Section 97. Ionization of the Substances. 2jj 



them is seen to be extremely large ; thus at 0.01 molal concentration the 

 constants are about 18 times as great at 18 as at 100, and 8 times as 

 great at 100 as at 156. 



The fair agreement at the same concentration and temperature of the 

 constants derived from the conductance data for the acid and from those 

 for the acid salt is also noteworthy; for, in consideration of the different 

 kinds of data and of approximate assumptions involved in the computa- 

 tions, this agreement is evidence of the substantial correctness of the 

 results. In this connection it may also be mentioned that our value (31 

 per cent) for the hydrogen-ion concentration at 100 in a 0.01 molal 

 solution of potassium hydrogen sulphate agrees almost completely with 

 the value (31.5 per cent) found by Trevor* for 0.01 molal sodium hydro- 

 gen sulphate from a study of its catalytic effect on the inversion of cane 

 sugar. 



The heat of ionization of the hydrosulphate-ion can be estimated in two 

 ways : first, from the change of its ionization-constant with the tempera- 

 ture ; and second, from existing heat-of-neutralization measurements com- 

 bined with our ionization values. Partly for the sake of a knowledge of 

 this quantity itself, and partly because an agreement of the values obtained 

 in the two ways would furnish further evidence of the correctness of the 

 ionization values derived above, it seems worth while to describe these 

 calculations and their results. 



By integrating the well-known equationf derived from the Second Law 



of Energetics ^ = ^F 9 under the assumption that the internal- 



a 1 Kl 



energy-increase Al7 attending the reaction is a linear function of the tem- 

 perature as expressed by the equation Al7 Al7 -f- aRT, we obtain the 

 expression : 



K 2 . T 2 Al/ / 1 1 \ 



log T - a log jr =~ ]r Kjr x T 2 ) 



By substituting in this the values of the ionization-constant K in one case 

 at 100 and 18 and in another case at 156 and 100$ two simultaneous 



*Z. phys. Chem., 10, 342 (1892). 



fThe application of this equation to a substance, likd hydrosulphate-ion, whose 

 dissociation does not follow the mass-action law, can hardly give accurate results ; 

 but it seems probable that it will yield a rough approximation to the truth, at any 

 rate in the case of a substance having an ionization intermediate between that of 

 salts and that of weak acids, provided the values of K at the two temperatures be 

 taken at the same concentration. 



JAs values of K at 100 and 18 we have used the means of the values derived 

 from the data for the 0.005 molal acid and for the 0.01 molal acid-salt; namely, 

 1220 X 10- 6 at 100, and 18500 X 10" at 18 ; and as values of K at 156 and 100 we 

 have used the corresponding means at 0.001 and 0.002 molal ; namely, 115 X 10- 

 at 156, and 920 X 10- at 100. We have taken for R the round value 2 calories 

 per degree. 



