Variation of the Dissociation Coefficient with Temperature. 287 



dissociation,- — a want of agreement for which no satisfactory 

 explanation has been given. 



However, even in the cases where the value of the disso- 

 ciation-coefficient remains constant with varying concentration, 

 it still varies in a definite way with change of temperature. 

 The law of this variation with temperature was first worked 

 out by van't Hoff, who investigated the general case of the 

 coefficient of equilibrium of any chemical reaction, by apply- 

 ing the second law of Thermodynamics. The algebraical 

 difficulties in the general case are so great, when the concen- 

 trations of the reacting substances are allowed to vary as they 

 naturally would on taking the solution round a cycle, that one 

 has to assume them kept constant by some artificial means 

 during the process. This assumption of course does not in 

 the least destroy the rigour of the deduction ; still it is always 

 satisfactory to have as many different methods of proof as pos- 

 sible, and in the simple case of a binary electrolyte whose 

 isotherm of dissociation is (2), the variation with temperature 

 of K may be obtained by the application of the second law in 

 the ordinary way, without the necessity of the assumptions 

 entailed in the proof for the general case. 



The cycle is carried out by obtaining the maximum osmotic 

 work W done by ihe solution in the expansion against a semi- 

 permeable partition from concentration C a to C 2 , applying 

 this work to compress it again to Ci at a slightly lower tem- 

 perature, and equating the excess to the work corresponding 

 to the reversible thermodynamic cycle. As the electrolyte is 

 diluted, the dissociation varies in accordance with (2), and 

 the work dore against the semipermeable partition consists of 

 two parts, that done by the undissociated and that done by the 

 dissociated molecules, which must be determined separately. 



Let Y be the volume of the solution in litres, and let 1 gr. 

 mol. of the electrolyte be dissolved ; so that if C is the total 

 concentration, 



VC=1 . (3) 



Taking, as before, c for the concentration of the undissociated 

 electrolyte, and c' for lhat of either of the ions, we have 



c + c'=C, (4) 



and 



Kc=c /2 (2) 



The work done by the undissociated part of the salt is 



w = \ Y2 pdY= pRTcvv/C, 

 'v Jc 2 *-' 



