The Os?notic Pressure of Solutions. 141 



The equation (11) includes the equations which have 



already been given by Van't Hoff for the case that 1— = o. 



In this case it is easy to see from (4) that k is positive, and 

 therefore, equation (n) becomes 



P(V-6) = RT. 



If the solutions considered are dilute, — that is V large 

 compared with 3, — this may be written — 



PV = RT. 



Again (11) may be written in the form 



dQ 



or for 



Pnv =±RT + J»M 



-7- = 0, this becomes ~: = -. 

 div Rl n 



And from (1) 







accordingly 







or for dilute solutions 









p -p_l 







Po n 



which is the well-known equation of Raoult. It was also 

 obtained in this form by Planck,* in 1887. 



The expression for the molecular depression of the freez- 

 ing point of a solution follows from equation 4. Putting 

 <T,-F) = * 



nS[ We T ¥ 2F 2 F'dwJ 



-M is called the molecular depression of the freezing point 

 of a solution, when t= the depression produced by g grams 



* Wied. Ann. 32, p. 502. 1887. 

 K 



