MIXTURES OF ELECTROLYTES MACGREGOR. 105 



solutions of the acids ; and the calculated values were found to 

 agree with those observed to within 0.5 and 0.2 per cent, respec- 

 tively. So far as result is concerned, this forms a much more 

 satisfactory test than those mentioned above ; but the number 

 of calculations is too small to exclude the possibility of accidental 

 -agreement. 



The calculation of the conductivity of a mixture of electro- 

 lytes is so severe a test of the ionisation theory of electrolysis 

 that I have thought it well to try its possibility on a larger 

 scale, especially as a considerable body of material is available 

 for this purpose in the observations of the conductivity of 

 mixtures of solutions of potassium and sodium chlorides made 

 by Bender*. The present paper contains the results of calcula- 

 tions of the conductivities of mixtures determined experimentally 

 by him. 



METHOD OF CALCULATION. 



In order to make such calculations by Arrhenius's method, it 

 Would be necessary to make a prelimmarj^ determination of a 

 number of isohydric solutions of the two salts, and to restrict 

 the calculations to very dilute solutions. They may be made 

 however, without such preliminary experiments, and without 

 such restriction, by employing a more general form of Arrhenius's 

 deduction. 



Two electrolytes, which have a common ion and are in a state 

 of equilibrium in the same solution, may be regarded as occupying 

 definite portions of the volume of the solution. If we apply the 

 equilibrium conditions to the parts of the solutions occupied by 

 the respective electrolytes, as well as to the whole solution, we 

 obtain equations which, mutatis mutandis, are identical with 

 those obtained by Arrhenius, as indicated above, for the iso- 

 hydric solutions and their mixture. Thus, if in the equations of 

 equilibrium given above, we take v l and V 2 to be the portions 

 of the volume of the mixture occupied by the respective electro- 

 lytes, and ctj and <* 2 to be their co-efficients of ionisation in the 



*Wicdemann's Annalen, xxn, p. 197, (1884). 



