424 SCIENCE PROGRESS. 



It could be calculated from known data how much heat 

 would be given out or absorbed when the equivalent of 

 the first acid replaced the equivalent of the second from its 

 salt. On actually performing the experiment the thermal 

 effect was always found to be less than that calculated for 

 total replacement. The ratio then of the observed to the 

 calculated heat gave the extent to which the action had 

 progressed. Methods similar in principle were afterwards 

 employed for ascertaining such ratios of distribution, e.g., 

 the change of volume, and the change of the refractive 

 index on reaction, were measured by Ostwald instead of 

 the heat-change. When the ratios obtained by balancing 

 a series of acids against the salt of one other acid were 

 tabulated, a set of numbers resulted which were called by 

 Thomsen the "avidities" of the acids. These avidities 

 were proportional to the square root of the velocity constant 

 K. Now the constant K has an important theoretical 

 significance, inasmuch as the maximum work to be obtained 

 from a reversible chemical change isothermally conducted 

 is equal to RT log e K, where R is a numerical constant, 

 and T the temperature on the absolute scale at which the 

 equilibrium occurs. This maximum external work is the 

 difference of the "free energy" of the two systems, if we 

 employ the term in the sense proposed by Helmholtz, and 

 is not proportional to the change of total energy of the two 

 systems, i.e., to the thermal effect of the reaction. As 

 every spontaneous natural process takes place in the direc- 

 tion in which external work is performed, the total amount 

 of external work which a system can perform must have 

 a close connection with the internal forces (in our case 

 "chemical affinities") causing the change. Thus it has 

 been proposed to take the change of "free energy" as a 

 measure of the affinity instead of the change of total energy 

 adopted by the earlier thermochemists. 



Little has been done as yet towards calculating affinity 

 constants on this basis, and chemists are at present content 

 with more empirical magnitudes. The relative affinities of 

 the acids in particular have been well investigated from 

 very many different points of view, and the results obtained 



