580 



SCIENCE. 



[N. S. Vol. XX. No. 514. 



volved the assumption that the ionization 

 varies with the concentration in accordance 

 with the mass-action law— an assumption 

 which is known not to be true of the ioniza- 

 tion values derived from conductivity. The 

 assumption is, therefore, an irrational one 

 — one by which the question at issue is pre- 

 judged. What should be done in calcula- 

 ting the electromotive force so as to de- 

 termine whether the conductivity ratio 

 gives ionization values consistent with the 

 measured electromotive forces, is evidently 

 to assume that the ionization changes with 

 the concentration in the way that the con- 

 di^ctivity indicates that it does. Arrhenius 

 recognized this error and partially correct- 

 ed for it by a method of approximation. 

 I have repeated the calculations by an 

 exact thermodynamic formula based on an 

 empirical law expressing the change of the 

 conductivity ratio with the concentration, 

 to which I will refer later. The results 

 are summed up in the statement that, 

 when the conductivity-ratio is assumed to 

 represent the degree of ionization of- the 

 salt, the calctdated values of the electro- 

 motive force of cowentration cells exceed 

 the measured ones hy only about one per 

 cent, in the case of potassium and sodium 

 chloride between the concentrations of 

 1/600 and 1/20 normal. The measured 

 electromotive force corresponds to an ion- 

 ization value at the latter concentration 

 about one per cent, less than the conduc- 

 tivity ratio. 



The thermodynamic relation involving 

 heat of solution has been accurately tested 

 with only one salt— potassium perchlorate ; 

 but since it is a different salt from those 

 used in the other experiments and since its 

 concentration was fairly high— one eighth 

 normal— the result is of interest. It was 

 found that the measured heat of solution 

 was less hy only 1.1 per cent, than that 

 calculated under the assumption that the 

 conductivity ratio is equal to the degree of 



ionization. The measured heat of solution 

 corresponds to an ionization value 2^ per 

 cent, lower than the conductivity ratio. 



With respect to these small deviations of 

 the results obtained by the three methods 

 of comparison, it is important to note that 

 they lie in opposite directions, the freezing- 

 point lowering corresponding to larger 

 values of the ionization, and the measured 

 electromotive forces and heat of solution to 

 smaller ones than the conductivity-ratio. 

 This fact makes it almost certain that they 

 are due to experimental errors. Neverthe- 

 less, further exact measurements of all 

 these properties are highly desirable. 



From a theoretical standpoint these three 

 methods are based on the same hypotheses, 

 namely, that the osmotic pressure con- 

 stant for ions and un-ionized molecules is 

 identical with the gas-constant; that the 

 conductivity-ratio is a correct measure of 

 ionization, and that complex molecules or 

 ions are not present in the solution. The 

 concordance of the results furnishes, there- 

 fore, a strong confirmation of the correct- 

 ness of these fundamental hypotheses. The 

 only alternative conclusion is that an error 

 in one of these hypotheses is compensated 

 by an error of opposite effect in one of the 

 others; but it seems very improbable that 

 such a compensation could occur in the ease 

 of so many salts of different chemical na- 

 ture and different types through the range 

 of concentration (1/200-1/4 normal) for 

 which the agreement of the experimental 

 results has been shown to hold true. It is 

 certainly more consistent with the modern 

 methods of science to adopt these simpler 

 hypotheses which are in full accord with 

 the considerable number of facts thus far 

 kno-\vn, than deliberately to introduce more 

 complicated assumptions for which there is 

 at present no experimental warrant. 



The combination of these hypotheses with 

 the experimental values of the quantities 

 involved at varying concentrations makes 



