A Text-book of Assaying: For the Use of Those Connected with Mines Part 11

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

Tr.i.m.m.i.n.g the results of an a.n.a.lysis 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 a.n.a.lytical 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 a.n.a.lysed. 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. b.i.+.c.hromate 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 quant.i.ty 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 haemat.i.te Fe_{2}O_{3}. What percentages of metal do these minerals contain?

CHAPTER 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 Beaume'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 Beaume."

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 a.s.sayer 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 quant.i.tative 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 gla.s.s. 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.

[Ill.u.s.tration: FIG. 34.]

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 Baume or Twaddell, or according to specific gravity, are most commonly used. The degrees on Baume'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 formulae:--

Sp. g. = 144.3/(144.3-degrees Baume.)

or putting the rule in words, subtract the degrees Baume from 144.3, and divide 144.3 with the number thus obtained. For example: 32 Baume 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 Baume.)

or in words divide 146 by the number of degrees Baume added to 136. For example: ammonia of 30 Beaume 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 Beaume 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.