BY MIXTURES OF ELECTROLYTES. BARNES. 157 



It is difficult to estimate the limit of error of the above 

 observations. The observed values are in all cases means of at 

 least three observations, which were found to differ from their 

 mean values in different cases by very different amounts up to 

 0.001 degree. There are also many sources of error in the 

 calculations and they do not admit of exact valuation. As & 

 rough estimate the limit of error due to both observation and 

 calculation may probably be put at 0.0015 degree. 



If this estimate is approximately correct, the above table 

 shows that the agreement between the observed and calculated 

 values is very satisfactory for both mixtures of potassium 

 chloride and sodium chloride, and of sodium chloride and hydro- 

 chloric acid. 



Mixtures of Solutions of Three Electrolytes. 



In the case of mixtures of the three electrolytes used as 

 equal volumes of the simple solutions were mixed, and there 

 was no change of volume on mixing, and as each molecule of 

 these electrolytes breaks down into two ions, expression (2) 

 becomes 



A=$L M i w i( 1+ *i) + M 2 7i 2 (l + 2 ) + M 3 n a (l + a )] (5) 



where the ris are the concentrations of the constituent solutions. 

 Thus in any mixture the ris are known, the M's can be obtained 

 as above, and the as can be determined by the method given 

 below. 



Determination of the lonization Coefficients in Mixtures of 

 Three Electrolytes. 



1 Professor MacGregor has shown how to obtain equations 

 sufficient for finding the ionization coefficients in a mixture of 

 any number of electrolytes having a common ion, and how to 

 solve them by a graphical procedure. As in the case of mixtures 

 of two electrolytes, 2 1 have, in the present case also, transformed 



1 Trans. Roy. Soc. Can. (2), 2, 69, 1896-97. 

 * Trans. N. S. Inst. Sci., 10, 124, 1899-1900, 



