434 Dr- F. Tinker on Osmotic Pressure. 



of any deci-normal aqueous solution *, and, as an extreme 

 case let 



(Y 2 —b 2 + .e) = ld(Vi— h x ) {cf. equation [5]}. 

 We have 



and — =^= — — 1 approx. 



7T ' N 1 



The error in counting — =-— ^ — is thus — on unity, 

 * 7TJ N+n 60 J 



or less than 2 per cent. The magnitude of the error is 

 evidently determined by the number of solute molecules 

 added to the solvent. If not many are added, their influence 

 on the mean free space F in the solution is overwhelmed by 

 the influence of the solvent, so that the internal conditions 

 inside the solvent remain more or less unchanged. 



We must not, however, suppose that because the solvent 

 undergoes no appreciable volume change in the case of 

 dilute solutions, the solute also undergoes no volume change, 

 and also that the total volume change is zero. Both these 

 latter hypotheses are in contradiction both to theory and 

 experiment f- The solute, for instance, has to change its 

 molecular volume in such a way that (Y 2 — b 2 ) alters itself to 

 (V 1 '-ft,)^=F = (V 1 '-6i) { = (V 1 -6 1 ) for dilute solutions}, 

 i. e. on adding the solute to the solvent, in the case of dilute 

 solutions, the free space of the solute readjusts itself to that 

 of the pure solvent ; whence the molecular volume of the 

 solute also alters from V 2 to (Vi~ bi + b 2 ). In the same 

 way it can be shown by developing the equation [4], that 

 the total expansion ne on mixing is given by the relation 



«e=n{(V 1 -& 1 )-(V 2 -t 2 )}-(N+_'i)(V I -V 1 '). [7] 

 The tolal volume change becomes zero in two cases only : 

 (a) when (V x — b^ = (V 2 — b 2 ) and Vi' = Vi simultaneously, 



i. e. when the original " free spaces " of pure solvent 



and solute are equal and undergo no volume change 



on mixing ; 

 (6) when 



(N + «))(V 1 ~V 1 ')=»{(V 1 -6 1 )-(V 2 -6 2 )} 



N 

 * A solution is usually taken as dilute up to a strength of y~. 



t It is well known that a slight total volume change on solution is the 

 rule, even with very dilute solutions. For a comprehensive set of deter- 

 minations see Cameron & Robinson, Journ. Phys. Chem. xiv. p. 1 (1910). 



