ELECTROLYSIS AND ELECTRO-CHEMISTRY. 239 



negative potential with regard to the solution, according as the kation or 

 the anion has the greater specific velocity and, therefore, the greater initial 

 rate of diflfusion. This idea can be developed to explain the difference of 

 potential at the surface of contact of two solutions or of a solution and a 

 metal. 



Taking the equation which expresses the relation that, when a steady 

 state is reached, the ions migrate at equal rates, viz. — 



\ax ax J \dx ax J 



we get 



t^p_l V-U ^ 



dx c V + TJ dx' 



or, since for dilute solutions ^=cRT, 



dP_RT Vj-U^ 

 dx p V+U dx 

 which gives on integration 



If we have absolutely pure water in contact with a solution, py is zero,, 

 and the difference of potential apparently becomes infinite. Absolutely 

 pure water cannot be obtained, and the table of Nernst's experimental 

 results, given on p. 242, shows too small a range of concentrations to fairly 

 test this equation. Nevertheless, cases will be described later in which 

 high potential-differences were observed when the concentration of the 

 ions on one side was made very small. 



When the solutions of two different electrolytes are placed in contact, 

 similar things occur. Thus (Nernst) let us suppose that we have a 

 solution of hydrochloric acid in contact with one of lithium bromide. On 

 the one hand more hydrogen ions than chlorine ions will diffuse from the 

 acid solution into the other, and therefore the salt solution will receive a 

 positive charge. On the other hand, more bromine ions than lithium ions 

 will diffuse from the salt solution into the acid, and thus the potential 

 difference will be increased. 



When a metal dissolves in a solution, Nernst traces an analogy with 

 the evaporation of a liquid. He ascribes to each metal a ' solution -pres- 

 sure ' with regard to water, depending only on the temperature, which 

 tends to drive the metal into solution in the form of positively charged 

 ions. But this process will electrify the solution positively, and leave 

 the metal negatively charged. Electric forces will therefore be set up, 

 which oppose the further solution of the metal, and seek to drive back 

 to it the ions already in solution. The electrostatic capacities of the ions 

 are very great, and hence equilibrium may be reached long before a weigh- 

 able quantity has been dissolved. 



As the quantity of ions in solution increases, we may get equilibrium 

 set up, the solution pressure being balanced by the osmotic pressure of 

 the dissolved ions and the electrostatic forces of their charges. This 

 happens, for example, when silver is dipped into a solution of sodium 

 chloride. If, however, the solution pressure is very great, the electric 

 forces may reach such an amount that positive ions must be driven out of 

 the solution. Such cases occur when hydrogen is evolved from acids or 



