the corrected standard would be 1.008×99.7/100 = 1.005.
In volumetric analysis the change brought about must be one in which the end of the reaction is rendered prominent either by a change of colour or by the presence or absence of a precipitate. If the end of the reaction or finishing-point is not of itself visible, then it must be rendered visible by the use of a third reagent called an indicator.
For example, the action of sulphuric acid upon soda results in nothing which makes the action conspicuous; if, however, litmus or phenolphthalein be added the change from blue to red in the first case, or from red to colourless in the second, renders the finishing-point evident. Some indicators cannot be added to the assay solution without spoiling the result; in which case portions of the assay solution must be withdrawn from time to time and tested. This withdrawal of portions of the assay solution, if rashly done, must result in loss; if, however, the solution is not concentrated, and if the portions are only withdrawn towards the end of the titration, the loss is very trifling, and will not show-up on the result. The usual plan adopted is to have a solution of the indicator placed in drops at fairly equal intervals distributed over a clean and dry white porcelain-plate: a drop or two of the solution to be tested is then brought in contact with one of these and the effect noted. Another plan is to have thin blotting-paper, moistened with a solution of the indicator and dried; a drop of the solution to be tested placed on this shows the characteristic change. When the assay solution contains a suspended solid which interferes with the test, a prepared paper covered with an ordinary filter-paper answers very well; a drop of the solution to be tested is placed on the filter-paper, and, sinking through, shows its effect on the paper below.
Except when otherwise stated, all titrations should be made at the ordinary temperature; cooling, if necessary, by holding the flask under the tap. When a titration is directed to be made in a boiling solution, it must be remembered that the standard solution is cold, and that every addition lowers the temperature of the assay.
On running the solution from the burette into the assay, do not let it run down the side of the flask. If a portion of the assay has to be withdrawn for testing, shake the flask to ensure mixing, and then take out a drop with the test-rod; the neglect of these precautions may give a finishing-point too early. This is generally indicated by a sudden finish, in which case on shaking the flask and again testing no reaction is got. Do not remove the drop on the point of the burette with the test-rod; let it remain where it is or drop it into the solution by carefully opening the clip.
Generally the methods of working are as follows:--
(1) When the finishing-point depends on a change of colour in the solution.--Increase the bulk of the assay up to from 100 to 150 c.c. with water. Boil or cool, as the case may be. Run in the standard solution from a burette speedily, until the re-agent appears to have a slower action, and shake or stir all the time. Then run 1 c.c. or so at a time, still stirring, and finally add drops until the colour change is got.
(2) When an outside-indicator is used.--Pour the standard solution from a burette into the assay until 5 or 6 c.c. from the finishing-point; then run in 1 c.c. at a time (stirring and testing on the plate between each) until the indicator shows the change wanted, and deduct 0.5 c.c. for excess. When greater accuracy is sought for a duplicate assay is made. In this case the standard solution is run in close up to the end, and the operation is finished off with a few drops at a time.
(3) Where the finishing-point depends upon the absence of a precipitate and no outside-indicator is used.--As in the last case, run in the standard solution up to within a few c.c. of the end, then run in 1 c.c. at a time until a precipitate is no longer formed, but here 1.5 c.c. must be deducted for excess, since it is evident that the whole of the last "c.c." must have been, and a portion of the previous one may have been, in excess.
~Indirect Titration.~--The action of permanganate of potash upon a ferrous solution is one of oxidation, hence it is evident that if any other oxidising agent is present it will count as permanganate. In such a case the titration can be used (indirectly) to estimate the quantity of such oxidising agent, by determining how much less of the permanganate is used. For example, suppose that 1 gram of iron dissolved in sulphuric acid requires 100 c.c. of standard permanganate to fully oxidise it, but that the same amount of iron only requires 35.6 c.c. of the same standard permanganate if it has been previously heated with 0.5 gram of black oxide of manganese. Here it is evident that 0.5 gram of black oxide does the work of 64.4 c.c.[4] of the permanganate solution, and that these quantities are equivalent; moreover, if 64.4 c.c. correspond with 0.5 gram, then 100 c.c. correspond with 0.7764 which is the standard. On theoretical grounds, and by a method of calculation which will be explained further on (under the heading "Calculations from Formulæ"), it can be found that if the standard for iron is 1 gram, that for the black oxide will be 0.7764 gram.
The principles of these indirect titrations become clearer when expressed in a condensed form. Thus, in the example selected, and using the formulæ Fe = Iron, KMnO_{4} = permanganate of potash, and MnO_{2} = oxide of manganese, we have:--
(1) 1 gram Fe = 100 c.c. KMnO_{4}
(2) 1 gram Fe = 35.6 c.c. KMnO_{4} + 0.5 gram MnO_{2} .'. 100 c.c. KMnO_{4} = 35.6 c.c. KMnO_{4} + 0.5 gram MnO_{2} (100-35.6) c.c. KMnO_{4} = 0.5 gram MnO_{2} 64.4 c.c. KMnO_{4} = 0.5 gram MnO_{2}
The iron does not enter into the calculation if the same quantity is present in the two experiments.
An indirect titration thus requires three determinations, but if more than one assay is to be carried on, two of these need not be repeated. The standard is calculated in the usual way.
~Colorimetric Assays.~--These are assays in which the colour imparted to a solution by some compound of the metal to be determined is taken advantage of; the depth of colour depending on the quantity of metal present. They are generally used for the determination of such small quantities as are too minute to be weighed. The method of working is as follows:--A measured portion of the assay solution (generally 2/3, 1/2, 1/3, or 1/4 of the whole), coloured by the substance to be estimated, is placed in a white glass cylinder standing on a sheet of white paper or glazed porcelain. Into an exactly similar cylinder is placed the same amount of re-agents, &c., as the portion of the assay solution contains, and then water is added until the solutions are of nearly equal bulk. Next, a standard solution of the metal being estimated is run in from a burette, the mixture being stirred after each addition until the colour approaches that of the assay. The bulk of the two solutions is equalised by adding water. Then more standard solution is added until the tints are very nearly alike. Next, the amount added is read off from the burette, still more is poured in until the colour is slightly darker than that of the assay, and the burette read off again. The mean of the readings is taken, and gives the quantity of metal added. It equals the quantity of metal in the portion of the assay. If this portion was one-half of the whole, multiply by two; if one-third, multiply by three, and so on. When the quantity of metal in very dilute solutions is to be determined, it is sometimes necessary to concentrate the solutions by boiling them down before applying the re-agent which produces the coloured compound. Such concentration does not affect the calculations.
~Gasometric Assays.~--Gasometric methods are not much used by assayers, and, therefore, those students who wish to study them more fully than the limits of this work will permit, are recommended to consult Winkler and Lunge's text-book on the subject. The methods are without doubt capable of a more extended application. In measuring liquids, ordinary variations of temperature have but little effect, and variations of atmospheric pressure have none at all, whereas with gases it is different. Thus, 100 c.c. of an ordinary aqueous solution would, if heated from 10° C. to 20° C., expand to about 100.15 c.c. 100 c.c. of a gas similarly warmed would expand to about 103.5 c.c., and a fall of one inch in the barometer would have a very similar effect. And in measuring gases we have not only to take into account variations in volume due to changes in temperature and atmospheric pressure, but also that which is observed when a gas is measured wet and dry. Water gives off vapour at all temperatures, but the amount of vapour is larger as the temperature increases.
By ignoring these considerations, errors of 3 or 4 per cent. are easily made; but, fortunately, the corrections are simple, and it is easy to construct a piece of apparatus by means of which they may be reduced to a simple calculation by the rule of three.
The volume of a gas is, in practice, usually reduced to that which it would be at a temperature of 0° C., when the column of mercury in the barometer is 760 mm. high. But, although convenient, this practice is not always necessary. The only thing required is some way of checking the variations in volume, and of calculating what the corrected volume would be under certain fixed conditions.
Suppose that at the time a series of standardisings is being made, 100 c.c. of air were confined in a graduated tube over moist mercury. These 100 c.c. would vary in volume from day to day, but it would always be true of them that they would measure 100 c.c. under the same conditions as those under which the standardisings were made. If, then, in making an actual assay, 35.4 c.c. of gas were obtained, and the air in the tube measured 105 c.c., we should be justified in saying, that if the conditions had been those of the standardising, the 105 c.c. would have measured 100 c.c., and the 35.4 c.c. would have been 33.7; for 105: 100:: 35.4: 33.7. The rule for using such a piece of apparatus for correcting volumes is:--Multiply the c.c. of gas obtained by 100, and divide by the number of c.c. of air in the apparatus.
If it is desired to calculate the volumes under standard conditions (that is, the gas dry, at 0° C. and 760 mm. barometric pressure) the calculations are easily performed, but the temperature and pressure must be known.
Correction for Moisture.--The "vapour tension" of water has been accurately determined for various temperatures, and it may be looked upon as counteracting the barometric pressure. For example, at 15° C. the vapour tension equals 12.7 millimetres of mercury; if the barometer stood at 750 mm., the correction for moisture would be made by subtracting 12.7 from 750, and taking 737.3 mm. to be the true barometric pressure.
The vapour tensions for temperatures from 0° C. to 20° C. are as follows:--
-------+----------++-------+----------++-------+---------- Temp. | Tension. || Temp. | Tension. || Temp. | Tension. -------+----------++-------+----------++-------+---------- 0° | 4.6 mm. || 7° | 7.5 mm. || 14° | 11.9 mm. 1° | 4.9 mm. || 8° | 8.0 mm. || 15° | 12.7 mm. 2° | 5.3 mm. || 9° | 8.6 mm. || 16° | 13.5 mm. 3° | 5.7 mm. || 10° | 9.2 mm. || 17° | 14.4 mm. 4° | 6.1 mm. || 11° | 9.8 mm. || 18° | 15.3 mm. 5° | 6.5 mm. || 12° | 10.5 mm. || 19° | 16.3 mm. 6° | 7.0 mm. || 13° | 11.2 mm. || 20° | 17.4 mm. -------+----------++-------+----------++-------+-----------
The correction for pressure is:--Multiply the volume by the actual pressure and divide by 760.
The correction for temperature:--Multiply the volume by 273 and divide by the temperature (in degrees Centigrade) added to 273.
For all three corrections the following rules hold good. To reduce to 0° C. and 760 mm. dry.
Volume × 0.3592 × (Pressure-tension) Corrected volume = -------------------------------------- Temperature + 273
To find the volume, which a given volume under standard conditions would assume, if those conditions are altered.
Volume × 2.784 × (Temperature + 273) Resulting volume = ------------------------------------ Pressure - tension
As an example, we will suppose that it is desired to enclose in the apparatus referred to on p. 45, a volume of air, which, when dry (at 0° C. and 760 mm.), shall measure 100 c.c., whilst the actual temperature is 15° C., and the pressure 750 mm.
The second formula is the one to be used, and we get 108.7 c.c.
100 c.c.×2.784×288 Required volume = ---------------------- 750-12.7
80179.2 = ------- 737.3
= 108.7 c.c.
FOOTNOTES:
[4] 100-35.6 = 64.4.
V. WEIGHING AND MEASURING
~Weighing.~--The system of weights and measures which we have adopted is the French or metric system; in this the gram (15.43 grains) is the unit of weight; the only other weight frequently referred to is the milligram, which is 0.001, or 1/1000 gram. The unit of volume is the cubic centimetre, which is approximately the volume of 1 gram of water, and which thus bears to the gram the same relation as grain-measures bear to grains. It is usual to write and even pronounce cubic centimetre shortly as c.c., and the only other denomination of volume we shall have occasion to use is the "litre," which measures 1000 c.c., and is roughly 1-3/4 pints.
The weights used are kept in boxes in a definite order, so that the weights on the balance can be counted as well by noting those which are absent from the box as by counting those present on the scale-pan. The weights run 50, 20, 10, 10, 5, 2, 1, 1 and 1 grams, and are formed of brass. The fractions of the gram are generally made of platinum or of aluminium, and are arranged in the following order:--0.5, 0.2, 0.1, 0.1, and 0.05, 0.02, 0.01, 0.01. These may be marked in this way, or they may be marked 500, 200, 100, 100, 50, 20, 10, 10; the 500 meaning 500 milligrams.
Some makers send out weights in the series 50, 20, 20, 10, &c.
Weights of less than 0.01 gram are generally present in a box, but it is much more convenient to work with a rider. This is a piece of wire which in the pan weighs 0.01 gram; it is made in such a form that it will ride on the beam, and its effective weight decreases as it approaches the centre. If the arm of the beam is divided into tenths, then each tenth counting from the centre outward equals 0.001 gram or 1 milligram, and if these tenths be further subdivided the fractions of a milligram are obtained; and these give figures in the fourth place of decimals. A fairly good balance should be sensitive to 0.0001 gram. The weights must never be touched with the fingers, and the forceps for moving them is used for no other purpose. When not in actual use the box is kept closed. The weights must not be allowed to remain on the pan of the balance. The balance-case must not be open without some reason. It must be fixed level, and, once fixed, must not be needlessly moved. The bench on which it stands should be used for no other purpose, and no one should be allowed to lean upon it.
When using a balance sit directly in front of it. Ordinarily the substance to be weighed is best put on the pan to the user's left; the weights and the rider are then easily manipulated. Powders, &c., should not be weighed directly on the balance; a counterpoised watch-glass or metal scoop (fig. 25) should be used. In some cases it is advisable to use a weighing-bottle. This is a light, well-stoppered bottle (fig. 3) containing the powdered ore. It is first filled and weighed; then some of the substance is carefully poured from it into a beaker or other vessel, and it is weighed again; the difference in the two weighings gives the weight of substance taken. A substance must always be cold when weighed, and large glass vessels should be allowed to stand in the balance-box a little while before being weighed. Always have the balance at rest when putting on or taking off anything from the pans. Put the weights on systematically. In using the rider (except you have a reason to the contrary), put it on at the 5; if this is too much, then try it at the 3; if then the weights are too little, try at the 4, if still not enough, the correct weight must be between the 4 and 5; try half-way between.
It is best to work with the balance vibrating; equilibrium is established when the vibration to the left is the mean of the preceding and succeeding vibrations to the right. For example, if it vibrates 6 divisions to the right on one swing, and 5 divisions on the next, the intermediate vibration to the left should have been 5-1/2.
Note whether the substance increases in weight whilst on the balance. If it does it may be because it was put on warm, and is cooling, or it may be because it is taking up moisture from the air. Substances which take up moisture rapidly should be weighed in clipped watch-glasses or in light-weighing bottles or tubes.
Students, in recording the weights, should first read off those missing from the box, writing down each order of figures as determined; first tens, then units, and so on. Remember that the first four platinum weights give the figures of the first place of decimals, the second four give the second place, and that the third and fourth places are given by the rider. Having taken down the figures, confirm them by reading off the weights as you put them back into the box. Do not rest a weight on the palm of your hand for convenience in reading the mark upon it. Remember one weight lost from a box spoils the set. Do not take it for granted that the balance is in equilibrium before you start weighing: try it.
~Measuring Liquids.~--For coarse work, such as measuring acids for dissolving ores, graduated glasses similar to those used by druggists may be used. It is well to have two sizes--a smaller graduated into divisions of 5 c.c. (fig. 26), and a larger with divisions equal to 10 c.c. No measurement of importance should be made in a vessel of this kind, as a slight variation in level causes a serious error.
~Graduated flasks~ must be used when anything has to be made up to a definite bulk, or when a fixed volume has to be collected. If, for example, a certain weight of substance has to be dissolved and diluted to a litre, or if the first 50 c.c. of a distillate has to be collected, a flask should be used. Each flask is graduated for one particular quantity; the most useful sizes are 1000 c.c., 500 c.c., 200 c.c., 100 c.c., and 50 c.c. The mark should be in the narrowest part of the neck, and should be tangential to the curved surface of the liquid when the flask contains the exact volume specified. The level of a curved surface of liquid is at first somewhat difficult to read: the beginner is in doubt whether the surface should be taken at A, B, or C (fig. 27). It is best to take the lowest reading C. In some lights it is difficult to find this; in such cases a piece of white paper or card held behind and a little below, so as to throw light up and against the curved surface, will render it clear. In reading, one should look neither up at nor down upon the surface, but the eye should be on the same level with it. It must be kept in mind that flasks contain the quantity specified, but deliver less than this by the amount remaining in them and damping the sides. If it is desired to transfer the contents say of a 100 c.c. flask to a beaker, it will be necessary to complete the transfer by rinsing out the flask and adding the washings; otherwise there will be a sensible loss. Graduated cylinders (fig. 28) are convenient for preparing standard solutions.
~Pipettes~ and burettes are graduated to deliver the quantities specified. The principle of the pipette, and the advantages and disadvantages of its various forms, may be understood by considering the first form shown in fig. 29. It is essentially a bulbed tube drawn out to a jet at its lower end, and having on each side of the bulb a mark so placed that when the surface of the liquid falls from the upper to the lower mark the instrument shall deliver exactly 100 c.c. The bore of the jet should be of such a size as will allow the level of the liquid to fall at the rate of about one foot in two minutes. If it runs more quickly than this, an appreciable error arises from the varying amount of liquid remaining, and damping the sides of the bulb. The flow of liquid from a pipette must not be hastened by blowing into it. The lower tube or nose of the pipette should be long enough to reach into the bottle or flask containing the liquid about to be measured. The pipette is filled by sucking at the open end with the mouth; this method of filling renders the use of the instrument dangerous for such liquids as strong acids, ammonia, and such poisonous solutions as that of potassic cyanide. One attempt with a fairly strong solution of ammonia will teach the beginner a very useful lesson. As soon as the liquid rises above the upper mark in the pipette, the mouth is withdrawn, and the pipette quickly closed by pressing the upper aperture with the index finger of the right hand; it is well to have the finger slightly moist, but not damp. The neck of the pipette should be long enough to allow its being firmly grasped by the fingers and thumb of the right hand without inconvenience. The pipette is first held in a vertical position long enough to allow any moisture outside the tube to run down, and then the liquid is allowed to run out to the level of the upper mark; this is easily effected by lessening the pressure. If the finger is wet, the flow will be jerky, and good work impossible. The pipette is next held over the vessel into which the 100 c.c. are to be put, and the liquid allowed to run out. When the bulb is nearly empty, the flow should be checked by replacing the finger, and the liquid allowed to escape slowly until the lower mark is reached. The pipette is then withdrawn; it is in the withdrawing that the disadvantage of this particular form[5] makes itself felt. It must be withdrawn very steadily, as the slightest shock causes the remaining column of liquid to vibrate, whereby air is drawn in and the liquid is forced out.
This disadvantage is got rid of by making the mouth of the jet the lower limit, or, in other words, allowing the instrument to empty itself. There are two forms of such pipettes; in the one generally recommended in Gay-Lussac's silver assay (the last shown in fig. 29) the nose is replaced by a jet. This is most conveniently filled by stopping the jet with the finger, and allowing the liquid to flow in a fine stream into the neck until the pipette is filled, and then working as just described. The other form is the one in general use; in fact, a long nose to a pipette is so convenient that it may almost be said to be necessary. But the accuracy is slightly diminished; a long narrow tube makes a poor measuring instrument because of the amount of liquid it finally retains. A defect possessed by both forms is the retention of a drop of varying size in the nozzle. Whatever method is adopted for removing this drop must be always adhered to. The most convenient form is the one last described, and the most useful sizes are 100 c.c., 50 c.c., 20 c.c., 10 c.c., and 5 c.c. Ten c.c. pipettes graduated into tenths of a cubic centimetre are very useful: those are best in which the graduation stops short of the bottom.
All measurements should be made at the ordinary temperature; and, before being used, the pipette should be rinsed out with a cubic centimetre or so of the solution to be measured. After using, it should be washed out with water.
~Burettes~ differ mainly from pipettes in having the flow of liquid controlled from below instead of from above. The best form is that known as Mohr's, one kind of which is provided with a glass stopcock, while the other has a piece of india-rubber tube compressed by a clip. The latter cannot be used for solutions of permanganate of potash or of iodine, or of any substance which acts on india-rubber; but in other respects there is little to choose between the two kinds. A burette delivering 100 c.c., and graduated into fifths (i.e., each division = 0.2 c.c.), is a very convenient size. For some kinds of work, 50 c.c. divided into tenths (i.e., each division = 0.1 c.c.) may be selected.
Burettes may be fixed in any convenient stand; they must be vertical and should be so placed that the assayer can read any part of the graduated scale without straining. When not in use, they should be kept full of water. When using a burette, the water must be run out; the burette is next rinsed with some of the solution to be used, and drained; and then it is filled with the solution. Next squeeze the india-rubber tube so as to disentangle air-bubbles and, by smartly opening the clip, allow the tube and jet to be filled; see that no bubbles of air are left. Then run out cautiously until the level of the liquid in the burette stands at zero. In reading the level with very dark-coloured liquids it is convenient to read from the level A (fig. 27), and, provided it is done in each reading, there is no objection to this. The accuracy of the reading of a burette is sensibly increased by the use of an Erdmann float. This is an elongated bulb, weighted with mercury, and fitting (somewhat loosely) the tube of the burette. It floats in the solution, and is marked with a horizontal line; this line is taken as the level of the liquid. If the burette is filled from the top, the float rises with aggravating slowness, and this is its chief disadvantage. The float must come to rest before any reading is made.
A convenient plan for filling a burette from below is shown in fig. 30. The diagram explains itself. The bottle containing the standard solution is connected with the burette by a syphon arrangement through the glass tube and T-piece. The flow of liquid into the burette is controlled by the clip. When this clip is opened, the burette fills; and when it is closed, the burette is ready for use in the ordinary way.
~Measuring Gases.~--Lange's nitrometer (fig. 69) is a very convenient instrument for many gasometric methods. It requires the use of a fair quantity of mercury. In fig. 31, there is a representation of a piece of apparatus easily fitted up from the ordinary material of a laboratory. It is one which will serve some useful purposes. It consists of a wide-mouthed bottle fitted (by preference) with a rubber cork. The cork is perforated, and in the perforation is placed a glass tube which communicates with the burette. The burette is connected by a rubber tube and a Y-piece, either with another burette or with a piece of ordinary combustion-tube of about the same size. The wide-mouthed bottle contains either a short test-tube or an ordinary phial with its neck cut off. In working the apparatus the weighed substance is put in the bottle and the re-agent which is to act on it, in the test-tube; the cork is then inserted. The liquid in the two burettes is next brought to the same level, either by pouring it in at A or running it out at B. The level of the liquid in the apparatus for correcting variation in volume is then read and noted. Next, after seeing that the level of the liquid in the burette has not changed, turn the bottle over on its side so that the re-agent in the test-tube shall be upset into the bottle. Then, as the volume of the gas increases, lower the liquid in the burette by running it out at B, and at the same time keep the level in A half an inch or so lower than that in the burette. When the action has finished bring the liquid in the two vessels to the same level and read off the burette. This part of the work must always be done in the same manner.
The volume corrector for gas analysis is a graduated glass tube of 120 c.c. capacity inverted over a narrow glass cylinder of mercury. It contains 0.2 or 0.3 c.c. of water and a volume of air, which, if dry and under standard conditions, would measure 100 c.c. The actual volume varies from day to day, and is read off at any time by bringing the mercury inside and outside to the same level. This is done by raising or lowering the tube, as may be required. Any volume of gas obtained in an assay can be corrected to standard temperature and pressure by multiplying by 100 and dividing by the number of c.c. in the corrector at the time the assay is made.
FOOTNOTES:
[5] It is best to use this form with a glass stopcock, or with an india-rubber tube and clip, after the manner of a Mohr's burette.
VI. RE-AGENTS.--ACIDS, ETC
~Acetic Acid~, H[=A=c] or C_{2}H_{4}O_{2}. (sp. gr. 1.044, containing 33 per cent. real acid).--An organic acid, forming a class of salts, acetates, which are for the most part soluble in water, and which, on ignition, leave the oxide or carbonate of the metal. It is almost always used in those cases where mineral acids are objectionable. To convert, for example, a solution of a substance in hydrochloric acid into a solution of the same in acetic acid, alkali should be added in excess and then acetic acid. Many compounds are insoluble in acetic acid, which are soluble in mineral acids, such as ferric phosphate, ferric arsenate, zinc sulphide, calcium oxalate, &c., so that the use of acetic acid is valuable in some separations. The commercial acid is strong enough for most purposes, and is used without dilution.
~"Aqua Regia"~ is a mixture of 1 part by measure of nitric acid and 3 parts of hydrochloric acid. The acids react forming what is practically a solution of chlorine.[6] The mixture is best made when wanted, and is chiefly used for the solution of gold and platinum and for "opening up" sulphides. When solutions in aqua regia are evaporated, chlorides are left.
~Bromine~, Br. (sp. gr. 3.0). Practically pure bromine.--It is a heavy reddish-brown liquid and very volatile. It boils at 60° C., and, consequently, must be kept in a cool place. It gives off brown irritating vapours, which render its use very objectionable. Generally it answers the same purpose as aqua regia, and is employed where the addition of nitric acid to a solution has to be specially avoided. It is also used for dissolving metals only from ores which contain metallic oxides not desired in the solution.
~"Bromine Water"~ is simply bromine shaken up with water till no more is dissolved.
~Carbonic Acid~, CO_{2}.--A heavy gas, somewhat soluble in water; it is mainly used for providing an atmosphere in which substances may be dissolved, titrated, &c., without fear of oxidation. It is also used in titrating arsenic assays with "iodine" when a feeble acid is required to prevent the absorption of iodine by the alkaline carbonate. It is prepared when wanted in solution, by adding a gram or so of bicarbonate of soda and then as much acid as will decompose the bicarbonate mentioned. When a quantity of the gas is wanted, it is prepared, in an apparatus like that used for sulphuretted hydrogen, by acting on fragments of marble or limestone with dilute hydrochloric acid.
~Citric Acid~ (H_{3}[=C=i] or C_{6}H_{8}O_{7}.H_{2}O) is an organic acid which occurs in colourless crystals, soluble in less than their weight of water. The solution must be freshly prepared, as it gets mouldy when kept. It forms a comparatively unimportant class of salts (citrates). It is used in the determination of phosphoric acid, chiefly for the purpose of preventing the precipitation of phosphates of iron and alumina by ammonia, and in a few similar cases. The commercial crystals are used; they should be free from sulphuric acid and leave no ash on ignition.
~Hydrochloric Acid~, HCl in water, (sp. gr. 1.16. It contains 32 per cent. of hydrogen chloride).--It is sometimes called "muriatic acid," and when impure, "spirit of salt." The acid solution should be colourless and free from arsenic, iron, and sulphuric acid. It forms an important family of salts, the chlorides. It is the best acid for dissolving metallic oxides and carbonates, and is always used by the assayer when oxidising agents are to be avoided. The acid is used without dilution when no directions are expressly given to dilute it. It has no action on the following metals: gold, platinum, arsenic, and mercury; it very slightly attacks antimony, bismuth, lead, silver, and copper. Tin is more soluble in it, but with difficulty; whilst iron, zinc, nickel, cobalt, cadmium, and aluminium easily dissolve with evolution of hydrogen and the formation of the lower chloride if the metal forms more than one class of salts. All the metallic oxides, except a few of the native and rarer oxides, are dissolved by it with the formation of chlorides of the metal and water.
~Dilute Hydrochloric Acid~ is made by diluting the strong acid with an equal volume of water. This is used for dissolving precipitates obtained in the general course of analysis and the more easily soluble metals.
~Hydrofluoric Acid, HF.~--A solution in water may be purchased in gutta-percha or lead bottles. It is of variable strength and doubtful purity. It must always be examined quantitatively for the residue left on evaporation. It is used occasionally for the examination of silicates. It attacks silica, forming fluoride of silicon, which is a gas. When the introduction of another base will not interfere with the assay, the substance may be mixed in the platinum dish with fluoride of ammonium, or of potassium, or of calcium, and hydrochloric acid, instead of treating it with the commercial acid. It is only required in special work. The fumes and acid are dangerous, and, of course, glass or porcelain vessels cannot be used with it.
~Iodine, I.~--This can be obtained in commerce quite pure, and is often used for standardising. It is very slightly soluble in water, but readily dissolves in potassium iodide solution. It closely resembles chlorine and bromine in its properties, and can be used for dissolving metals without, at the same time, attacking any oxide which may be present. It is chiefly used as an oxidizing agent in volumetric work, being sharp in its reactions and easily detected in minute quantities. It cannot be used in alkaline solutions, since it reacts with the hydrates, and even with the carbonates, to form iodides and iodates. Iodine is soluble in alcohol.
~Nitric Acid, HNO_{3}.~ (Sp. gr. 1.42; boiling point 121° C.; contains 70 per cent. by weight of hydrogen nitrate).--It is convenient to remember that one c.c. of this contains 1 gram of real acid. It combines the properties of an acid and of an oxidising agent. One c.c. contains 0.76 gram of oxygen, most of which is very loosely held, and easily given up to metals and other oxidisable substances. Consequently it will dissolve many metals, &c., upon which hydrochloric acid has no action. All sulphides (that of mercury excepted) are attacked by it, and for the most part rendered soluble. It has no action on gold or platinum, and very little on aluminium. The strong acid at the ordinary temperature does not act on iron or tin; and in most cases it acts better when diluted. Some nitrates being insoluble in nitric acid, form a protecting coat to the metal which hinders further action. Where the strong acid does act the action is very violent, so that generally it is better to use the dilute acid. When iron has been immersed in strong nitric acid it not only remains unacted on, but assumes a passive state; so that if, after being wiped, it is then placed in the dilute acid, it will not dissolve. Tin and antimony are converted into insoluble oxides, while the other metals (with the exception of those already mentioned) dissolve as nitrates. During the solution of the metal red fumes are given off, which mainly consist of nitrogen peroxide. The solution is often coloured brown or green because of dissolved oxides of nitrogen, which must be got rid of by boiling. Generally some ammonium nitrate is formed, especially in the cases of zinc, iron, and tin, when these are acted on by cold dilute acid. Sulphur, phosphorus, and arsenic are converted into sulphuric, phosphoric, and arsenic acids respectively, when boiled with the strong acid.
~Dilute Nitric Acid.~--Dilute 1 volume of the strong acid with 2 of water.
~Oxalic Acid~, H_{2}[=O] or (H_{2}C_{2}O_{4}.2H_{2}O.)--This is an organic acid in colourless crystals. It forms a family of salts--the oxalates. It is used in standardising; being a crystallised and permanent acid, it can be readily weighed. It is also used in separations, many of the oxalates being insoluble. For general use make a 10 per cent. solution. Use the commercially pure acid. On ignition the acid should leave no residue.
~Sulphuretted Hydrogen.~ Hydrosulphuric acid, SH_{2}.--A gas largely used in assaying, since by its action it allows of the metals being conveniently classed into groups. It is soluble in water, this liquid dissolving at the ordinary temperature about three times its volume of the gas. The solution is only useful for testing. In separations, a current of the gas must always be used. It is best prepared in an apparatus like that shown in fig. 32, by acting on ferrous sulphide with dilute hydrochloric acid. When iron has to be subsequently determined in the assay solution, the gas should be washed by bubbling it through water in the smaller bottle; but for most purposes washing can be dispensed with. The gas is very objectionable, and operations with it must be carried out in a cupboard with a good draught. When the precipitation has been completed, the apparatus should always be washed out. The effect of this acid on solutions of the metals is to form sulphides. All the metallic sulphides are insoluble in water; but some are soluble in alkaline, and some in acid, solutions. If sulphuretted hydrogen is passed through an acid solution containing the metals till no further precipitation takes place, a precipitate will be formed containing sulphides insoluble in the acid. On filtering, adding ammonia (to render the filtrate alkaline), and again passing the gas, a further precipitate will be obtained, consisting of sulphides insoluble in an alkaline solution, but not precipitable in an acid one; the filtrate may also contain sulphides not precipitable in an acid solution, which are soluble in an alkaline one; these will be thrown down on neutralising. Again, the metals precipitated in the acid solution form sulphides which may be divided into groups, the one consisting of those which are soluble, and the other of those which are not soluble, in alkalies. This classification is shown in the following summary:--
1. Precipitable in an acid solution.
(a) Soluble in Alkalies.--Sulphides of As, Sb, Sn, Au, Pt, Ir, Mo, Te, and Se.
(b) Insoluble in Alkalies.--Sulphides of Ag, Pb, Hg, Bi, Cu, Cd, Pd, Rh, Os, and Ru.
2. Not precipitated in an acid solution, but thrown down in an alkaline one.
Sulphides of Mn, Zn, Fe, Ni, Co, In, Tl, and Ga.
These can again be divided into those which are dissolved by dilute acids and those which are not.
3. Not precipitated in an acid or alkaline solution, but thrown down on neutralising the latter.
Sulphides of V and W.
Sulphuretted hydrogen is a strong reducing agent. Ferric salts are thereby quickly reduced to ferrous; in hot solutions nitric acid is decomposed. These changes are marked by a precipitation of sulphur, and the student must be careful to pass the gas sufficiently long, and not be too hasty in concluding that no sulphide will form because it does not at once make its appearance. The best indication that it has been passed long enough is the smell of the gas in the solution after shaking.
~Sulphurous Acid~, H_{2}SO_{3}.--The reagent used may be regarded as a saturated solution of sulphur dioxide in water. It may be purchased, and keeps for a long time. It may be made by heating copper with sulphuric acid and passing the gas formed into water. The heat should be withdrawn when the gas is coming off freely. It is used as a reducing agent, and should not be diluted.
~Sulphuric Acid~, H_{2}SO_{4}. (Sp. gr. 1.84, containing 96 per cent. of real acid, H_{2}SO_{4}.)--This acid forms insoluble sulphates with salts of lead, strontium, and barium. It has a high boiling point, 290° C., and, when evaporated with salts of the more volatile acids, converts them into sulphates. When nitrates or chlorides are objectionable in a solution, evaporation with sulphuric acid removes them. In working with this acid caution is necessary, since, on mixing with water, great heat is evolved; and, if either the acid or water has been previously heated, a serious accident may result. In diluting the acid it should be poured into cold water. Glass vessels containing boiling sulphuric acid should be handled as little as possible, and should not be cooled under the tap. The action of diluted sulphuric acid on metals closely resembles that of dilute hydrochloric acid. Magnesium, aluminium, iron, zinc, nickel, cobalt, manganese, and cadmium dissolve, with evolution of hydrogen, in the cold acid, or when warmed. The action of hot and strong sulphuric acid is altogether different; it acts as an oxidising agent, and is itself reduced to sulphur dioxide or even to sulphur. The following metals are attacked in this way:--copper, bismuth, mercury, silver, antimony, tin, and lead. Gold, platinum, and arsenic are not affected. This property is made use of in parting silver from gold and platinum. Metallic sulphides are similarly attacked; but this method of opening up minerals has the disadvantage of giving rise to the formation of anhydrous sulphates of iron, &c., which are not readily dissolved when afterwards diluted. The use of sulphuric acid in assaying is (for these reasons) to be avoided. Its chief use is as a drying agent, since it has a strong affinity for water. Air under a bell jar may be kept dry by means of a basin of sulphuric acid, and gases bubbled through it are freed from water-vapour.
~Dilute Sulphuric Acid.~--This is made by diluting 1 volume of the strong acid with 4 of water.
~Tartaric Acid~, H_{2}[=T] or C_{4}H_{6}O_{6}.--A crystallised organic acid, soluble in less than its own weight of water, or in less than three parts of alcohol. It is used for the same purposes as citric acid is. The solution is made when required.
BASES, SALTS, &c.
~Alcohol~, C_{2}H_{6}O. (Commercial alcohol of sp. gr. 0.838; it contains 84 per cent. by weight of alcohol.)--It should burn with a non-luminous flame and leave no residue. It is used for washing precipitates where water is inapplicable, and for facilitating drying.
~Ammonia~, NH_{3}. (Commercial ammonia, a solution having a sp. gr. of 0.88 to 0.89, and containing about 33 per cent. of ammonia.)--It is used as an alkali (more commonly than soda or potash), since an excess of it is easily removed by boiling. The salts of ammonium formed by it may be removed by igniting, or by evaporating in a porcelain dish with an excess of nitric acid. It differs in a marked way from soda or potash in its solvent action on the oxides or hydrates of the metals. Salts of the following metals are soluble in an ammoniacal solution in the presence of ammonic chloride:--copper, cadmium, silver, nickel, cobalt, manganese, zinc, magnesium, sodium, potassium, and the alkaline earths.
~Dilute Ammonia~ is made by diluting 1 vol. of commercial ammonia with 2 of water. The dilute ammonia is always used; but in assays for copper a stronger solution (1 of strong ammonia to 1 of water) is required.
~Ammonic Carbonate~ (Am_{2}CO_{3}) is prepared by dissolving one part of the commercial sesquicarbonate of ammonia in four parts of water, and adding one part of strong ammonia.
~Ammonic Bicarbonate~ (HAmCO_{3}) is prepared by saturating a solution of the sesquicarbonate of ammonia with carbon dioxide.
~Ammonic Chloride~, AmCl.--Use the commercial salt in a 20 per cent. solution in water. The salt should leave no residue on ignition.
~Ammonic Molybdate.~--The solution is prepared as follows:--Dissolve 100 grams of the powdered commercial salt in 200 c.c. of dilute ammonia, and pour the solution in a slow stream into 750 c.c. of dilute nitric acid; make up to 1 litre, and allow the mixture to settle before using. It is used for the purpose of separating phosphoric oxide from bases and from other acids, and also as a test for phosphates and arsenates. In using this solution the substance must be dissolved in nitric acid, and a considerable excess of the reagent added (50 c.c. is sufficient to precipitate 0.1 gram P_{2}O_{5}); when the phosphate is in excess no precipitate will be got. The precipitate is phospho-molybdate of ammonia.
~Ammonic Nitrate~ (AmNO_{3}) is used in the separation of phosphoric oxide by the molybdate method, and occasionally for destroying organic matter. It is soluble in less than its own weight of water. The solution is made when wanted.
~Ammonic Oxalate~ (Am_{2}C_{2}O_{4}.2H_{2}O) is used chiefly for the separation of lime. The solution is made by dissolving 15 grams of the salt in 100 c.c. of water.
~Ammonic Sulphide~ may be purchased in the state of a strong solution. It is yellow, and contains the disulphide, S_{2}Am_{2}. It serves the same purpose as is obtained by passing a current of sulphuretted hydrogen through an ammoniacal solution; but has the disadvantage of loading the solution with sulphur, which is precipitated when the solution is subsequently acidified. It is useful for dissolving the lower sulphide of tin (SnS).
~Baric Carbonate~ (BaCO_{3}) is sometimes used for precipitating the weaker bases. It should be prepared when wanted by precipitating a solution of baric chloride with ammonic carbonate and washing. The moist precipitate is used without drying.
~Baric Chloride~, BaCl_{2}.2H_{2}O.--A crystallised salt, soluble in 2-1/2 parts of water. It is used for the detection and separation of sulphates. Make a 10 per cent. solution.
"~Black Flux.~"--A mixture of finely divided carbon with carbonate of potash or with carbonates of potash and soda. It is prepared by heating tartar or "rochelle salt" until no more combustible gas is given off. One gram will reduce about 2 grams of lead from litharge.
~Borax~, Na_{2}B_{4}O_{7}.10H_{2}O.--It is chiefly used as a flux in dry assaying, as already described. It is also used in testing before the blowpipe; many metallic oxides impart a characteristic colour to a bead of borax in which they have been fused.
~Calcium Chloride.~--The crystallised salt is CaCl_{2}.6H_{2}O; dried at 200° C. it becomes CaCl_{2}.2H_{2}O, and when fused it becomes dehydrated. The fused salt, broken into small lumps, is used for drying gases. It combines with water, giving off much heat; and dissolves in a little more than its own weight of water. Strong solutions may be used in baths in which temperatures above the boiling-point of water are required. One part of the salt and 2 of water give a solution boiling at 112°, and a solution of 2 parts of the salt in 1 of water boils at 158°. The salt is very little used as a reagent.
~Calcium Fluoride~ or "~Fluor Spar~," CaF_{2}.--The mineral is used as a flux in dry assaying; it renders slags which are thick from the presence of phosphates, &c., very fluid. Mixed with hydrochloric acid it may sometimes be used instead of hydrofluoric acid.
~Calcium Carbonate~, CaCO_{3}.--It is precipitated in a pure state by ammonic carbonate from a solution of calcium chloride. It is used for standardising. In the impure state, as marble or limestone, it is used in the preparation of carbonic acid.
~Calcium Hydrate~ or ~"Lime Water."~--This is used in testing for carbon dioxide and in estimating the amount of that gas present in air. It may be made by slaking quicklime and digesting the slaked lime with water. One hundred c.c. of water at 15° C. dissolves 0.1368 grams of the hydrate (CaH_{2}O_{2}), and hot water dissolves still less. "Milk of lime" is slaked lime suspended in water.
~Cobalt Nitrate~ (Co(NO_{3}){2}.6H{2}O) is used in a 10 per cent. solution for the detection of oxides of zinc, aluminium, &c.; on ignition with which it forms characteristically coloured compounds.
~Copper~, Cu.--Pure copper, as obtained by electrolysis, can be purchased. This only should be used.
~Copper Oxide~, CuO.--It occurs as a black, heavy, and gritty power, and is used for the oxidation of carbon and hydrogen in organic substances. It should be ignited and cooled out of contact with air just before using, since it is hygroscopic. Oxide of copper which has been used may be again utilised after calcination.
~Copper Sulphate~ (CuSO_{4}.5H_{2}O) contains 25.4 per cent. of copper. It is used in the outer cell of a Daniell-battery. The commercial salt is used for this purpose. The re-crystallised and pure salt is used for preparing the anhydrous sulphate, which is used for detecting moisture in gases. For this purpose it is dried at 200° C. till no trace of green or blue colour remains. It must be prepared when wanted. It may be conveniently used in the form of pumice-stone, saturated with a solution of the salt and dried. Traces of moisture develop a green colour.
~Ferric Chloride~, Fe_{2}Cl_{6}. (When crystallised, Fe_{2}Cl_{6}.6H_{2}O.)--The solution is prepared as described under iron. The commercial salt contains arsenic, and, since the chief use of ferric chloride is for the determination of this substance, it must be purified (see under ARSENIC).
~Ferric Sulphate~ (Fe_{2}(SO_{4}){3}) is a yellowish white deliquescent salt. It is used as an indicator in volumetric silver assaying, and for the separation of iodine from bromine. It may be purchased as iron alum, Am{2}Fe_{2}(SO_{4}){4}.24H{2}O. But it is best prepared by adding strong sulphuric acid to ferric hydrate in equivalent proportions. Use it as a solution containing 2 or 3 per cent. of iron.
~Ferrous Sulphate~, FeSO_{4}.7H_{2}O.--The granulated form is best, and can be purchased pure. It is used for standardising. It keeps better in crystals than in solution. It is readily soluble in water, but the solution is best made with the help of a little free acid. As a re-agent use a 10 per cent. solution. The crystals should be clear bluish-green; if their colour is dark green, brown, or blue, they should be rejected.
~Ferrous Sulphide~ (FeS) is used for the preparation of sulphuretted hydrogen. It may be purchased and broken in small lumps, nut-size, for use.
"~Fusion Mixture~" (K_{2}CO_{3}.Na_{2}CO_{3}) is a mixture of potassic and sodic carbonates in the proportions of 13 of the former to 10 of the latter, by weight. It is hygroscopic. A mixture of the bicarbonates is better, being purer and less apt to get damp.
~Gallic Acid~ (C_{7}H_{6}O_{5}.H_{2}O) is an organic acid, occurring as a pale fawn-coloured crystalline powder, soluble in 100 parts of cold water, or in 3 parts of boiling water. It is used for the determination of antimony. A 10 per cent. solution in warm water is made when required.
~Hydrogen~ (H) is a gas. It is obtained by acting on zinc with dilute hydrochloric or sulphuric acid. It is used as a reducing agent, and for providing an atmosphere free from oxygen. It reduces metallic oxides at a high temperature. It must be freed from water; and special precautions should be taken to prevent an admixture with air. It is generally required in a current which can be continued for an hour or more without interruption. The preparation can be conveniently carried out in the apparatus shown (fig. 33). A quart bottle is half filled with sheet zinc, and connected with bulbs filled with sulphuric acid, and with a calcium chloride tube. The last is connected with the apparatus through which the gas has to be passed. Dilute hydrochloric acid mixed with a few cubic centimetres (20 c.c. to 1 pint) of stannous chloride sol. to fix any dissolved oxygen, is placed in the funnel, and let into the bottle by opening the stopcock when required. Care must be taken to let the hydrogen escape for some time before starting the reduction.
~Gold~, Au.--Gold, obtained by cupelling and "parting," is for most purposes sufficiently pure. It is best kept in the shape of foil. When the purer metal is required, gold should be dissolved in aqua regia, the solution evaporated to a paste, diluted, allowed to stand, and filtered. The filtered solution is acidified with hydrochloric acid, warmed, and precipitated with sodium sulphite. The precipitate is collected, washed, and fused on charcoal.
~Iron~, Fe.--The soft wire (thin) is used for standardising. Rods are used in dry assays as a desulphurising agent. Steel must not be used, since it is not pure, and contains a variable amount of iron.
~Lead~, Pb.--Granulated lead or lead-foil is used in the dry assay for silver and gold, and in the preparation of lead salts. It can be obtained very pure, but always contains more or less silver, 1 or 2 milligrams in 100 grams. The amount of silver it contains must be determined and recorded.
~Lead Acetate~ (Pb[=A=c]{2}.3H{2}O, or Pb(C_{2}H_{3}O_{2}){2}.3H{2}O) is used as a test, specially for the detection and estimation of sulphuretted hydrogen. Prepare a 10 per cent. solution for use.
~Lead Nitrate~ (Pb(NO_{3})_{2}) can be purchased pure. It is used for standardising.
~Lead Dioxide~ (PbO_{2}) occurs as a dark-brown powder. It is used as an oxidizing agent and for absorbing sulphurous oxide. It can be prepared by digesting red lead with warm dilute nitric acid; washing and drying the residue.
"~Litharge~," PbO.--It can be purchased as a yellow heavy powder. It is used in dry assaying as a flux, as a desulphurising agent, and also as a source of lead. It always contains some silver, the amount of which must be determined.
~Litmus.~--This is an organic colouring matter which is turned red by acids and blue by alkalies. For ordinary purposes it is best used as litmus paper, which may be purchased in small books. A solution is prepared by digesting 15 or 20 grams of the commercial litmus in 100 c.c. of water on the water bath. After being allowed to settle, it is filtered and made just faintly red with acetic acid. Then there is added a drop or two of a solution of soda and 10 c.c. of alcohol. It should be kept in a loosely-covered bottle.
~Magnesia~, MgO.--It may be purchased as "calcined magnesia." It is used for making "magnesia mixture," and should be kept in a corked wide-mouthed bottle.
"~Magnesia Mixture.~"--Dissolve 22 grams of magnesia in about a quarter of a litre of dilute hydrochloric acid, avoiding excess. Add 5 grams of magnesia, boil, and filter. Add 300 grams of ammonic chloride, and 250 c.c. of strong ammonia; and dilute with water to 2 litres. It should be kept in a stoppered winchester.
~Magnesium Sulphate~, MgSO_{4}.7H_{2}O.--It can be purchased very pure, and is occasionally used as a standard salt.
~Manganese Dioxide~, MnO_{2}.--It is used in the preparation of chlorine. The commercial article is not pure, but is sufficiently so for this purpose.
~Marble~, CaCO_{3}.--Fragments of the white crystalline variety only should be used. It is used as a source of lime and of carbon dioxide.
~Mercury~, Hg.--This can be purchased pure. It should have a bright surface, flow without a tail, and leave no residue on ignition. It is used as a standard; for amalgamation; and as a confining liquid in gas analysis.
~Mercuric Chloride~ (HgCl_{2}) may be purchased pure. Make a 5 per cent. solution in water. It is used for destroying an excess of stannous chloride; for removing sulphuretted hydrogen from solution; and as a test for stannous salts.
~Microcosmic Salt~, HAmNaPO_{4}.8H_{2}O.--When fused NaPO_{3} is formed. It is used in testing for metallic oxides and silica before the blowpipe. The crystals are sometimes used as a standard for phosphoric acid.
"~Nessler's Solution.~"--Mode of preparation: Dissolve 35 grams of potassium iodide in 100 c.c. of water; dissolve 17 grams of mercuric chloride in 300 c.c. of water, and pour this solution into that of the iodide till a permanent precipitate is produced; make up to 1 litre with a 20 per cent. solution of potash; add mercuric chloride till a precipitate is again formed; allow to settle and decant. It is used for detecting ammonia.
~Nitre.~--This is potassium nitrate.
~Platinum Chloride~, 2HCl.PtCl_{4}. (In the crystallised form it has 6H_{2}O).--It may be made as follows:--Take 5 grams of clean platinum scrap and dissolve in a flask at a gentle heat in 50 c.c. of hydrochloric acid with the occasional addition of some nitric acid; evaporate to a paste; and then dissolve in 100 c.c. of water. It is used for separating and determining potassium.
~Phenolphthalein~ is an organic compound used as an indicator; more especially in determining the weaker acids, it cannot be used in the presence of ammonia. Dissolve half a gram in 100 c.c. of dilute alcohol.
~Potassium Bicarbonate~, KHCO_{3}.--It may be purchased pure; on ignition it leaves the carbonate, K_{2}CO_{3}, which may be used as a standard.
~Potassium Cyanide~, KCN.--It is used in the dry assay as a reducing agent. The commercial salt is very impure. Purchase that sold as potassic cyanide (gold) which contains about 95 per cent. of KCN. It is used for copper assaying and occasionally in separation. Make a 10 per cent. solution when wanted.
~Potassium Bichromate~, K_{2}Cr_{2}O_{7}. It may be purchased nearly pure. It is used as an oxidising agent, for determining iron; and as a test solution. For this last purpose a 10 per cent. solution is prepared.
~Potassium Chlorate~ (KClO_{3}) can be purchased pure. It is used with hydrochloric acid as a substitute for aqua regia.
~Potassium Ferrocyanide~ (K_{4}Fe(CN){6}.3H{2}O), or "yellow prussiate of potash," is used as a test; as an indicator; and for the determination of zinc. Make a 5 per cent. solution.
~Potassium Ferricyanide~ (K_{6}Fe_{2}(CN)_{12}), or "red prussiate of potash," is used for testing; and as an indicator. Make a 5 per cent. solution when wanted, as it decomposes on keeping.
~Potassium Hydrate~, KHO. Purchase that purified with alcohol. It is an alkali, and is used for absorbing carbonic acid, &c.
~Potassium Iodide~, KI. It may be purchased nearly pure. It is used as a test and for dissolving iodine. It should be used in a 10 per cent. solution freshly made. The solution decomposes on exposure to light, with separation of iodine.
~Potassium Nitrate~ (KNO_{3}) can be purchased pure. It is used in the dry way as an oxidizing agent. It is very fusible. It decomposes at a low temperature into potassium nitrite (KNO_{2}) and free oxygen; and at a higher temperature leaves potash (K_{2}O). It oxidizes sulphur and carbon with explosive violence. This action may be moderated by mixing the nitre with carbonate of soda, common salt, or some other inert body.
~Potassium Nitrite~, KNO_{2}.--The commercial article is not pure, but is sufficiently so for the purpose required. A saturated solution is used in the separation of cobalt; the solution is made when wanted.
~Potassium Permanganate~, KMnO_{4}.--This salt can be purchased sufficiently pure. It is much used as an oxidizing agent.
~Potassium Bisulphate~ (KHSO_{4}) is used as a dry reagent for opening up minerals. It fuses; and at a much higher temperature is converted into potassium sulphate with loss of sulphuric acid.
~Potassium Sulphocyanate~ (KCNS) is used for the detection and determination of traces of ferric iron; as also in the separation of silver and copper from some of the other metals. Make a 10 per cent. solution. It should show no colour on the addition of hydrochloric acid.
"~Red Lead~" (Pb_{3}O_{4}) is used in the dry assay as a flux instead of litharge, from which it differs in containing a little more oxygen. When acted on by nitric acid a brown residue of lead dioxide is left, nitrate of lead going into solution. Like litharge it always carries silver; about 2 milligrams in 100 grams.
~Silver~, Ag.--Pure silver in foil is required as a standard. It may be prepared as follows:--Dissolve scrap silver in dilute nitric acid and decant off from any residue; dilute the solution with hot water and add hydrochloric acid until there is no further precipitate, stir; allow the precipitate to settle; decant and wash; dry the precipitate, mix it with twice its bulk of carbonate of soda and fuse the mixture in a crucible until tranquil; clean the button and roll or hammer it into foil.
~Sodium Acetate~, NaC_{2}H_{3}O_{2}.3H_{2}O.--The crystals may be purchased sufficiently pure. Make a 20 per cent. solution in water. It is used for replacing mineral acids by acetic acid.[7]
~Sodium Acetate and Acetic Acid.~--A solution is used in the determination of phosphates and arsenates; 100 grams of the salt is dissolved in 500 c.c. of acetic acid, and diluted with water to one litre.
~Sodium Bicarbonate~ (NaHCO_{3})is used as a flux in dry methods. On ignition it leaves the carbonate (Na_{2}CO_{3}), which is used as a standard reagent. Make a 20 per cent. solution of the carbonate for use. It should be free from chlorides or sulphates, or if impure the amount of impurities must be determined.
~Sodium Hydrate~, NaHO. It may be purchased in sticks, which should be kept in a well-corked bottle. It is sometimes called "caustic soda." It is a strong alkali. It is used for neutralizing acid solutions and for separations where ammonia is unsuitable. Make a 5 per cent. solution for use.
~Sodium Hyposulphite~, Na_{2}S_{2}O_{8}.5H_{2}O.--It may be purchased pure. It is generally known as "hypo." It is used as a standard.
~Sodium Sulphite~ (Na_{2}SO_{3}.7H_{2}O) is used as a reducing agent.
~Sodium Phosphate~, Na_{2}HPO_{4}.12H_{2}O. The crystals may be purchased pure, but they effloresce in dry air with loss of water. It is used as a standard and for precipitating magnesia, &c. Make a 10 per cent. solution.
~Stannous Chloride~, SnCl_{2}.2H_{2}O.--The crystals are best purchased. If kept dry and free from air they are fairly permanent. A solution is made by dissolving 20 grams in 10 c.c. of hydrochloric acid and diluting to 1 litre. The solution is not permanent. It is a strong reducing agent, and is chiefly used in solution for this purpose.
~Tin~, Sn.--Grain tin should be purchased. It is not pure, but contains 99.5 per cent. of the metal. The chief impurity is copper. It can be used as a standard. When acted on with hot hydrochloric acid it slowly dissolves (more rapidly in contact with platinum) and forms stannous chloride.
~Uranium Acetate~, UO_{2}(C_{2}H_{3}O_{2}){2}.H{2}O.--It is best purchased in crystals. The solution is used for the determination of phosphates and arsenates. A solution of 3 per cent. strength is occasionally used as an indicator.
~Uranium Nitrate~, UO_{2}(NO_{3}){2}.6H{2}O.--This salt is very soluble in water and is sometimes used instead of the acetate, which is somewhat difficult to dissolve.
"~Water~," H_{2}O.--Spring or well water is sufficiently pure for most purposes, 100 c.c. will leave a residue of from 10 to 30 milligrams, so that where a salt has to be dissolved out, evaporated, and weighed it should be replaced by distilled water. Rain water, melted snow, &c., always leave less residue than spring water; but in other respects they are often dirtier. Distilled water is best prepared in the office, a glass or tin condenser being used.
~Zinc~, Zn.--It is sold in a granulated form or in sticks. It generally contains over 1 per cent. of lead, with a little iron and arsenic. It is used for separating metals from their solutions, and generally as a reducing agent. For the preparation of hydrogen, and in most other cases, scrap sheet zinc may be used.
~Zinc Oxide~, ZnO.--The commercial oxide sometimes contains carbonate.
~Zinc Sulphate~, ZnSO_{4}.7H_{2}O.--It is occasionally used as a standard, and can be purchased nearly pure.
FOOTNOTES:
[6] 3HCl + HNO_{3} = Cl_{2} + NOCl + 2H_{2}O.
[7] NaC_{2}H_{3}O_{2} + HCl = H_{4}C_{2}O_{2} + NaCl.
VII. FORMULÆ, EQUATIONS, ETC
Formulæ and equations are a kind of short hand for expressing briefly and in the language of the atomic theory the facts of chemical composition and reaction. The convenience of this method of expressing the facts justifies a short description of it here.
On comparing the percentage composition of a series of compounds the proportions in which the elements combine appears to be regulated by no simple law. For example:
Realgar. Orpiment. Mispickel. Pyrites. Arsenic 71.4 60.9 46.0 -- Sulphur 28.6 39.1 19.6 53.3 Iron -- -- 34.4 46.7 ------ ------ ------ ------ 100.0 100.0 100.0 100.0
But if in these examples the composition is calculated, not on 100 parts, but on 107, 246, 163, and 120 parts respectively, evidence of a simple law becomes apparent.
Realgar. Orpiment. Mispickel. Pyrites. Arsenic 75.0 150.0 75.0 -- Sulphur 32.0 96.0 32.0 64.0 Iron -- -- 56.0 56.0 ------ ------ ------ ------ 107.0 246.0 163.0 120.0
It will be seen that the proportion of arsenic is 75 or twice 75, that of iron is 56, and that of sulphur 32 or some simple multiple of 32. The series of examples might be extended indefinitely, and it would still be found that the "combining proportions" held good. The number 75 is spoken of as the "combining weight," or, more frequently, as the "atomic weight" of arsenic. Similarly 56 is the atomic weight of iron, and 32 the atomic weight of sulphur. The importance of this law of chemical combination is altogether independent of the atomic theory; but this theory furnishes the simplest explanation of the facts. According to it a chemical compound is made up of exactly similar groups of particles. The particles of each elementary substance are all alike, but differ from those of other elements in weight. Ultimate particles are called atoms, and the groups of atoms are called molecules. The atomic weight of any particular element is the weight of its atom compared with the weight of an atom of hydrogen. The atom of sulphur, for instance, is 32 times as heavy as the atom of hydrogen, and the atomic weight of sulphur is 32. The molecular weight is the sum of the atomic weights of the group. The molecule of pyrites contains two atoms of sulphur and one of iron: on referring to the table of atomic weights it will be seen that the atomic weights are--sulphur 32, and iron 56. The molecular weight, therefore, is 32+32+56--that is, 120. The meaning of this is, 120 parts by weight of iron pyrites contain 64 parts of sulphur and 56 parts of iron; and this is true whether the "parts by weight" be grains or tons.
The symbol or formula of an atom is generally the initial letter or letters of the Latin or English name of the substance. The atom of hydrogen is written H, that of oxygen O, of sulphur S, of iron (ferrum) Fe, and so on. A list of these symbols is given in the table of atomic weights.
The formula of a molecule is obtained by placing together the symbols of the contained atoms. Thus, Fe represents an atom of iron, S an atom of sulphur, while FeS represents the molecule of sulphide of iron as containing one atom of each element.
When more than one atom of an element is present this is shown by writing a figure under and after the symbol; thus, FeS_{2} represents a molecule with one atom of iron and two atoms of sulphur, Fe_{2}S_{3} similarly shows one with two atoms of iron and three of sulphur. When a group of atoms is enclosed in brackets, a figure after and under the bracket multiplies all within it; for example, Pb(NO_{3}){2} is another way of writing PbN{2}O_{6}. Sometimes it is convenient to represent the atoms of a molecule as divided into two or more groups; this may be done by writing the formulæ of the groups, and separating each simple formula by a full stop. Slaked lime, for instance, has the formula CaH_{2}O_{2}; or, as already explained, we may write it Ca(HO){2}; or, if for purposes of explanation we wished to look on it as lime (CaO) and water (H{2}O), we could write it CaO.H_{2}O. A plus sign (+) has a different meaning; CaO + H_{2}O indicates quantities of two substances, water and lime, which are separate from each other. The sign of equality (=) is generally used to separate a statement of the reagents used from another statement of the products of the reaction; it may be translated into the word "yields" or "becomes." The two statements form an equation.
Ignoring the quantitative relation, the meaning of the equation CaO + H_{2}O = CaO.H_{2}O is: "lime and water yield slaked lime." By referring to a table of atomic weights we can elicit the quantitative relations thus:--
CaO + H_{2}O = CaH_{2}O_{2} | | | V V V Ca = 40 H_{2} = 2 = 1×2 Ca = 40 O = 16 O = 16 H_{2} = 2 = 1×2 -- -- O_{2} = 32 = 16×2 56 18 -- 74
Or, putting it in words, 56 parts of lime combine with 18 parts of water to form 74 parts of slaked lime. This equation enables one to answer such a question as this:--How much lime must be used to produce 1 cwt. of slaked lime? for, if 74 lbs. of slaked lime require 56 lbs. of lime, 112 lbs. will require (56×112)/74, or about 84-3/4 lbs.
As another example having a closer bearing on assaying take the following question:--"In order to assay 5 grams of 'black tin' (SnO_{2}) by the cyanide process, how much potassic cyanide (KCN) will be required?" The reaction is
SnO_{2} + 2KCN = Sn + 2KCNO | | V V Sn = 118 K = 39 O_{2} = 32 C = 12 --- N = 14 150 -- 65×2 = 130
What is sought for here is the relation between the quantities of SnO_{2} and KCN. Note that a figure before a formula multiplies all that follows up to the next stop or plus or equality sign. The question is now resolved to this: if 150 grams of oxide of tin require 130 grams of cyanide, how much will 5 grams require?
150 : 130 :: 5 : x x = 4.33 grams.
A problem of frequent occurrence is to find the percentage composition of a substance when its formula has been given. For example: "What percentage of iron is contained in a mineral having the formula 2Fe_{2}O_{3}.3H_{2}O?" Bringing this formula together we have Fe_{4}H_{6}O_{9}. Find the molecular weight.
Fe_{4} = 224 = 56×4 H_{6} = 6 = 1×6 O_{9} = 144 = 16×9 --- 374
Then we get: 374 parts of the mineral contain 224 of iron. How much will 100 contain?
374 : 224 :: 100 : x x = 59.89.
And the answer to the question is 59.89 per cent.
Again, suppose the question is of this kind:--"How much crystallised copper sulphate (CuSO_{4}.5H_{2}O) will be required to make 2 litres of a solution, 1 c.c. of which shall contain 0.0010 gram of copper?"
A litre is 1000 c.c., so, therefore, 2 litres of the solution must contain 0.001 gram × 2000, or 2 grams. How much crystallised copper sulphate will contain this amount of metal?
Cu = 63.3 S = 32.0 O_{4} = 64.0 = 16×4 5H_{2}O = 90.0 = 18×5 ----- 249.3
If 63.3 grams of copper are contained in 249.3 grams of sulphate, in how much is 2 grams contained.
63.3 : 249.3 :: 2 grams : x x = 7.8769 grams.
The answer is, 7.8769 grams must be taken.
As a sample of another class of problem similar in nature to the last (but a little more complicated) take the following:--"What weight of permanganate of potash must be taken to make 2 litres of a solution, 100 c.c. of which shall be equivalent to 1 gram of iron?" In the first place the 2 litres must be equivalent to 20 grams of iron, for there are 20 × 100 c.c. in two litres. In the titration of iron by permanganate solution there are two reactions. First in dissolving the iron
Fe + H_{2}SO_{4} = FeSO_{4} + H_{2} | V 56
and second, in the actual titration,
10FeSO_{4} + 2KMnO_{4} + 9H_{2}SO_{4}= 2MnSO_{4} | + 5Fe_{2}(SO_{4}){3} + 2KHSO{4} + 8H_{2}O V K = 39 Mn = 55 O_{4}= 64 --- 158 × 2 = 316
As before, attention is confined to the two substances under consideration--viz., Fe and KMnO_{4}. In the second equation, we find 316 parts of the permanganate are required for 10 molecules of FeSO_{4}; and in the first equation 56 parts of iron are equivalent to one molecule of FeSO_{4}, therefore 560 of iron are equivalent to 316 of permanganate; and the question is, How much of the permanganate will be equivalent to 20 grams of iron?
560 : 316 :: 20 grams : x. x= 11.286 grams.
The answer is 11.286 grams.
Very similar to this last problem is the question suggested under the head "Indirect Titration" (p. 43). "If 100 c.c. of the standard permanganate solution are equivalent to 1 gram of iron, how much peroxide of manganese will they be equivalent to?" The equation for dissolving the iron is already given; the second equation is
2FeSO_{4} + MnO_{2} + 2H_{2}SO_{4} | = Fe_{2}(SO_{4}){2} + MnSO{4} + 2H_{2}O | V Mn = 55 O_{2} = 32 -- 87
It will be seen that 87 grams of peroxide of manganese are equivalent to 112 grams of iron. How much then is equivalent to 1 gram of iron?
112 : 87 :: 1 gram : x x = 0.7767 gram.
It is sometimes convenient to calculate the formula of a substance from its analysis. The method of calculating is shown by the following example. Required the formula of a mineral which gave the following figures on analysis:--
Cupric oxide (CuO) 10.58 Ferrous oxide (FeO) 15.69 Zinc oxide (ZnO) 0.35 Sulphuric oxide (SO_{2}) 28.82 Water (H_{2}O) 44.71 ------ 100.15
First find the molecular weights of CuO, FeO, &c., and divide the corresponding percentages by these figures. Thus, CuO = 63.3+16 = 79.3 and 10.58 divided by 79.3 gives 0.1334. Similarly FeO = 56+16 = 72 and 15.69 divided by 72 gives 0.2179. Treated in the same way the oxide of zinc, sulphuric oxide and water give as results 0.0043, 0.3602 and 2.484.
Classify the results as follows:--
Bases. Acids. Water.
CuO 0.1334 SO_{3} 0.3602 H_{2}O 2.484 FeO 0.2179 ZnO 0.0043 ---------- ------------- ------------ RO 0.3556 RO_{3} 0.3602 R_{2}O 2.484
The figures 0.3556, 0.3602 and 2.484 should be then divided by the lowest of them--i.e., 0.3556; or where, as in this case, two of the figures are very near each other the mean of these may be taken--i.e., 0.3579. Whichever is taken the figures got will be approximately 1, 1 and 7. The formula is then RO.SO_{3}.7H_{2}O in which R is nearly 2/5ths copper, 3/5ths iron and a little zinc.
This formula requires the following percentage composition, which for the sake of comparison is placed side by side with the actual results.
Calculated. Found. Cupric oxide 11.29 10.58 Ferrous oxide 15.37 15.69 Zinc oxide nil 0.35 Sulphuric oxide 28.47 28.82 Water 44.84 44.71 ----- ------ 99.97 100.15
Trimming the results of an analysis to make them fit in more closely with the calculations from the formula would be foolish as well as dishonest. There can be no doubt that the actual analytical results represent the composition of the specimen much more closely than the formula does; although perhaps other specimens of the same mineral would yield results which would group themselves better around the calculated results than around those of the first specimen analysed. It must be remembered that substances are rarely found pure either in nature or in the arts; so that in most cases the formula only gives an approximation to the truth. In the case of hydrated salts there is generally a difficulty in getting the salt with exactly the right proportion of water.
PRACTICAL EXERCISES.
The following calculations may be made:--
1. Calculate standards in the following cases-- (a) Silver taken, 1.003 gram. Standard salt used, 100.15 c.c. (b) Iron taken, 0.7 gram. Bichromate used, 69.6 c.c.
2. Calculate percentages:-- (a) Ore taken, 1 gram. Solution used, 65.2 c.c. Standard, 0.987 gram.
(b) Ore taken, 1 gram. Barium sulphate got, 1.432 gram. Barium sulphate contains 13.73 per cent. of sulphur, and the percentage of sulphur in the ore is wanted.
(c) Barium sulphate is BaSO_{4}. Calculate the percentage of sulphur it contains, for use in the preceding question.
3. A method of estimating the quantity of peroxide in a manganese ore is based on the following reactions:--
(1) MnO_{2} + 4HCl = MnCl_{2} + Cl_{2} + 2H_{2}O.
(2) Cl + KI = KCl + I.
To how much MnO_{2} is 1 gram of Iodine (I) equivalent?
4. A mineral has the following composition:--
Carbonic acid (CO_{2}) 19.09 Copper oxide (CuO) 71.46 Water (H_{2}O) 9.02
What is its formula?
5. How much copper is contained in 1.5 gram of crystallized copper sulphate (CuSO_{4}.5H_{2}O)? How much of these crystals must be taken to give 0.4 gram of copper?
6. How much ferrous sulphate crystals (FeSO_{4}.7H_{2}O) must be taken to yield 2 litres of a solution, 100 c.c. of which shall contain 0.56 gram of iron?
7. Galena is PbS, and hæmatite Fe_{2}O_{3}. What percentages of metal do these minerals contain?
VIII. SPECIFIC GRAVITY
The relation of the weight of a substance to its volume should be kept in mind in all cases where both weight and volume are dealt with. Students are apt to imagine that on mixing equal volumes of, say, sulphuric acid and water, an acid of half the strength must be obtained. If the statement of strength is in parts by weight this will lead to considerable error. For example, 100 c.c. of sulphuric acid containing 98 per cent. by weight of real acid, will, if diluted with 100 c.c. of water, yield a solution containing not 49 per cent. by weight, but about 63.5 per cent. of the acid. The reason is this: the 100 c.c. of sulphuric acid weighs 184 grams, and contains 180.32 grams of real acid, while the 100 c.c. of water weighs only 100 grams; the mixed water and acid weighs 284 grams, and contains 180.32 of real acid, which is equivalent to nearly 63.5 per cent. by weight. If, however, the method of statement be volumetric, it would be correct to say that doubling the volume halves the strength: if 100 c.c. of brine contains 10 grams of salt, and is diluted with water to 200 c.c., it would be of one-half the former strength, that is, 100 c.c. of the solution would contain 5 grams of salt.
This confusion is avoided by always stating the strengths as so many grams or "c.c." in 100 c.c. of the liquid. But obviously it would be advantageous to be able to determine quickly the weight of any particular substance corresponding to 1 c.c. or some other given volume. Moreover, in descriptions of processes the strengths of acids and solutions are frequently defined neither by their gravimetric nor volumetric composition, but by a statement either of specific gravity or of the degrees registered by Twaddell's or Beaumé's hydrometer. Thus, in the description of the process of gold parting, one writer gives: "The acid should be of 1.2 specific gravity"; and another says: "The acid must not be stronger than 32° Beaumé."
These considerations justify an account of the subject in such a work as this. And on other grounds the determination of a specific gravity is one of the operations with which an assayer should be familiar.
The meaning of "specific gravity" is present in the mind of every one who uses the sentence "lead is heavier than water." This is meaningless except some such phrase as "bulk for bulk" be added. Make the sentence quantitative by saying: "bulk for bulk lead is 11.36 times heavier than water," and one has the exact meaning of: "the specific gravity of lead is 11.36." A table of the specific gravities of liquids and solids shows how many times heavier the substances are than water.
It is better, however, to look upon the specific gravity (written shortly, sp. g.) as the weight of a substance divided by its volume. In the metric system, 1 c.c. of water at 4° C. weighs with sufficient exactness 1 gram; consequently, the sp. g., which states how many times heavier than water the substance is, also expresses the weight in grams of one c.c. of it. So that if a 100 c.c. flask of nitric acid weighs, after the weight of the flask has been deducted, 120 grams, 1 c.c. of the acid weighs 1.2 gram, and the sp. g. is 1.2. The specific gravity, then, may be determined by dividing the weight of a substance in grams by its volume in c.c.; but it is more convenient in practice to determine it by dividing the weight of the substance by the weight of an equal volume of water. And since the volumes of all substances, water included, vary with the temperature, the temperature at which the sp. g. is determined should be recorded. Even then there is room for ambiguity to the extent that such a statement as the following, "the specific gravity of the substance at 50° C. is 0.9010," may mean when compared with water at 50° C. or 4° C., or even 15.5° C. For practical purposes it should mean the first of these, for in the actual experiments the water and the substance are compared at the same temperature, and it is well to give the statement of results without any superfluous calculation. In the metric system the standard temperature is 4° C., for it is at this point that 1 c.c. of water weighs exactly 1 gram. In England, the standard temperature is 60° F. (15.5° C.), which is supposed to be an average temperature of the balance-room. The convenience of the English standard, however, is merely apparent; it demands warming sometimes and sometimes cooling. For most purposes it is more convenient to select a temperature sufficiently high to avoid the necessity of cooling at any time. Warming to the required temperature gives very little trouble.
~Determination of Specific Gravity.~--There is a quick and easy method of determining the density or sp. g. of a liquid, based upon the fact that a floating body is buoyed up more by a heavy liquid than by a light one. The method is more remarkable for speed than accuracy, but still is sufficiently exact. The piece of apparatus used for the purpose is endowed with a variety of names--sp. g. spindle, hydrometer, areometer, salimeter, alcoholimeter, lactometer, and so on, according to the special liquid upon which it is intended to be used. It consists of a float with a sinker at one end and a graduated tube or rod at the other. It is made of metal or glass. Generally two are required, one for liquids ranging in sp. g. from 1.000 to 2.000, and another, which will indicate a sp. g. between 0.700 and 1.000. The range depends on the size of the instrument. For special work, in which variations within narrow limits are to be determined, more delicate instruments with a narrower range are made.
In using a hydrometer, the liquid to be tested is placed in a cylinder (fig. 34) tall enough to allow the instrument to float, and not too narrow. The temperature is taken, and the hydrometer is immersed in the fluid. The mark on the hydrometer stem, level with the surface of the liquid, is read off. With transparent liquids it is best to read the mark under and over the water surface and take the mean.
The graduation of hydrometers is not made to any uniform system. Those marked in degrees Baumé or Twaddell, or according to specific gravity, are most commonly used. The degrees on Baumé's hydrometer agree among themselves in being at equal distances along the stem; but they are proportional neither to the specific gravity, nor to the percentage of salt in the solution. They may be converted into an ordinary statement of specific gravity by the following formulæ:--
Sp. g. = 144.3/(144.3-degrees Baumé.)
or putting the rule in words, subtract the degrees Baumé from 144.3, and divide 144.3 with the number thus obtained. For example: 32° Baumé equals a sp. g. of 1.285.
144.3/(144.3-32) = 144.3/(112.3) = 1.285
This rule is for liquids heavier than water; for the lighter liquids the rule is as follows:--
Sp. g. = 146/(136 + degrees Baumé.)
or in words divide 146 by the number of degrees Baumé added to 136. For example: ammonia of 30° Beaumé has a sp. g. of 0.880 (nearly).
146/(136+30) = 146/166 = 0.8795
A simple series of calculations enables one to convert a Beaumé hydrometer into one showing the actual sp. g. Graduation, according to sp. g. is the most convenient for general purposes. In these instruments the distances between the divisions become less as the densities increase.
Twaddell's hydrometer is graduated in this way: Each degree Twaddell is 0.005 in excess of unity. To convert into sp. g. multiply the degrees Twaddell by 0.005, and add 1. For example: 25° Twaddell equals a sp. g. of 1.125.
25×.005 = 0.125; + 1.000 = 1.125.
There is a practice which ignores the decimal point and speaks of a sp. g. of 1125 instead of 1.125. In some cases it is convenient, and inasmuch as no substance has a real sp. g. of much over 20, it can lead to no confusion. The figures expressed in this way represent the weight of a litre in grams.
Some hydrometers are graduated so as to show at a glance the percentage composition of the liquid they are intended to be used with. Gay-Lussac designed one to show the alcoholic strength of mixtures of alcohol and water; the construction of others upon the same principle is easy and perhaps useful. But when the principle is applied to complex liquids and mixed solutions, it is misleading.
The various methods of graduation ought all to give place to one showing a simple statement of the sp. g.
The method of determining sp. g. with the hydrometer is obviously inapplicable to the case of solids, and in the case of liquids it should not be used where exact figures are required. There are several other methods which may be used, but on the whole those with the specific gravity bottle are most convenient.
~The specific gravity bottle~ (fig. 35) is a light flask of about 25 c.c. capacity, provided with a well-fitting perforated stopper. It is essentially a graduated flask, which measures a constant volume, but it does not much matter what the volume is.
In taking the sp. g. of a liquid (or, what is the same thing, a fused solid) there is wanted the weights (1) of the flaskful of water and (2) of the flaskful of the liquid. Dividing the second by the first gives the required sp. g. The actual weighings required are--
(1) of the dry and empty flask,
(2) of the flask filled with water, and
(3) of the flask filled with the liquid.
The weighing of the flask once made need not be often repeated. It is well to do so now and then for safety's sake; but one weighing will serve for a large number of determinations. The same remarks apply to the weighing of the bottle filled with water. The bottle is dried by rinsing out first with alcohol and afterwards with ether; ether is very volatile, and a short exposure in a warm place will soon drive off the little remaining about the sides. The ether vapour should be sucked out through a glass tube. See that the bore of the stopper is dry as well as the bottle. Let the dry bottle stand in the box of the balance for a minute or two before weighing. The weight is, strictly speaking, not that of the empty bottle, but of the bottle filled with air. The empty bottle would weigh from 20 to 30 milligrams less. Correcting for this would, in most cases, only make a difference in the fourth place of decimals,[8] so that it is better to ignore the error.
The weight of the flask filled with water is got by filling it with distilled water, and inserting the stopper. The excess of water will overflow at the margin and through the bore. The bottle is wiped with a soft, dry cloth, taking care not to squeeze or warm the bottle. The bottle will remain filled to the top of the stopper. It is allowed to stand in the balance box for a minute or two, and then weighed.
Distilled water, as stated, should be used; the use of ordinary water may increase the weight by 5 or 6 milligrams. Many waters, if they have not previously been boiled, give off bubbles of air which render the weighing worthless.
The temperature of the water is of greater importance; lowering the temperature 2° will increase the weight by 10 or 12 milligrams. A beaker of water may be warmed or cooled to the required temperature; then the bottle is filled from it, and quickly weighed. If the balance-room is cooler than the water, the latter will draw back into the bottle, and a few small bubbles of air will enter; but even in extreme cases this will only increase the weight by a very small fraction of a milligram. There is more trouble caused when the room is warmer, for the liquid then expands and protrudes as a drop resting on the top of the stopper. There will in this case be loss by evaporation, which in the case of the more volatile liquids, such as alcohol, is serious. To prevent this loss, as well as any that may arise by overflow, the stopper should be dilated above into a small cup, A (fig. 36), which may itself be stoppered. In a bottle of this kind the neck of the stopper is graduated, and the bottle is considered full when the liquid stands at the level of the mark in the neck. On inserting the stopper, the liquid rises into the cup, and is reduced to the level of the mark by absorption with pieces of filter-paper.
For most purposes, however, there is no need for cooling and allowing room for subsequent expansion. The assayer, as a rule, can select his own standard temperature, and may choose one which will always necessitate warming. It will be handier in this case to have a bottle with a thermometer stopper. Of the two types shown in fig. 37, that with the external thermometer tube (A) is more generally useful.
The bottle is filled at a lower temperature, and is then gently warmed so as to slowly raise the temperature to the required degree. The superfluous liquid is then at once wiped off, and the bottle cooled and weighed.
The weight of the flask filled with the liquid whose sp. g. has to be determined is ascertained in a similar way. Of course the temperature must be the same. If the liquid does not mix with water, the bottle should be dried before filling, but otherwise the flask need only be rinsed out two or three times with the liquid.
Having obtained the three weighings, deduct the weight of the bottle from each of the others to get the weights of the water and liquid respectively. Divide the latter by the former, the result shows the sp. g. As an example, take the following, in which a rather large sp. g. bottle was used:--
1. Weight of bottle 39.299 gram
2. Weight of bottle and water 81.884 "
3. Weight of bottle and paraffin 73.146 "
By subtracting 1 from 2 and 3 the result is as follows:--
81.884 grams 73.146 grams 39.299 " 39.299 " ------ ------ 42.585 of water. 33.847 of paraffin.
Divide the weight of the paraffin by that of the water--
42.585)33.8470(0.7948 29.8095 ------- .......
The sp. g. of the paraffin is 0.7948.
The sp. g. of a fusible solid may be obtained in the same way at a temperature some degrees above its fusing point.
The sp. g. of a solid in powder or gravel sufficiently fine to pass through the neck of the bottle is easily determined. If the bottle filled with water weighs 50 grams, and there is placed on the pan alongside of it 20 grams of a sand, the weight of the two together will of course be 70 grams. But if the sand is put in the bottle, it evidently displaces its own bulk of water; and if, on again weighing, the weight is found to be 62 instead of 70 grams, it is because the 20 grams of sand has displaced 8 grams of water. Bulk for bulk, the sand is 2-1/2 times as heavy.
In practice, the weight of the bottle filled with water will probably be already known; if not, it must be determined. A certain quantity, say 20 grams, of the powdered substance is then transferred carefully to the bottle. The bottle need not be dry inside, but its neck and outside must be. In making this transference a careful worker will make no loss, and the mode of working saves a little time. But it is better to weigh the dry flask; put into it 10 to 20 grams of the powder, and weigh again. The increase in weight gives accurately the weight of powder in the bottle. About two-thirds fill the bottle with distilled water, and mix with the powder by gentle shaking. Air bubbles will disentangle themselves, and rise to the surface of the water. Wash back anything adhering to the stopper with a jet of water, and fill the bottle almost to overflowing. Allow it to stand for a minute or so; replace the stopper; warm to the required temperature; take off the superfluous moisture; wipe and weigh. As an example, take the following:--
1. Weight of bottle 12.681 grams 2. " " bottle filled with water 37.708 " 3. " " bottle with wolfram 40.821 " 4. " " bottle with wolfram and water 61.199 "
Subtract (1) from (3) to get the weight of wolfram taken:
40.821 grams 12.681 " ------ 28.140 "
add the weight of the wolfram to the weight of the bottle filled with water:
28.140 grams 37.708 " ------ 65.848 "
subtract (4) from this to get the weight of water displaced:
65.848 grams 61.199 " ------ 4.649 "
Divide the weight of the wolfram by the weight of the water displaced to get sp. g.:
4.649)28.140(6.053 27.894 ------ ......
If the solid is soluble in water, or has a tendency to float, some liquid other than water is used. Paraffin oil or oil of turpentine will do. The process is as follows:--The weight of the dry and empty bottle having been determined, add a sufficiency of the substance and weigh again to find how much has been added. Fill up with paraffin oil and weigh again. Clean out the substance by rinsing with paraffin; fill up and weigh. Calculate the sp. g. as if water had been used, and multiply by the sp. g. of the paraffin.
For example:
1. Weight of bottle 39.299 grams 2. " " bottle and nitre 57.830 " 3. " " bottle and paraffin 73.146 " 4. " " bottle and paraffin and nitre 84.665 " 5. " " bottle and water 81.884 "
First from (1),(3), and (5), calculate the sp. g. of the paraffin as already shown. It will be 0.7948. Deduct (1) from (2) to get the weight of the nitre:
57.830 grams 39.299 " ------ 18.531 "
add this to (3):
18.531 grams 73.146 " ------ 91.677 "
and deduct (4) to find the weight of the equal bulk of paraffin.
91.677 grams 84.665 " ------ 7.012 "
divide the weight of the nitre by the weight of the paraffin:
7.012)18.531(2.6427 ------ ......
The sp. g., taking paraffin as the standard instead of water, is 2.6427. Multiply this by the sp. g. of paraffin, 0.7948, and the result is 2.1004 as the sp. g. of nitre compared with water.
Similarly, a sp. g. compared with water at say 50° C. can be converted into one compared with water at standard temperature, by multiplying by the sp. g. of water at 50° C. The following table gives the sp. g. of water at various temperatures:--
-----------+------++-----------+------++-----------+------- Degrees | || Degrees | || Degrees | Centigrade.|Sp. G.||Centigrade.|Sp. G.||Centigrade.|Sp. G. -----------+------++-----------+------++-----------+------- 4° |1.0000|| 20° |0.9982|| 40° |0.9923 10° |0.9997|| 25° |0.9971|| 50° |0.9881 15° |0.9991|| 30° |0.9957|| 100° |0.9586 -----------+------++-----------+------++-----------+-------
If, for example, a substance at 50° C. has a sp. g. of 0.9010 as compared with water at 50° C., it will have (compared with water at 4° C.) a sp. g. of 0.9010×0.9881; or 0.8903. The figures 0.8903 represent the sp. g. of the substance at 50° C. compared with water at 4° C. Except in comparing the sp. gravities of the same substance at different temperatures, a calculation of this kind serves no useful purpose.
In taking the specific gravity of a solid not in powder, a lump of it is freed from loose particles and its exact weight determined. By means of a horse hair with a slip knot it is suspended to the balance, and beneath it is placed, out of contact with the balance pan, a beaker of distilled water. The horse hair must be long enough to keep the mineral well beneath the surface of the water so as to allow the balance to vibrate. Air bubbles are removed by touching with a camel-hair pencil. Whilst the mineral is suspended in water the weight is again taken. It will weigh less than before, and the difference between the two weighings gives the weight of water (and consequently the volume) displaced by the mineral. The weight in air divided by the difference is the specific gravity. Thus
Weight in air 3.2170 grams Weight in water 2.7050 " ------ Difference 0.5120 gram
3.2170/0.5120 equals 6.28, the sp. g.
The sp. g. of a substance depends mainly on its composition, but is affected by certain conditions. The effect of temperature has been already considered. Air holes and empty spaces lessen the specific gravity of otherwise solid bodies; and metals, which after fusion become imperfect solids, have their density increased by hammering or rolling. But metals when free from pores have their density diminished when rolled, without annealing. The effects of these conditions are slight when compared with those due to the presence of impurities.
For simple substances, or mixtures of only two substances, a determination of sp. g. is a sufficient check on the composition for many practical purposes; and with more complex mixtures, such as slags and some of the products of dressing operations in which the material does not differ much in its nature from time to time, such a determination will yield information of considerable value, and afford a check upon the proper working of a process.
When the mixing of two substances is accompanied by a change in volume, the sp. g. of the mixture can only be learnt by experiment. But when the substances have no such action on each other the resulting sp. g. can be calculated. Some of these calculations have a practical interest as well as an educational value. Students should practise them so as to become familiar with the relations between weight and volume.
When substances are mixed by volume, the sp. g. of the mixture is the mean of those of its constituents, and may be calculated in the usual way for obtaining averages. 1 c.c. of a substance having a sp. g. of 1.4 mixed with 1 c.c. of another having a sp. g. of 1.0 will yield 2 c.c. of a substance having a sp. g. of 1.2. If, however, we write gram instead of c.c. in the above statement, the resulting sp. g. will be 1.16. The simplest plan is to remember that the sp. g. is the weight divided by the volume (sp. g. = w/v) and the sp. g. of a mixture is the sum of the weights divided by the sum of the volumes (sp. g. = (w + w' + w", &c.)/(v + v' + v", &c.)). In the above example the sum of the volumes is 2 c.c.; the weights (got by multiplying each volume by its corresponding sp. g.) are 1.4 gram and 1 gram. The sum of the weights divided by the sum of the volumes is 2.4/2 or 1.2.
The sp. g. of a mixture of 10 c.c. of a substance having a sp. g. of 1.2, with 15 c.c. of another having a sp. g. of 1.5 may be thus found:--
sp. g. = (12+22.5)/(10+15) = 1.38
multiply each volume by its sp. g. to get its weight:
10×1.2 = 12 15×1.5 = 22.5
add these together (12+22.5 = 34.5) and divide by the sum of the volumes (10+15 = 25):
25)34.5(1.38 25 -- 95, &c.
The sp. g. will be 1.38, provided the mixture is not accompanied by any change of volume.
The same formula will serve when the proportion of the ingredients is given by weight. A mixture of 4 parts by weight of galena (sp. g. 7.5) with 5 parts of blende (sp. g. 4) will have a sp. g. of 5.06:
sp. g. = (4+5)/(0.53+1.25) = 9/1.78 = 5.06
It is necessary in this case to calculate the volumes of the galena and of the blende, which is done by dividing the weights by the sp. gravities: thus, 4 divided by 7.5 gives 0.53 and 5 divided by 4 gives 1.25.
The converse problem is a little more difficult. Given the sp. g. of a mixture and of each of the two ingredients, the percentage by weight of the heavier ingredient may be ascertained by the following rule, which is best expressed as a formula. There are three sp. gravities given; if the highest be written H, the lowest L and that of the mixture M, then:
Percentage of heavier mineral = (100×H×(M-L))/(M×(H-L))
Suppose a sample of tailings has a sp. g. of 3.0, and is made up of quartz (sp. g. 2.6) and pyrites (sp. g. 5.1): then the percentage of pyrites is 27:
(100×5.1×(3-2.6))/(3×(5.1-2.6)) = (510×0.4)/(3×2.5) = 204/7.5 = 27.2
The same problem could be solved with the help of a little algebra by the rule already given, as thus: the sp. g. of a mixture equals the sum of the weights of the constituents divided by the sum of the volumes. Then 100 grams of the tailings with x per cent. of pyrites contain 100-x per cent. of quartz. The sum of the weights is 100. The volume of the pyrites is x/5.1 and of the quartz (100-x)/2.6.
Then we have by the rule
3 = 100/((x/5.1)+(100-x)/2.6) 3 = 1326/(510-2.5_x_) 204 = 7.5_x_ and x = 27.2
If the percentage (P) and sp. g. (H) of one constituent and the sp. g. (M) of the mixture are known, the sp. g. of the other constituent may be calculated by the following formula, in which x is the required sp. g.:
x = ((100-P)×M×H)/((100×H)-(P×M))
For example, "tailings" (sp. g. 3.0) containing 27.2 per cent. of pyrites (sp. g. 5.1) will contain (100-27.2), 72.8 per cent. of earthy matter having a mean sp. g. of x:
x = ((100-27.2)×3×5.1)/((100×5.1)-(27.2×3)) = 1113.84/428.4 = 2.6
The differences in sp. g. corresponding to differences in strength have been carefully determined and tabulated in the case of the stronger acids and of many other liquids. Such tables are given at the end of this book.
To Calculate the Weight of a Measured Volume of Mineral or Rock.--Multiply the cubic feet by 62.4 and then multiply by the sp. g. of the stuff, the answer gives the weight in pounds. For example, 100 cubic feet of quartz weighs 100×62.4×2.6 = 16,224 lbs. The weight of any mass of mineral of known extent and sp. g. is ascertained in this way.
The following table gives the specific gravities of some of the commoner minerals.
Barytes 4.5 Blende 4.0 Calcite 2.6 Cassiterite 6.9 Chalybite 3.8 Copper pyrites 4.2 Fluor 3.1 Galena 7.5 Hæmatite 5.0 Mispickel 6.2 Pyrites 5.0 Quartz 2.6
FOOTNOTES:
[8] The difference of 20 or 30 milligrams is disregarded here because it detracts equally from the actual weight of the water and liquid to be determined. If the liquid is a heavy one the difference shows itself in the third or second place of decimals. The correction may be made by deducting from the weight of the flask 0.0012 grams for each gram of water it holds.