INFLUENCE OF TEMPERATURE ON CHEMICAL REACTION 213 
That is, "The diminution in the total energy which accompanies 
any change in an isolated system is exactly equal to the work done 
by the system, less the heat absorbed."^ 
This statement simply formulates the distinction between free 
and bound energy. The two expressions may legitimately be com- 
bined, since their premises are identical, and their terms have the same 
meaning in both cases. Thus we may write (10) : 
A~U=T§ (IV) 
In this expression, we have a quantitative representation of the 
relation that exists between the free and total energies of a process, 
in terms of a quantity involving the temperature coefficient of the 
free energy. Specifically, their difference is equal to this coefficient 
multiplied by the absolute temperature. Thus, the influence of a 
change of temperature on the free energy of a process is defined by this 
formulation, as its influence on the total energy is defined by the law 
of Kirchoff, though, of course, in dissimilar terms. 
Theoretically, then, we have a sufficient analysis of the matter. 
How now may these generalizations be applied to show the actual 
influence of temperature change on reaction velocities and on equi- 
libria? 
As is well known, it has been experimentally established that the 
speed of a reaction, if this be conducted isothermally, is proportional 
to the product of the molecular concentrations of the several substances 
involved in the reaction. This generalization, the familiar concentra- 
tion law, needs only to be formulated to be recalled. To illustrate 
^ Or, *'plus the heat evolved." This sounds more natural; for commonlyj 
spontaneous chemical reactions evolve heat and do work by decrease in the total 
energy of the reacting substances. Of course, in this formulation, U, A, and Q 
may be either positive or negative quantities; and as seen above it is wholly a matter 
of taste whether in the first instance A mean work done by the system or upon it; 
Q, heat evolved or heat absorbed, and so on, providing that the equation be corre- 
spondingly written. In the formulation above, U in the positive sense is taken to be 
a diminution in total energy; because spontaneous reactions at ordinary tempera- 
tures are usually attended by such diminution, developing free energy. If, instead 
of a chemical change, a fusion had been in mind, it would have been more natural 
to think of an increase in total energy. If, then, U in the positive sense had this 
meaning, we should have written: Q = A -j- U, or U = Q — A, Q and A having 
the meanings here assigned. Every such formulation becomes clear in a physical 
sense, only by successive applications to particular cases. 
