826 Vain Name and Bill — Solution of Metals 



fusion stage, thus giving a concentration at the surface of the 

 metal which is not sensibly different from that in the solution. 

 The possibilities represented by these three figures will be 

 hereafter referred to as cases I, II, and III, respectively. 



For Case I, Nernst's explanation, given above, is sufficient 

 to account for the fact that the reaction velocity obeys the 

 equation for a monomolecular reaction. In Cases II and III, 

 however, there is a finite concentration of the reagent at the 

 surface of the metal. This can only occur when a part (in 

 Case III, nearly all) of the molecules of the reagent which 

 strike the surface of the solid phase fail to react with it, and 

 hence remain in the solution. Now the frequency of the 

 impacts will be proportional to the concentration of the reagent 

 in the layer of liquid immediately adjacent to the solid, and 

 the percentage of such impacts which result in reaction will, 

 in a given case, be practically constant, independent of that 

 concentration. It follows, therefore, that the rate of the 

 chemical stage of the reaction will always be proportional to 

 the concentration of the oxidizing agent in the layer of liquid 

 which is in contact with the solid, that is, the concentration at 

 the inner surface of the diffusion layer. 



Our results seem to furnish no example of Case III, but it 

 is clear that here, just as in Case I, the rate would be propor- 

 tional to the concentration of the solution, for this is the same 

 as the concentration at the surface of the solid, which, in turn, 

 determines the rate. 



It only remains to be explained why Case II* shows the 

 same behavior. As we have already shown that the rate must 

 be proportional to the concentration at the surface of the 

 metal, the problem resolves itself into proving that the con- 

 centration at the surface of the metal is proportional at every 

 instant to the concentration in the solution. It is a simple, 

 matter to show that this is necessarily true except during a 

 preliminary period of extremely short duration. 



Let C m represent the concentration of the oxidizer at the 

 surface of the metal, and C s its concentration in the solution. 

 Further, let din^ be the weight of the oxidizer diffusing to the 

 metal during the time interval dt, and dm^ the weight used up 

 during time dt. 



The rate of the diffusion process is proportional to the dif- 

 ference in concentration on opposite sides of the diffusion 

 layer. Hence 



dmJdt = K 1 (C.- C m ), 



*Case II is evidently the general one, I and III being merely limiting 

 cases. 



