THERMODYNAMICS OF CHANGE OF STATE, ETC. 325 



It will be useful to collect the results which we have obtained. We 

 have for very dilute solutions 



Osmotic pressure P = (w-a>') (1) 



Raising of boiling-point or lowering of freezing-point of liquid density p 



d9 = ~ p (2) and (3) 



Raoult's experimental value of the difference of vapour-pressure, 



w to' en en 



= _ nearly 



ft> N + n 



where c is nearly 1 for non- electrolytes. For such non-electrolytes by 

 substituting in (1) 



,..- (5) 



<} 



Whence Van t'Hoff's result P-^r &# 00 



S 



For the purpose of illustration let us calculate the actual values for 

 1 gramme molecule in solution in water. It must be remembered that 

 as a rule aqueous solutions are electrolytic, and it is only for non- 

 electrolytic solutions, such as one of cane sugar, that the results hold. 



We may determine the value of R from the density of hydrogen 

 0000896 at 0. and 1 atmo. or 1014000 dynes/sq. cm. 



we get R = 4 - 15 x 10 T when o> is in dynes/sq. cm. 



or 40'9 when to is in atmos. 



8 



When the solution is 1 gramme molecule per litre of water, ~- which is 

 the number of gramme molecules per c.c., is j^rry Then (7) becomes 



P = 8-3 x 10 4 x dynes/sq. cm. 

 or '08180 atmos., 



and if the temperature is C., putting = 273, this becomes 



P = 22-3 atmos. 

 If there are n gramme molecules per litre 



P = 22-3xraatO 

 or =22-3n(l+a*)at c O. 



It must be noted that this only holds for dilute solutions, so that in 

 general n must be small, indeed a small fraction. 



