ELECTROLYTES AND THEIR ACTION 191 



done in compressing a gas isothermally from a pressure p to P. This is, as we 

 have seen (page 35 above), 



RT log,? 

 * e p 



We may, in fact, regard the two pressures of the formula as being the osmotic 

 pressure of the metallic ions of the solution (;:>) and the electrolytic solution 

 pressure of the metallic electrode (P). We have, then, merely to express the 

 terms of this formula in the appropriate electrical units in order to obtain the 

 relation between potential and concentration of ions in the solution. This is 

 done by dividing by the charge in coulombs on one gram ion, the Faraday constant ; 

 by doing this, we convert pressure in mechanical units into electrical force. If 

 the ion in question is multivalent, the Faraday constant (F) must naturally be 

 multiplied by the number of charges carried, that is by the valency (n). R, the 

 gas constant, must also be expressed in electrical units. We have, then : 



RT, P 



^F lo S' 



R, in electrical units, is 8-3, and F, in coulombs, is 96,540, so that, at the 



RT 



temperature of 18 ( = 273 + 18 absolute), the value of -, when multiplied by 



F 



2 - 3 to allow the use of ordinary logarithms, becomes 



8-3x291x2-3 

 96,540 



Another method of calculating this number will be found in the book by Nernst 

 (1911, p. 753). 



We need, then, only to know P, the electrolytic solution pressure of the metal 

 used, in order to be able to determine p, the osmotic pressure of the ions in the 

 solution and, therefore, their concentration. P has been determined for a number 

 of metals. In the case of a concentration battery, it is eliminated thus : 



The total electromotive force of the combination is 



RT , P RT , P RT , /P P \ RT , , RT , . 



or ~ ** 



where p 1 and p 2 are the respective concentrations of the two solutions. 



We may note that the electrolytic solution pressure may be looked upon as that osmotic 

 pressure of the ions in the solution which just balances the tendency of the ions of the 

 electrode to pass out ; so that the electrode would have zero potential if it were possible to 

 obtain a solution of the correct concentration. 



Certain metals, such as platinum and copper, have a very low electrolytic solution pressure, 

 so that they are always positive in solutions of their salts, and it will be clear that the higher 

 the concentration of the salt is, the greater will be its tendency to send positive ions into the 

 metal, or, in other words, the greater will be its potential. Ziuc, on the other hand, is an 

 example of a metal with a very high electrolytic solution pressure, so that the osmotic pressure 

 of the ions in solutions of its salts will always be lower than its own ; in this case the potential 

 will be higher, the lower the concentration of the solution, since it is due to the sending out of 

 ions by the electrode. 



We may now proceed to the description of the hydroyen electrode. It will 

 have been sufficiently obvious from the preceding pages that, if we could make an 

 electrode of this gas and immerse it in a solution containing hydrogen ions, that 

 is, an acid solution, we should have the means of measuring the concentration of 

 the hydrogen ions by the potential of the electrode. It will probably occur to the 

 reader that, if we saturate palladium with hydrogen, we have what is required so 

 long as our solution does not attack the metal chemically. It will, of course, be 

 remembered that the potential is determined only by ions common to both 

 electrode and solution. Palladium, however, is attacked by some acids which we 

 require to take account of hydrochloric acid, for example. We must therefore 

 use platinum, which also takes up hydrogen, although in less amount than 

 palladium does, so that it needs more care to saturate it and keep it saturated. 

 In practice, the electrode is sometimes made of gold, merely plated with platinum 



