composition of the solution, but by the necessity for the composition of the solution remaining constant.
Barium Carbonate and Potassium Sulphate.—As has been found by Meyerhoffer,[[397]] these two salts form the stable pair, not only at the ordinary temperature, but also at the melting point. For the ordinary temperatures this was proved in the following manner: A solution with the solid phases K2SO4 and K2CO3.2H2O in excess can only coexist in contact either with BaCO3 or with BaSO4, since, evidently, in one of the two groups the stable system must be present. Two solutions were prepared, each with excess of K2SO4 + K2CO3.2H2O,
and to one was added BaCO3 and to the other BaSO4. After stirring for a few days, the barium sulphate was completely transformed to BaCO3, whereas the barium carbonate remained unchanged. Consequently, BaCO3 + K2SO4 + K2CO3.2H2O is stable, and, therefore, so also is BaCO3 + K2SO4. That BaCO3 + K2SO4 is the stable pair also at the melting point was proved by a special analytical method which allows of the detection of K2CO3 in a mixture of the four solid salts. This analysis showed that a mixture of BaCO3 + K2SO4, after being fused and allowed to solidify, contains only small amounts of K2CO3; and this is due entirely to the fact that BaCO3 + K2SO4 on fusion deposits a little BaSO4, thereby giving rise at the same time to the separation of an equivalent amount of K2CO3.
The different solubilities are shown in Fig. 128. In this diagram the solubility of the two barium salts has been neglected. A is the solubility of K2CO3.2H2O; addition of BaCO3 does not alter this. B is the solubility of K2CO3.2H2O + K2SO4 + BaCO3. A and B almost coincide, since the potassium sulphate is very slightly soluble in the concentrated solution of potassium carbonate. D gives the concentration of the solution in equilibrium with K2SO4 + BaSO4. The most interesting point is C. This solution is obtained by adding a small quantity of water to BaCO3 + K2SO4, whereupon, being in the transition interval, BaSO4 separates out and an equivalent amount of K2CO3 goes into solution. C is the end point of the curve CO, which is called the Guldberg-Waage curve, because these investigators determined several points on it.
In their experiments, Guldberg and Waage found the ratio K2CO3 : K2SO4 in solution to be constant and equal to 4. This result is, however, not exact, for the curve CO is not a straight line, as it should be if the above ratio were constant; but it is concave to the abscissa axis, and more so at lower than at higher temperatures.
The following table refers to the temperature of 25°. The Roman numbers in the first column refer to the points in Fig. 128. The numbers in the column Σk2 give the amount,
in gram-molecules, of K2CO3 + K2SO4 contained in 1000 gram-molecules of water:—
Solubility Determinations at 25°.
| No. | Solid phases. | 100 gms. of the solution contain, in grams, | 1000 moles of water contain, in moles, | Σk2 | K2CO3 K2SO4 | ||||||
| K2CO3 | K2SO4 | K2CO3 | K2SO4 | ||||||||
| I. | K2CO3.2H2O + BaCO3 | 53.2 | — | 147.9 | — | — | — | ||||
| II. |
| K2CO3.2H2O + K2SO4 + BaCO3 |
| 53.0 | 0.023 | 147.8 | 0.051 | — | — | ||
| III. IV. |
| K2SO4 + BaCO3 |
| 28.5 22.1 | 0.886 1.72 | 52.58 37.79 | 1.296 2.333 | — — | — — | ||
| V. | BaCO3 + K2SO4 + BaSO4 | 17.81 | 2.485 | 29.11 | 3.220 | 32.32 | 9.03 | ||||
| VI. VII. |
| K2SO4 + BaSO4 |
| 12.6 5.85 | 3.92 6.76 | 19.66 8.724 | 4.853 7.995 | — — | — — | ||
| VIII. | K2SO4 | — | 10.76 | — | 12.47 | — | — | ||||
| IX. X. |
| BaCO3 + BaSO4 |
| 7.35 2.85 | 0.602 0.173 | 10.43 3.828 | 0.676 0.184 | 11.11 4.0 | 15.0 21.0 | ||
