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: