ELECTRODE POTENTIALS 157 



centration of the dissolved Ag+-ions. On the other hand, the 

 addition of NaCl would precipitate almost all of the Ag+ as AgCl, 

 and only insofar as the precipitation is concerned has NaCl an effect 

 upon the potential. 



Therefore, at the very beginning of our theoretical derivation of 

 Nernst's electrode potential we shall state the experimental fact 

 that the potential difference of a metal toward a solution depends 

 only upon the concentration of the ions of the same metal present 

 in the solution. This can be formulated as: 



^ = f (c) 



where tt is the potential and c is the concentration of the ionic species 

 concerned. Now it is our purpose to define the function f (c) in 

 greater detail. To this end let us utihze the principle of thermo- 

 dynamics : 



When a chemical system passes reversihly from one state into another, 

 the maximal work which can he gained from such change of state is 

 independent of the manner in which this change occurs as long as it 

 remains reversible. 



Now then, when a metal electrode is used as one pole of a galvanic 

 element, experience shows that the process occurring at this electrode, 

 on closing the circuit, is in many cases reversible. According to the 

 conditions and according to the direction of the resulting current, 

 the metal will be either dissolved or deposited. Thus, if the current 

 is allowed to flow until one gram ion of Ag+ is dissolved, and then by 

 means of another source of current an oppositely directed current 

 of the same ampere-hour value as the first is sent through the same 

 system, then exactly the same amount of silver will be deposited as 

 had been previously dissolved. Hence the process is reversible. 

 The initial and final states of this system (if the process is not re- 

 versed) differ, inasmuch as at the end there is one gram-ion of Ag+ 

 more in the solution than in the beginning. This change in the 

 system can be brought about in another reversible way, different 

 from the electrolytic process, i.e., by removing water from the solution 

 until it is correspondingly concentrated and then restoring the 

 volume by the addition of a solution of the same higher concentration. 

 The removal of the water must needs be performed in a reversible 

 manner, such as by means of an osmotic piston impermeable to 

 Ag-ions. With such a piston the solution is compressed, as it were^ 

 until its concentration reaches the desired value. 



