PROPERTIES OF AQUEOUS SALT SOLUTIONS 315 



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. 

 Nevertheless, 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-constant 

 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, therefore, a strong confirmation 

 of the correctness of these fundamental hypotheses. The only alter- 

 native conclusion is that an error in one of these hypotheses is com- 

 pensated by an error of opposite effect in one of the others; but it 

 seems very improbable that such a compensation could occur in the 

 case of so many salts of different chemical nature and different types 

 through the range of concentration (^-g- to 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 known, 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 necessary 

 the further conclusion that the degree of ionization of salts, whether 

 derived from the conductivity-ratio or from thermodynamic relations 

 involving the equality of the osmotic pressure-constant and the gas- 

 constant, does not vary with the concentration even approximately in 

 accordance with the Law of Chemical Mass-Action. 



This empirical consequence of the fundamental hypotheses of the 

 ionic theory has led several investigators to raise a theoretical objec- 

 tion to them, it being contended that the laws of thermodynamics 

 require that the validity of these hypotheses involves that of the Mass- 

 Action Law itself. This apparent inconsistency between the inductive 

 and deductive conclusions makes it probable that some unproved, 

 erroneous assumption is tacitly involved in the theoretical derivation. 

 That there is, in fact, a possible alternative, which has, I believe, been 

 previously overlooked in the thermodynamic discussions, will be evi- 

 dent from the following considerations. The thermodynamic relations 

 between ionization and freezing-point, electromotive force, or heat of 

 solution, involve only the assumption that the work done in reversibly 

 separating water from a solution at constant concentration is equal to 



