326 HEAT. 



The lowering of the vapour-pressure per 1 gramme molecule per litre is 



co -a/ _ n _ 1 18 1 

 a> ~N~ 1000 = 1000 ^SJHT 

 ~18~ 



since N, the number of gramme molecules of water in a litre, is 1000/18. 

 Thus at the boiling-point the lowering per gramme molecule in mm. of 

 mercury is 



The raising of the boiling-point is obtained from (3) and (7) by putting 

 0=373; L = 537 x 4-19 xlO 7 ; p = 1/1-043 



jfi - 8 ' 3 x 10 4 x 373 2 x 1 -043 

 537 x 4- 19 x 10 7 



= 0-54. 



The lowering of the melting-point is obtained from the same formulae by 

 putting = 273; L = 80 x 4-19 x 10 7 ; p=l 



, 8-3x 10*x273 2 

 80x4-19xl0 7 



= 1-85. 



Thus for cane sugar, C 12 H 22 O n , S = 342, and a solution containing 342 

 grammes per litre of water will boil at 1 00*54 C., will freeze at - 1-85 C., 

 and will have a vapour-pressure less than that of pure water by 1 in 55. 

 These results agree very closely with direct observation.* Observations 

 have been made with a large number of salts and solvents, and when 

 the solutions are non-electrolytic the agreement is equally close. 



If the lowering of the freezing-point or the raising of the boiling-point 

 is greater than the values obtained from Van t'Hoff's formula if, in 

 fact, c in Kaoult's formula is greater than 1 we can reconcile the observa- 

 tions with the theory that each gramme molecule has the same effect by 

 supposing that dissociation of the salt molecules has taken place, and that 

 the dissociated ions are acting independently, each producing its own 

 effect. Thus, if we have such a salt as KC1, and if a fraction A of it is 

 dissociated, then of the total n molecules originally present only n (1 A) 

 remain single, while nX. have split each into two, so that we have 

 n (1 - A) + 2nA = n(l + A) molecules actually in solution. 



Hence the results just obtained must be multiplied by 1 + A, where 

 1 + A may rise to 2 if dissociation is complete. 



Thus with KOI in water a solution of 1 gm. molecule per 10 litres of 

 water gives a depression not of 0'185, but about 1'86 times as much; 

 whence we may conclude that 86 per cent, of the salt is dissociated. As 

 the dilution increases so does the molecular depression of the freezing- 

 point, whence it is concluded that the dissociation also increases. This 

 supposition of dissociation is confirmed by observations on the electric 



* Wbetham, Solution, chap. vL 



