

524 Dr. S. A. Shorter on the Kinetic 



A similar error occurs in the deduction of the expression 

 for the osmotic pressure of a dilute solution. Dr. Tinker's 

 general expression is 



2P V' m g \ N N\ L Vx-ftt If 



... [20] 

 from which he deduces, for a dilute solution, the expression 



PV, = ET|-+Q, [21] 



which is erroneous, since the logarithm, when n/N is small, 

 is equal, not to n/N", but to 



'Y 2 —b 2 + e ia) \ 



n /V 2 — 6 2 + 6 (a) \ 

 NV V 3 -6, >/' 



so that in the imaginary case considered above, the value of 

 the osmotic pressure given by Dr. Tinker's theory is 10 times 

 that given by the " Gas law."' 



An error in the manipulation of small quantities also occurs 

 in the case of the equation 



r i e=n{(V 1 -M-(V 2 -i 2 )}-(N + »)(V 1 -V 1 '). . [7] 



considering the application of this equation to the case of a 

 dilute solution, Dr. Tinker states : — 



"In the case of dilute solutions (in which Vi' = Vi) 

 equation [7] indicates that the total volume change 



M=n{(V 1 -6,)-(V,-6 i )} (C) 



There will thus be an expansion or contraction on mixing 

 according as (Yi — b{) is greater or less than (V 2 — b 2 )." 



Now equation [7] defines mathematically the quantity V/ 

 in terms of the volume change, the concentration of the 

 solution, and the molecular " free spaces " of the pure 

 components. From it we see that as w/N is decreased 

 Y 1 — V/ becomes a small quantity of the first order, and 

 that instead of equation (C) holding, we have 



e-{(V 1 -6i)-(V 2 -&,)} = Lt -^-± — -^-* 



The falsity of equation (C) is evident if we consider the 

 application of it, first to a dilute solution of a liquid A in a 

 liquid B, and then to a dilute solution of B in A. It follows 

 at once that if one solution is formed with expansion, the 

 other is formed with contraction, the volume changes per 

 grm.-mol. of solute being arithmetically equal in the two 



