RICHARDS. — CHANGING HEAT CAPACITY. 313 



In this paper galvanic cells have been used as the most convenient 

 means of measuring change of free energy, and therefore of testing the 

 relation of this quantity to chemical affinity, change of total energy, heat 

 capacity, and contraction of volume. It is clear, however, that all reac- 

 tions, including such physical ones as vaporization, should indicate the 

 same relationship. 



As examples of the effects of changing heat capacity upon free energy, 

 the familiar successes and failures of the law of Guldherg and Waage may 

 be cited. In the most frequent case, when no outside work is done, the 

 concentrations adjust themselves until their combined effect just balances 

 the algebraic sum of the other sources of free energy.* The chief of these, 

 the sum of the chemical affinities C concerned, has already been discussed 

 in a previous paper ; but to this must be added the free-energy change 

 concerned in change of heat capacity p. Since there is now no outside 

 work, equation on page 309 becomes 



o = r Tin ^-^ - (or - mt 



c . . . 



or 



XT\n~°^ = ©-$; 



c . . . 



therefore In ^ - = ®^2 = " k ." 



c . . . A 1 



Obviously this value will be constant only when the work concerned 

 in the change of the heat capacity and the chemical affinity alter in the 

 same way at the same time. In many cases this simultaneous change 

 actually occurs, especially when the substances concerned are all similar, 

 as in the case of the ester-formation, or the dilution of weak acids. The 

 slight change in the heat capacity in these cases is not enough to cause a 

 serious effect on the result. 



The amount of the irregularity is often too small to be observed, but a 

 single example may be given in order to show the real analogy to the case 

 of the galvanic cells. It is well known, from the results of Berthelot and 

 Saint Gilles and others, that the formation of ethyl acetate from equiva- 

 lent amounts of alcohol and acetic acid is a reaction which attains equi- 

 librium when two-thirds completed. That is to say, the tendency to run 



* "The Driving Tendency of Physico-chemical Reaction," Richards, Journ. 

 Phys. Chem., 4, 385 (1900). 



t In this case, since (£, — ^ is working in the opposite direction from the other 

 term, its sign will be minus. 



