ELECTRODE POTENTIALS 165 



hi being known, then h2 can be found by determining E. The 

 appHcation of this principle in practice will be discussed in detail 

 when the methods of determination of [H+] are described later. 



But at present it is always assumed that the Ho-pressure at both 

 electrodes is the same. When such is not the case, then the theory 

 of gas chain requires certain amplifications. In such a case an 

 E.M.F. is developed, even when the [H+] on both sides is the same. 

 The original equation for concentration chains 



^ RT, c, RT, c, 

 may assume the simphfied form of 



£ = ■?•"- 



F C2 



only when the constant C has the same value in both terms on the 

 right side of the equation. But this is not true when the gas pressure 

 varies, i.e., the potential of a gas electrode also depends upon the gas 

 pressure about it. Our problem now is to measure the E.M.F. of a 

 gas chain in which the [H+] is the same throughout, but in which 

 the pressure of hydrogen gas at the two electrodes is different. The 

 platinum electrodes are in equilibrium with two hydrogen atmos- 

 pheres whose respective partial pressures are pi and P2: the solution 

 in which they are immersed is the same on both sides and of the 

 same [H+] designated by h. On closing the circuit we observe 

 that on the side of the higher partial pressure H2-gas goes into solution 

 as H+-ions and on the other side gaseous hydrogen is formed. If we 

 permit the current to pass long enough until 1 mol of H2-gas dis- 

 appears on the left and as much is formed on the right side, then 

 the change of the state of the system is the same as would occur 

 when 1 mol of H2-gas passes from a vessel in which it was under a 

 pressure of pi into another whose pressure is p2. And the work 

 performed is hence equal to the work yielded by a gas, when 1 mol 

 of it expands from a pressure pi to a lesser pressure p2, or to the work 



W = RT In — . The electric work resulting in the same final state 



P2 



of the system is equal to the product of the electromotive force E 

 by the number of transported coulombs. Since 1 mol of hydrogen 



