Concise Physical Chemistry

c07 JWBS043-Rogers September 13, 2010 11:25 Printer Name: Yet to Come

VARIATION OF THE EQUILIBRIUM CONSTANT WITH TEMPERATURE 99

7.5.1 Le Chatelier’s Principle

Le Chatelier’s principle states that, in a stressed chemical reaction, the equilibrium

will be displaced in such a way as to relieve the stress. First, we need to define

“stress.” An exothermic reaction

A→←B+q

whereqis heat given off, will be stressed backward by application of heatq—that

is, by a temperature rise. Application of heat will drive the reaction backward to give

more A and less B. The opposite will be true for an endothermic reaction. Looking

at the integrated van’t Hoff equation

ln

K′eq

Keq

=

rH◦

R

(

1

T

−

1

T′

)

we see that for a temperature riseT′>Twe have (1/T)>(1/T′). For
rH◦<0,

ln (K′eq/Keq)<0 and the new equilibrium constantKeq′ is smaller than the original

one,Keq. The thermal condition
rH◦<0 is the characteristic of an exothermic

reaction, so Le Chatelier’s principle applied to the heat of reaction agrees with the

van’t Hoff equation. Le Chatelier’s principle is a qualitative statement giving the

sign but not the magnitude of the effect of a temperature change on the equilibrium

constant.

7.5.2 Entropy from the van’t Hoff Equation

If
rH◦is independent of the temperature, then fromd
rH◦=
rCpdT=0. Since

dTis not zero,
rCpmust be zero. From

rCp=

∑

Cp(prod)−

∑

Cp(react)

the heat capacity of the reactant system must be equal to that of the product system. In

practical terms, we take this equality to be approximately true over short temperature

intervals. We have already found the equations

rG◦=−RTlnKeq

and

rG◦=
rH◦−T
rS◦

so

−RTlnKeq=
rH◦−T
rS◦