62 Mr Ghittock, The Migration Constants of 



obtained with the most dilute solutions are not very trustworthy, 

 mainly owing to the fact that the measured resistances did not 

 remain constant, but generally increased with time. We can 

 easily see however that the change is too great to be explained 

 by a decrease in the mobility of the hydrogen ion. It has already 

 been mentioned that the curve obtained by plotting the con- 

 ductivity A; of a solution of hydrochloric acid against the concen- 

 tration n is a straight line which does not pass through the 

 origin ; it can however be made to do so by increasing the values 

 of A; by a constant quantity, equal to 3"7 x 10~®. This " corrected" 

 curve we may then take to represent the relation between k and n 

 which would hold if the acid were completely ionized, and the 

 hydrogen ion possessed its maximum mobility. From the difference 

 between the ordinates of the actual and the " corrected " curve 

 for any given value of n, we can find what reduction in the 

 velocity of the hydrogen ion would produce the observed dimi- 

 nution of conductivity. Making the calculation for a concentration 



6 X 10~* (n^ = '084), we find that the decrease in velocity would 

 be such as to cause an increase in the migration constant from 

 •167 (the normal value) to -170. The value given by the curve 

 (Fig. 2) for this concentration is "lOl. The theory of diminished 

 mobility of the hydrogen ion is thus seen to be insufficient to 

 account for the observed change. 



Let us now consider the alternative hypothesis, that the in- 

 crease in the migration constant is an apparent one merely, and 

 is due to the presence, in addition to the acid, of some neutral 

 substance of which the velocities of the anion and cation are 

 more nearly equal to one another than are those of hydrogen and 

 chlorine. Whetham and Paine have calculated the effect of such 

 an impurity, and have shown that if the difference of mobility 

 of its anion and cation is small compared with the mobility of 

 the hydrogen ion, the migration constant is increased in the ratio 

 {ku -f k'v)/{k + k') u, where k, k' are the partial conductivities of 

 the hydrochloric acid and of the second substance respectively, 

 u the mobility of the chlorine ion, and v that of the hydrogen 

 ion. If then we calculate from this result the value of k' which 

 would give the observed rise in the migration constant, we find 

 k' = 8-7 X 10-«. 



The conductivity of the water used as solvent in the two 

 experiments, in which the concentration was approximately 

 6 X 10~* gram-equivalents, was 9"7 x 10~^ reciprocal ohms. It 

 is clear therefore that this water did not contain a sufficient 

 quantity of any neutral salt to produce the observed effect. It 

 was preserved in vessels of Jena glass or of platinum ; the pipette 

 in which the solutions were made up, and the migration cell 



