48 Dr. H. J. S. Sand on the Concentration 



It should be noted that our assumption that any heating 

 effect which may take place is proportional to the number of 

 ions deposited, excludes the liberation of heat owing to 

 anything in the nature of electrolytic resistance in the vicinity 

 of the electrode, being bound up with the deposition of the 

 ions — electrolytic heating in a given electrolyte being, as is 

 well known, proportional to the square of the current. In 

 arriving at our result, we also excluded the supposition that at 

 high current-densities ions of the two salts should enter into 

 chemical combination, forming complex ions. 



As is well known, the E.M.F. necessary to deposit an ion 

 from a solution on a given electrode varies within certain 

 limits with its concentration in the solution. In the case of 

 reversible processes it can be calculated in volts by Nernst's 



formula: E = 0*860 X 10" 4 - Tin -, T being the absolute tem- 



n p' n 



perature, n the valency of the ion, p its osmotic pressure in 

 the solution, and P its so-called solution-tension. When two 

 monovalent metals of solution-tension P : and P 2 are being 

 simultaneously deposited as a mechanical mixture, this equa- 

 tion in connexion with E X = E 2 leads to 



0-860 T//3= 0-860 Tin- 2 or pl = ^ 



Pi lh P2 "2 



a formula which is given by Nernst in the paper quoted *. 



* Note. — In his paper Nernst also gives a formula for the ratio y of the 

 quantity of the metal (1) deposited in g. -equivalents to the total number 

 of equivalents liberated, the conditions being as above. This formula is 

 based on the consideration which follows from the results just obtained,, 

 that if we have a solution containing the salts of two metals in a pro- 

 portion in which they are not simultaneously deposited, the metal which 

 is in excess of this proportion will at first be deposited alone until the 

 proportion for simultaneous deposition be again attained. If w r e there- 

 fore start with a solution which contains the salts of two monovalent 



1h _ Pi 



metals in the proportion given by the equation — — p~, or, assuming- 

 complete dissociation and indicating concentrations by c, 



c "IV * ' 



(A> 



then if we stir in such a manner as to keep the concentration uniform 

 as nearly as possible, the ratio of concentrations which before stirring 

 varied throughout the electrolyte, will have the tendency to become 

 again uniformly 



, tf-R (B > 



