[50 bis] Pickering (1890) showed (a) that dilute solutions of sulphuric acid containing up to H2SO4 + 10H2O deposit ice (at -0°·12 when there is 2,000H2O per H2SO4, at -0°·23 when there is 1,000H2O, at -1°·04 when there is 200H2O, at -2°·12 when there is 100H2O, at -4°·5 when there is 50H2O, at -15°·7 when there is 20H2O, and at -61° when the composition of the solution is H2SO4 + 10H2O); (b) that for higher concentrations crystals separate out at a considerable degree of cold, having the composition H2SO44H2O, which melt at -24°·5, and if either water or H2SO4 be added to this compound the temperature of crystallisation falls, so that a solution of the composition 12H2SO4 + 100H2O gives crystals of the above hydrate at -70°, 15H2SO4 + 100H2O at -47°, 30H2SO4 + 100H2O at -32°, 40H2SO4 + 100H2O at -52°; (c) that if the amount of H2SO4 be still greater, then a hydrate H2SO4H2O separates out and melts at +8°·5, while the addition of water or sulphuric acid to it lowers the temperature of crystallisation so that the crystallisation of H2SO4H2O from a solution of the composition H2SO4 + 1·73H2O takes place at -22°, H2SO4 + 1·5H2O at -6°·5, H2SO4 + 1·2H2O at +3°·7, H2SO4 + 0·75H2O at +2°·8, H2SO4 + 0·5H2O at -16°; (d) that when there is less than 40H2O per 100H2SO4, refrigeration separates out the normal hydrate H2SO4, which melts at +10°·35, and that a solution of the composition H2SO4 + 0·35H2O deposits crystals of this hydrate at -34°, H2SO4 + 0·1H2O at -4°·1, H2SO4 + 0·05H2O at +4°·9, while fuming acid of the composition H2SO4 + 0·05SO3 deposits H2SO4 at about +7°. Thus the temperature of the separation of crystals clearly distinguishes the above four regions of solutions, and in the space between H2SO4 + H2O and +25H2O a particular hydrate H2SO44H2O separates out, discovered by Pickering, the isolation of which deserves full attention and further research. I may add here that the existence of a hydrate H2SO44H2O was pointed out in my work, The Investigation of Aqueous Solutions, p. 120 (1887), upon the basis that it has at all temperatures a smaller value for the coefficient of expansion k in the formula St = S0/(1 - kt) than the adjacent (in composition) solutions of sulphuric acid. And for solutions approximating to H2SO410H2O in their composition, k is constant at all temperatures (for more dilute solutions the value of k increases with t and for more concentrated solutions it decreases). This solution (with 10H2O) forms the point of transition between more dilute solutions which deposit ice (water) when refrigerated and those which give crystals of H2SO44H2O. According to R. Pictet (1894) the solution H2SO410H2O freezes at -88° (but no reference is made as to what separates out), i.e. at a lower temperature than all the other solutions of sulphuric acid. However, in respect to these last researches of R. Pictet (for 88·88 p.c. H2SO4 -55°, for H2SO4H2O +3·5°, for H2SO42H2O -70°, for H2SO44H2O -40°, &c.) it should be remarked that they offer some quite improbable data; for example, for H2SO475H2O they give the freezing point as 0°, for H2SO4300H2O +4°·5, and even for H2SO41000H2O +0°·5, although it is well known that a small amount of sulphuric acid lowers the temperature of the formation of ice. I have found by direct experiment that a frozen solidified solution of H2SO4 + 300H2O melted completely at 0°.

[51] With an excess of snow, the hydrate H2SO4,H2O, like the normal hydrate, gives a freezing mixture, owing to the absorption of a large amount of heat (the latent heat of fusion). In melting, the molecule H2SO4 absorbs 960 heat units, and the molecule H2SO4H2O 3,680 heat units. If therefore we mix one gram molecule of this hydrate with seventeen gram molecules of snow, there is an absorption of 18,080 heat units, because 17H2O absorbs 17 × 1,430 heat units, and the combination of the monohydrate with water evolves 9,800 heat units. As the specific heat of the resultant compound H2SO4,18H2O = 0·813, the fall of temperature will be -52°·6. And, in fact, a very low temperature may be obtained by means of sulphuric acid.

[52] For example, if it be taken that at 19° the sp. gr. of pure sulphuric acid is 1·8330, then at 20° it is 1·8330 - (20 - 19)10·13 = 1·8320.

[53] Unfortunately, notwithstanding the great number of fragmentary and systematic researches which have been made (by Parks, Ure, Bineau, Kolbe, Lunge, Marignac, Kremers, Thomsen, Perkin, and others) for determining the relation between the sp. gr. and composition of solutions of sulphuric acid, they contain discrepancies which amount to, and even exceed, 0·002 in the sp. gr. For instance, at 15°·4 the solution of composition H2SO43H2O has a sp. gr. 1·5493 according to Perkin (1886), 1·5501 according to Pickering (1890), and 1·5525 according to Lunge (1890). The cause of these discrepancies must be looked for in the methods employed for determining the composition of the solutions—i.e. in the inaccuracy with which the percentage amount of H2SO4 is determined, for a difference of 1 p.c. corresponds to a difference of from 0·0070 (for very weak solutions) to 0·0118 (for a solution containing about 73 p.c.) in the specific gravity (that is the factor ds/dp) at 15°. As it is possible to determine the specific gravity with an accuracy even exceeding 0·0002, the specific gravities given in the adjoining tables are only averages and most probable data in which the error, especially for the 30–80 p.c. solutions cannot be less than 0·0010 (taking water at 4° as 1).

[53 bis] Judging from the best existing determinations (of Marignac, Kremers, and Pickering) for solutions of sulphuric acid (especially those containing more than 5 p.c. H2SO4) within the limits of 0° and 30° (and even to 40°), the variation of the sp. gr. with the temperature t may (within the accuracy of the existing determinations) be perfectly expressed by the equation St = S0 + At + Bt2. It must be added that (1) three specific gravities fully determine the variation of the density with t; (2) ds/dt = A + 2Bt—i.e. the factor of the temperature is expressed by a straight line; (3) the value of A (if p be greater than 5 p.c.) is negative, and numerically much greater than B; (4) the value of B for dilute solutions containing less than 25 p.c. is negative; for solutions approximating to H2SO43H2O in their composition it is equal to 0, and for solutions of greater concentration B is positive; (5) the factor ds/dp for all temperatures attains a maximum value about H2SO4H2O; (6) on dividing ds/dt by S0, and so obtaining the coefficient of expansion k (see Note [53]), a minimum is obtained near H2SO4 and H2SO44H2O, and a maximum at H2SO4H2O for all temperatures.

[53 tri] These data (as well as those in the following table) have been recalculated by me chiefly upon the basis of Kremer's, Pickering's, Perkin's, and my own determinations; all the requisite corrections have been introduced, and I have reason for thinking that in each of them the probable error (or difference from the true figures, now unknown) of the specific gravity does not exceed ±0·0007 (if water at 4° = 1) for the 25–80 p.c. solutions, and ±0·0002 for the more dilute or concentrated solutions.

[54] The factor dS/dp passes through 0, that is, the specific gravity attains a maximum value at about 98 p.c. This was discovered by Kohlrausch, and confirmed by Chertel, Pickering, and others.

[55] Naturally under the condition that there is no other ingredient besides water, which is sufficiently true. For commercial acid, whose specific gravity is usually expressed in degrees of Baumé's hydrometer, we may add that at 15°

Specific gravity11·11·21·31·41·51·61·71·8
Degree Baumé0132433·341·248·154·159·564·2

66° Baumé (the strongest commercial acid or oil of vitriol) corresponds to a sp. gr. 1·84.