where s is the specific gravity at t (degrees Celsius) if the sp. gr. of water at 4° = 10,000. Therefore K = 10·65 - 0·026t. This means that at 0° the sp. gr. of the acid H2SO4 decreases by 10·65 for every rise of a degree of temperature, at 10° by 10·39, at 20° by 10·13, at 30° by 9·87.[52] And for solutions containing slightly more anhydride than the acid H2SO4 (i.e. for fuming sulphuric acid), as well as for solutions containing more water, K is greater than for the acid H2SO4. Thus for the solution SO3,2H2SO4, at 10° K = 11·0. On diluting the acid H2SO4 K again increases until the formation of the solution H2SO4,H2O (K = 11·1 at 10°), and then, on further dilution with water, it again decreases. Consequently both hydrates H2SO4 and H2SO4,H2O are here expressed by an alteration of the magnitude of K.
Fig. 89.—Diagram showing the variation of the factor (ds/dp) of the specific gravity of solutions of sulphuric acid. The percentage quantities of the acid, H2SO4, are laid out on the axes of abscissæ. The ordinates are the factors or rises in sp. gr. (water at 4 = 10,000) with the increase in the quantity of H2SO4.
This shows that in liquid solutions it is possible by studying the variation of their properties (without a change of physical state) to recognise the presence or formation of definite hydrate compounds, and therefore an exact investigation of the properties of solutions, of their specific gravity for instance, should give direct indications of such compounds.[53] The mean result of the most trustworthy determinations of this nature is given in the following tables. The first of these tables gives the specific gravities (in vacuo, taking the sp. gr. of water at 4° = 1), at 0° (column 3), 15° (column 4), and 30° (column 5),[53 bis] for solutions having the composition H2SO4 + nH2O (the value of n is given in the first column), and containing p (column 2) per cent. (by weight in vacuo) of H2SO4.[53 tri]
| n | p | 0° | 15° | 30° |
| 100 | 5·16 | 1·0374 | 1·0341 | 1·0292 |
| 50 | 9·82 | 1·0717 | 1·0666 | 1·0603 |
| 25 | 17·88 | 1·1337 | 1·1257 | 1·1173 |
| 15 | 26·63 | 1·2040 | 1·1939 | 1·1837 |
| 10 | 35·25 | 1·2758 | 1·2649 | 1·2540 |
| 8 | 40·50 | 1·3110 | 1·2649 | 1·2998 |
| 6 | 47·57 | 1·3865 | 1·3748 | 1·3622 |
| 5 | 52·13 | 1·4301 | 1·4180 | 1·4062 |
| 4 | 57·65 | 1·4881 | 1·4755 | 1·4631 |
| 3 | 64·47 | 1·5635 | 1·5501 | 1·5370 |
| 2 | 73·13 | 1·6648 | 1·6500 | 1·6359 |
| 1 | 84·48 | 1·7940 | 1·7772 | 1·7608 |
| 0·5 | 91·59 | 1·8445 | 1·8284 | 1·8128 |
| H2SO4 | 100 | 1·8529 | 1·8372 | 1·8221 |
In the second table the first column gives the percentage amount p (by weight) of H2SO4, the second column the weight in grams (S15) of a litre of the solution at 15° (at 4° the weight of a litre of water = 1,000 grams), the third column, the variation (dS/dt) of this weight for a rise of 1°, the fourth column, the variation dS/dp of this weight (at 15°) for a rise of 1 per cent. of H2SO4, the fifth column, the difference between the weight of a litre at 0° and 15° (S0 - S15), and the sixth column, the difference between the weight of a litre at 15° and 30° (S15 - S30).
| p | S15 | dS15/dt | dS15/dp | S0-S15 | S15-S15 |
| 0 | 999·15 | 0·148 | 7·0 | 0·7 | 3·4 |
| 5 | 1033·0 | 0·27 | 6·8 | 3·1 | 5·0 |
| 10 | 1067·7 | 0·28 | 7·1 | 5·2 | 6·4 |
| 20 | 1141·9 | 0·58 | 7·7 | 8·6 | 8·9 |
| 30 | 1221·3 | 0·69 | 8·2 | 10·4 | 10·4 |
| 40 | 1306·6 | 0·75 | 8·8 | 11·3 | 11·2 |
| 50 | 1397·9 | 0·79 | 9·9 | 11·9 | 11·8 |
| 60 | 1501·2 | 0·86 | 10·8 | 13·0 | 12·7 |
| 70 | 1613·1 | 0·93 | 11·6 | 14·1 | 13·8 |
| 80 | 1731·4 | 1·04 | 11·0 | 15·8 | 15·4 |
| 90 | 1819·9 | 1·08 | 5·4 | 16·4 | 16·0 |
| 95 | 1837·6 | 1·03 | +1·7 | 15·8 | 15·1 |
| 100 | 1837·2 | 1·03 | -1·9[54] | 15·7 | 15·1 |
The figures in these tables give the means of finding the amount of H2SO4 contained in a solution from its specific gravity,[55] and also show that ‘special points’ in the lines of variation of the specific gravity with the temperature and percentage composition correspond to certain definite compounds of H2SO4 with OH2. This is best seen in the variation of the factors (dS/dt and dS/dp) with the temperature and composition (columns 3, 4, second table). We have already mentioned how the factor of temperature points to the existence of hydrates, H2SO4 and H2SO4,H2O. As regards the factor dS/dp (giving the increase of sp. gr. with an increase of 1 per cent. H2SO4) the following are the three most salient points: (1) In passing from 98 per cent. to 100 per cent. the factor is negative, and at 100 per cent. about -0·0019 (i.e. at 99 per cent. the sp. gr. is about 1·8391, and at 100 per cent. about 1·8372, at 15°, the amount of H2SO4 has increased whilst the sp. gr. has decreased), but as soon as a certain amount of SO3 is added to the definite compound H2SO4 (and ‘fuming’ acid formed) the specific gravity rises (for example, for H2SO4 0·136 SO3 the sp. gr. at 15° = 1·866), that is the factor becomes positive (and, in fact, greater by +0·01), so that the formation of the definite hydrate H2SO4 is accompanied by a distinct and considerable break in the continuity of the factor[55 bis]; (2) The factor (dS/dp) in increasing in its passage from dilute to concentrated solutions, attains a maximum value (at 15° about 0·012) about H2SO42H2O, i.e. at about the hydrate corresponding to the form SX6; proper to the compounds of sulphur, for S(OH)6 = H2SO42H2O; the same hydrate corresponds to the composition of gypsum CaSO42H2O, and to it also corresponds the greatest contraction and rise of temperature in mixing H2SO4 with H2O (see Chapter I., Note [28]); (3) The variation of the factor (dS/dp) under certain variations in the composition proceeds so uniformly and regularly, and is so different from the variation given under other proportions of H2SO4 and H2O, that the sum of the variations of dS/dp is expressed by a series of straight lines, if the values of p be laid along the axis of abscissæ and those of dS/dp along the ordinates.[56] Thus, for instance, for 15°, at 10 per cent. dS/dp = 0·0071, at 20 per cent. = 0·0077, at 30 per cent. = 0·0082, at 40 per cent. = 0·0088, that is, for each 10 per cent. the factor increases by about 0·0006 for the whole of the above range, but beyond this it becomes larger, and then, after passing H2SO42H2O, it begins to fall rapidly. Such changes in the variation of the factor take place apparently about definite hydrates,[56 bis] and especially about H2SO44H2O, H2SO42H2O and H2SO4H2O. All this indicating as it does the special chemical affinity of sulphuric acid for water, although of no small significance for comprehending the nature of solutions (see Chapter [I.] and Chapter [VII.]), contains many special points which require detailed investigation, the chief difficulty being that it requires great accuracy in a large number of experimental data.