28 HYDROGEN ION CONCENTRATION 



by the heat of neutrahzation of HCl + NaOH (13700 cal., Berthe- 

 lot's value). This gives us the value of the coefficient as 



^" = - 0.0349 

 dT 



This value calculated from the author's figures given above for 

 the interval of 16 — 26° is = —0.0340, which is in good agreement 

 with the theory. 



The smaller variations in the newer as compsftred with the older 

 measurements is explained by a better elimination of errors es- 

 pecially those due to the diffusion potential. In view of the fact 

 that the very numerous studies of S0rensen were all made at the same 

 temperature, and yield a very reliable average value, while those 

 of the author cover a wide range of temperature, the S0rensen figure 

 for 18° is recommended as the most credible, and the author's 

 figures are to be used for the determination of the temperature 

 coefficient. S0rensen's figure for 18° is lO"^''-^'*, which is an average 

 obtained from a number of values varying between 10~^*-^^ and 

 IQ-u.m 'pj^g author's values for 18° obtained at different times 

 varied between IQ-^^-''^ and lO""^'*-^^ The author's average value 

 obtained in 1913 as given in the above table (7) is 10~^*-^^ which 

 agrees well with S0rensen's average. 



It will be shown later that all of the pH measurements made 

 until the present will have to be subjected to a certain correction. 

 The uncertainty is based on the following considerations. The 

 [H+] of a dilute NaOH solution is measured by comparison with 

 the [H+] of a dilute HCl solution, whose [H+] is assumed to be 

 known. On the other hand the [OH"] of the NaOH solution is 

 assumed to be known. Until recently there was no doubt as to 

 the value of the [H+] of a HCl solution of definite concentration, 

 or as to the [OH"] of a NaOH solution of definite concentration. 

 These were calculated from the respective degrees of dissociation 

 of the acid and base, which in turn were calculated by comparing 

 the molar conductivities of the solutions at a definite dilution and 

 those at infinite dilutions. As will be seen later these calculations 

 are erroneous. It is possible that the values for pkw provisionally 

 recommended above are really smaller (at most 10 per cent smaller) . 



