46 IONIZATION COEFFICIENTS OF CERTAIN 



The above table shews the degree of accuracy with which 

 the depression of the freezing-point can be calculated in the case 

 of simple solutions. If the ionization coefficients for the mix- 

 tures are determined by Prof. MacGregor's method as closely as 

 they are for the simple solutions by putting a=///u<, the differ- 

 ences between the calculated and observed values of the depres- 

 sions in the case of the mixtures may be expected to be no 

 greater than those of the above table. 



Depression of the Freezing -point by the Mixtures. 

 The following Table contains the observed and calculated 



CT 



values of the depression of the freezing-point in the case of the 

 mixtures examined. The observations were made in the manner 

 described above. The calculations were made by the following 

 formula for which I am indebted to Professor MacGregor : 



A=1.86(l+a 1 +a a )N/2 



where a^ and a 2 are the ionization coefficients of the respective 

 electrolytes in the mixture and N the number of gramme-equiva- 

 valents per litre in the solutions mixed, which were in all cases 

 equimolecular. This expression may be readily obtained as. 

 follows : In each litre of the mixture there will be N/4 gramme- 

 molecules of each electrolyte. There will therefore be (1 o^) N/4 

 and (1 2 ) N/4 undissociated gramme-molecules of the respec- 

 tive electrolytes, and, if we assume the ionization in each case 

 to be complete, 3a l N/4 and 3 a 2 N/4 free gramme-ions. Hence 

 the total number of undissociated gramme-molecules and free 

 gramme-ions will be (l + a l +a 2 ) N/2, and the expression for 

 the depression will consequently be as above. 



The first column of Table V gives the concentration of the 

 solutions mixed, in gramme-equivalents of anhydrous salt per 

 litre at 18C. The fifth and sixth columns give the ionization 

 coefficients of the respective electrolytes in the mixture at 0C 

 as determined by Prof. MacGregor's method. The second, third 

 and fourth give the quantities obtained directly by this method, 

 viz., the common concentration of ions, and the dilutions of the 

 respective electrolytes in the mixture. (By the concentration of 



