INFLUENCE OF TEMPERATURE ON CHEMICAL REACTION 215 
laws of energy as applied to molecular systems : the common achieve- 
ment of Horstmann, Willard Gibbs and van t'Hoff. It possesses an 
independent interest in yielding yet another concordance between the 
implications of the molecular-kinetic and thermodynamical views of 
nature; while demonstrating anew the consistence of both with 
experimental results. 
Now, the general effect of temperature changes on chemical equi- 
librium will be completely expressed by a formulation in thermodynam- 
ical terms which shows how the equilibrium constant is thus affected. 
Such an expression was worked out by van t'Hoff, who, by combining 
the fundamental equation A ~ U = T{dA/dT) with that which in 
the thermodynamical derivation of the Guldberg-Waage equation 
represents the maximal work of the chemical process, arrived at the 
expression (10) : 
'^=-^ (VI) 
This may be read: The negative temperature coefficient of the natural 
logarithm of the equilibrium constant for any reaction, dlnK/dT, is 
equal to the total energy change in the process (U) divided by the 
square of the absolute temperature, times a constant (R).^ 
While the equation of Guldberg and Waage defines the influence 
of concentration on chemical equilibrium at constant temperature, 
that of van t'Hoff shows the influence of temperature changes on the 
equilibrium thus conditioned at constant volume. The tacitly as- 
sumed premises of these formulations are easily kept in mind if, fol- 
lowing the suggestion of Nernst, we call them respectively the equa- 
tions of the reaction isotherm and of the reaction isochore. The 
equation of the isochore in its integrated form^ has been used in 
^ This is the "gas constant"; which in the equation pv = (poVo/2'/T,)T (which 
describes the behavior of a perfect gas with change of pressure and temperature) 
equals ^ofo/273. In this formulation, p a.nd v are pressure and volume at T degrees 
absolute temperature; po is one atmosphere, and Vo the gram-molecular volume. 
For other generalizations involving p and v, these quantities may be expressed of 
course in other units, with the obvious restriction that they shall be comparable 
magnitudes. 
■ 9 The integral of dlnK = - dT{UIRT^ is InK = {U/RT) + C, where C is the 
integration constant. Hence, if Ki and K2 be values of the equilibrium constant 
at Ti and T2, we get: lnK2 — InKi = U/R(ilT2 — i/Ti). This procedure pre- 
supposes that U over the interval Ti to T2 is constant. The approximation involves 
no appreciable error if this difference is small. If it is large, a general integration 
must be used. 
