ELECTROLYSIS AND ELECTRO-CHEMISTRY. 



237 



and we get the same equation as Nernst — 



c?N=--|^ RT^^^ dt. 

 U + V ^ dx 



From the general theory of diffusion we may take the quantity of sub- 

 stance diffusing through unit area in one second to be proportional to the 

 gradient of concentration, so that the quantity crossing an area 5' in a time 

 dt is 



m= -V)q f- dt 

 dx 



where D is a constant. 



By comparing this with our last equation, we see that, for electrolytes, 



the diffusion constant is given by the expression 



2UV 



D= 



U + V 



RT. 



T is the absolute temperature, R the gas constant corresponding to one 

 gram-equivalent of substance (viz. 1-974 calories per degree or 8-29 x 10'^ 

 ergs per degree), so that it only remains to calculate U and V, the 

 velocities with which the ions move under the action of unit force. 



We have already seen that the charge of electricity carried by one 

 gram-equivalent of a kation is +I/17, and the charge on one gram- 

 equivalent of an anion is — 1 /ri, where r) represents the electro-chemical 

 equivalent of hydrogen. The quantity of electricity associated with one 

 gram-equivalent of any ion is therefore 1/ -00010352 =9653 electro- 

 magnetic units. If the potential gradient is one volt (10® C.G.S. units) 

 per centimetre, the force acting on this gram-equivalent will be 9,653 x 10® 

 dynes. This, in dilute solution, gives the ion its specific velocity, say u. 

 Thus the force required to give the ion unit velocity is 



p^^9 -653xl0n ^ 9J4 x 10' ^^^^^^^^ ^^,^^,^ 



u u 



If the ion have an equivalent weight A, the force producing unit 



10^ 

 velocity when acting on one gram is P,=9-84x-j— kilograms weight. 



Thus, in order to drive one gram of potassium ions ■<vith a velocity of one 

 centimetre per second through a very dilute water solution, we must exert 

 a force equal to the weight of 38,000,000 kilograms. The table gives 

 other examples.' 



" KoLlrausch, Wied. Ann. 1893, vol. 1. p. 385. 



