432 Dr. F. Tinker on Osmotic Pressure. 



We then have 

 Total free space in mixture 



= (N + nJF=('N + *i)(V 1 , -6 1 ) = (N + n)(y > '-6,)- W 



Employing theequation postulated in the second assumption, 

 we get immediately for the partial pressure tt/ of the solvent 

 inside the solution 



,(N + n) F = RT; 



and for the pressure ir x inside the pure solvent 



7r 1 (Y 1 -b 1 ) = nT., 

 and hence 



7T/ N Vx-^x 



7T! N + W 



[2] 



Similarly, for the partial pressure 7r 2 ' of the solute inside 

 the solution 



7T 2 -JST + 72 * F LdJ 



The equations [2] and [3] can be developed further by 

 considering in detail the volume changes which take place 

 on mixing. 



Let the increase in the total volume * on mixing be ne 

 (e can be looked on as the expansion of the total volume per 

 molecule of solute added). We have 



Total volume of solution = NV 1 + nY 2 + ?ie, 



Total free space in solution = NW X — b 1 ) + n(V 2 — b 2 ) + ne. 



But the total free space in solution is also =(N + w)F. 

 Hence 



= (K + n)(Y 1 -b 1 )-n{(V 1 -b 1 )-(V 2 -b 2 +6)}. 

 Dividing throughout by (N + n) ( V x — Z> : ) , we get 



* I. e. the excess of the volume of the solution over the sum of the 

 volumes of the two components. It is to be noted that e varies with 

 the pressure to which the solution is subjected; and that W and V 2 ' 

 are also variable with the pressure. But since in the present paper no 

 pressures are ever put on the pure solvent or solute, V L and V 2 are 

 regarded as being constant and equal to the molecular volumes at 

 atmospheric pressure. 



