380 Dr. R. A. Lehfeldt on Electromotive 



In the above deduction use has been made (as in all similar 

 arguments) of a semipermeable partition, and it is important 

 to consider exactly what character must be attributed to this. 

 It seems to me that, on the one hand, it is impossible to assume 

 impermeability for the metallic ions alone, since then it would 

 be possible to allow the acid radical to diffuse through the 

 partition, and leave behind a solution containing more positive 

 than negative ions ; a state of things which, according to all 

 our experimental knowledge, cannot exist. On the other 

 hand, if the partition is impermeable for both ions, it must 

 be (at least effectively) impermeable for the undissociated 

 salt too, since, if some of the salt were to diffuse out, the ions 

 remaining in the solution would no longer be in equilibrium 

 with the undissociated salt remaining, and some of the ions 

 would combine : thus (effectively) ions as well as salt would 

 have diffused out of the solution. I have therefore assumed 

 a partition permeable only to water, but not to the salt or its 

 ions. From this follows the important conclusion that the 

 electromotive force depends not on the osmotic pressure of the 

 metallic ions only, but on that of the solution as a whole. 



(ii.) Graphical Representation. 



Equation (2) becomes, of course, identical with (1) if the 

 dissociation be complete, i. e. if y be put =1. It is, however, 

 in any case capable of graphic representation in an interesting 

 manner. 



In fig, 1, showing relations between dilution (V) and 

 osmotic pressure (P), let the dotted curve be the rectangular 

 hyperbola representing (at constant temperature) the behaviour 

 of a substance wdiich obeys Boyle's law and does not dissociate; 

 while the full curve represents the behaviour of the actual (dis- 

 sociating) substance, w T hich, however, is also assumed to obey 

 Boyle's law. Then a rectangle under the dotted curve, such 

 as OABO, will have the area 



PV = RT. 



A similar rectano-le ODEC under the full curve has the 



area 



VY = UT{l + {n-l) 7 } = RTc, 



since the pressure of the dissociating substance is greater in 

 the ratio 1+ {n — l)y, or as it may be more briefly written i 

 (van't Hoft's factor). If another point G be taken on the 

 full curve and the rectangle OFGH drawn, its area will repre- 

 sent the value of RTt corresponding to the dilution OH: the 

 difference between the two areas (using the suffixes 1 and 2 



