RICHARDS. CHANGING HEAT CAPACITY. 315 



the equation of van't Hoff is obtained only when P — 0, that is to say, 

 when the heat capacity remains unchanged during the reaction. Evi- 

 dently, therefore, the equation of van't Hoff, even in its differential form, 

 represents an approximation of only the same order of accuracy as Ber- 

 thelot's rule, and its deviations from exact fulfilment depend upon the 

 same modifying circumstance. This fact also was inferred by Lewis in 

 the paper already cited on theoretical grounds. 



The study of the preceding data shows at once the reason why 

 Berthelot's " rule of maximum work " holds in so many cases. "When- 

 ever the change of heat capacity is negligible, the total energy seems to 

 express both the free energy and the attractive affinity. In most cases 

 of simple reactions, the change of heat capacity is very small, and in 

 such cases Berthelot's rule applies. Even in such an intense reaction as 

 that of magnesium upon plumbic oxide the heat capacity changes by only 

 about 6 mayers per gram molecule, which probably could not cause a 

 difference of more than 10 kilo-joules between the change of free energy 

 due to affinity and the change of total energy, judging from the figures 

 on page 297. This is a quantity so small in relation to the total heat of 

 reaction (392 kilojoules) that it would not be noticed in an approximate 

 comparison. When concentration effects come into play, in such simple 

 reactions, it is evident that the heat of reaction expresses the affinity more 

 nearly than the total free energy change, although of course it does not 

 express the tendency of the reaction to take place. 



The free energy of a reaction is that which can overcome outside 

 obstacles, and hence can enable the change to occur. The heat of 

 reaction seems to be due primarily to affinity, but its magnitude is 

 modified by change of heat capacity. Hence a cooling reaction can 

 occur from two causes : first, because of the loosening of affinities by 

 an overpowering concentration effect working against those affinities, 

 where A is positive in the expression, — 



A = HTln- A 1} 



c n 



and secondly, because of a sudden increase in heat capacity during the 

 reaction which causes a lowering of temperature without change in 

 the quantity of heat present. These two effects often occur together, 

 because the release from the compression caused by chemical union 

 often involves gain of heat capacity. The former of these cooling 

 causes is strictly endothermic in the sense that heat energy disappears, 

 but the latter is not necessarily so, although it of course always tends to 



