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 BaSO4. 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) MnO2 + 4HCl = MnCl2 + Cl2 + 2H2O.
(2) Cl + KI = KCl + I.
To how much MnO2 is 1 gram of Iodine (I) equivalent?
4. A mineral has the following composition:—
Carbonic acid (CO2) 19.09
Copper oxide (CuO) 71.46
Water (H2O) 9.02
What is its formula?
5. How much copper is contained in 1.5 gram of crystallized copper sulphate (CuSO4.5H2O)? How much of these crystals must be taken to give 0.4 gram of copper?
6. How much ferrous sulphate crystals (FeSO4.7H2O) 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 Fe2O3. 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 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.