494 Professor H. L. Calhmdar [Feb. 26, 



With the simple formula — 



p' Ip" = (N - an + n) / (N - an) 



the values of the vapour-pressure are very easily calculated from the 

 molecular concentration n for simple integral values of the hydration 

 factor a. The osmotic pressures are also readily deduced from the 

 ratio of the vapour-pressures (|//p") by the formula 



PU = RT log (///')• 



The value a = b fits the osmotic pressures for cane-sugar very well, 

 as shown in the column headed C in Table I. The value «^ = 2 fits 

 Lord Berkeley's observations on dextrose equally well up to pressures 

 of 130 atmospheres. The same value a =b for cane-sugar also fits 

 the observations on the depression of the freezing-point and the rise 

 of the boiling-point, as it necessarily must, since these phenomena 

 also depend on the vapour-pressure. The freezing-point method is 

 the easiest for getting the ratio of the vapour-pressures to com- 

 pare with the formula. Ki the freezing-point of an aqueous solu- 

 tion, the vapour-pressure of the solution must be the same as that 

 of ice, provided that ice separates on freezing in the pure state. 

 The ratio of the vapour-pressure of ice to that of water at any 

 temperature below ()° C. is easily calculated. All the best recorded 

 results, except those of a few associating substances, give simple 

 positive integral values of a. Even in the case of associating sub- 

 stances, like Formic Acid and x^cetone, the curves are of the same 

 type, but the value of a is negative. Dissociating substances, like 

 strong electrolytes, present greater difficulties, on account of the 

 ionisation factor. But allowing for the uncertainty of the ionisation 

 data, they seem to follow satisfactorily the same law of vapour- 

 pressure. 



It appears from the form of the proposed law that the hydration 

 factor a makes very little difference to the vapour-pressure in weak 

 solutions, which follow Raoult's law as a limiting case, but it makes 

 a very great difference in strong solutions, when nearly all the free 

 water is used up, and the denominator N — an is small. Thus the 

 depression of the freezing-point of a strong solution of calcium 

 chloride is more than five times as great as that calculated from the 

 number of ions present in the solution. Each ion appears to appro- 

 priate no less than 9 molecules of water. The factor « = 9 gives a 

 very good approximation to the freezing-point curve, as far as the 

 uncertainty of the data permit. When N = an, the vapour-pressure 

 would be reduced to zero, according to the formula, but the formula 

 ceases to apply when the vapour-pressure of the compound molecules 

 themselves becomes equal to that of the solution. At or before this 

 point the molecules will dissociate with the formation of lower 

 hydrates. Many analogous phenomena are already known, and a 



