88 ELECTRICAL CONDUCTIVITIES, ETC. 



solutions of such weakly dissociated substances. This method is based upon Kahl- 

 rausch's law of the independent migration velocities of the ions. If we knew the 

 value of M^ f r ^ ne sodium salt of the acid it is only necessary to subtract from this 

 the constant for sodium and add the constant for hydrogen to obtain the value of p^ 

 for the acid in question. Thus: 



M^acid =M 00 HCl+/x oo Na. salt of acid /x^NaCl. (1) 



The n x for hydrochloric acid, as calculated from the equation, /^ =245.4 +6.062 

 0.007762 2 , for the increase in conductivity with temperature (/ = temperature), is 33 1.1 

 at 14.82, while the value obtained by direct measurement is 331.0. The value of ^ 

 for sodium chloride at 12.13 calculated from the equation 



/^ =63.04+2042 -0.00823/ 2 



is 88.99, while the value found is 88.98. 



From equation (1) we see that it is also necessary to know the value of m w for the 

 sodium salt of the acid in question. This has been determined directly for a number 

 of the acids. 



Values of n x for the Sodium Salts of tlie Organ ic Acids. Ostwsdd obtained /z^ for 

 the sodium salts of the organic acids, by calculating the difference between the con- 

 ductivity of sodium chloride at a certain dilution, c. g., V = 32, and at infinite dilu- 

 tion. This difference he assumed to be constant for all sodium salts, and, therefore, 

 by adding it to the conductivity of the sodium salt of any acid at the dilution F = 32, 

 \x v for that acid could be obtained. Instead of using this method in this investigation, 

 n x for the sodium salts was determined directly from conductivity measurements. 



The sodium salts were prepared as follows: A dilute solution of the acid (usually 

 about n / 128) was titrated with a standard solution of sodium hydroxide, using a drop 

 of phenolphthaline as indicator. Alizarine is also a good indicator, and was used 

 in later work because it is less sensitive to carbonic acid. 



In a few cases the purified sodium salts were weighed out and made up to the 

 desired concentrations. The sodium hydroxide used for titrating the organic acids 

 was prepared as follows : 



One hundred grams of sodium hydroxide, purified from alcohol, was dissolved in 

 100 grams of conductivity water (obtained as above described) and the concentrated 

 solution wa* allowed to stand in a closed vessel for about a week. By that time 

 practically all the carbonate, etc., was precipitated, and there was left a perfectly 

 clear solution of sodium hydroxide, portions of which were pipetted out and diluted 

 to the proper strength with conductivity water. The dilute solution was then 

 standardized by means of the standard sulphuric acid, and otherwise. When thus 

 prepared the solution is very nearly free from carbonate, as is shown by the fact that 

 it does not give a precipitate of barium carbonate with barium hydroxide, and that 

 when titrated with indicators, both those that are sensitive and those that are not 

 sensitive to carbonates, the results are practically the same. 



The conductivities of the sodium salts of a large number of the acids used in this 

 work are given in the table on pp. 89 and 90. 



