508 J. W. Gihhs — Equilihriwm of Heterogeneous ISuhstances. 



ions are determined at the surface of the electrodes with reference to 

 the ion in the condition in which it is brought thei'e or taken away 

 by an electrolytic current, without any attendant irreversible pro- 

 cesses. But in a complete discussion of the properties of the surface 

 of an electrode it may be necessary to distinguish (both in respect to 

 surface-densities and to potentials) between the substance of the ion 

 in this condition and the same substance in other conditions into 

 which it cannot pass (directly) without irreversible processes. No 

 such distinction, however, is necessary when the substance of the ion 

 can pass at the surface of the electrode by reversible processes from 

 any one of the conditions in which it appears to any other. 



The formulae (687), (688) afford as many equations as there are 

 ions. These, however, amount to only one independent equation 

 additional to those which relate to the independently variable com- 

 ponents of the electi'olytic fluid. This appears from the considera- 

 tion that a flux of any cation may be combined with a flux of any 

 anion in the same direction so as to involve no electrical current, and 

 that this may be regarded as the flux of an independently variable 

 component of the electrolytic fluid. 



General Properties of a Perfect Electro-chemical Apparatus. 



When an electrical current passes through a galvanic or electro- 

 lytic cell, the state of the cell is altered. If no changes take place in 

 the cell except during the passage of the current, and all changes 

 which accompany the current can be reversed by reversing the cur- 

 rent, the cell may be called a perfect electro-chemical apparatus. 

 The electromotive force of the cell may be determined by the equa- 

 tions which have just been given. But some of the general relations 

 to Avhich such an apparatus is subject may be conveniently stated in 

 a form in which the ions are not explicitly mentioned. 



In the most general case, we may regard the cell as subject to 

 external action of four different kinds. (1) The supply of electricity 

 at one electrode and the withdrawal of the same quantity at the 

 other. (2) The supply or withdrawal of a certain quantity of heat. 

 (3) The action of gravity. (4) The motion of the surfaces enclosing 

 the apparatus, as wdien its volume is increased by the liberation of 

 gases. 



The increase of the energy in the cell is necessarily equal to that 

 which it receives from external sources. We may express this by the 

 equation 



d8 = ( F' - V") de + dQ + dW^ + d TTp, (691) 



