The Osmotic Pressure of Solutions. 135 



A number of interesting conclusions may be obtained 

 from equation 6. 



(a) At the freezing point of a solution the external work 

 done when solvent is added to it in a reversible way is inde- 

 pendent of the nature of the dissolved substance, and it is 

 the same for all solutions in the same solvent which have 

 the same freezing point. The equation for the osmotic 

 work becomes at F — 



r T -F cF/T.-FVH 



This equation was first obtained by Arrhenius * in 1892, 

 in a slightly different form, and in a different way. 



(b) Again dividing equation 6 by T and bringing all the 

 terms which are independent of T together into one con- 

 stant, we get 



Pv . jm dq 



-=const + — - 



It is easy to see from equations (1) and (2) that this may 

 also be written 



P, = RTC + JM„g (7) 



Differentiating this with respect to T at constant volume 

 (or concentration) — 



bT 



For any given solution v may be regarded as indepen- 

 dent of temperature, and we get 



constant. (b) 



/bP\ ^Kk 



VjV, v n 



This result is quite analogous to the result obtained by 



*Zeit. Ph. Chem. io, p. 92, 1892. 



