Following Le Chatelier’s principle, the response of a system to a change
in temperature can be predicted. For a system in equilibrium, an endo-
thermic reaction will shift in favor of the products for a temperature
increase. Likewise, for an exothermic reaction, an increase in the temper-
ature will favor the reactants. Whereas Le Chatelier’s principle provides
qualitative guidelines, the effect of a temperature change on the equilib-
rium constant can be quantified by writing the Gibbs energy in terms of
enthalpy and entropy (Chapter 6):
(ΔG)°rec=(ΔH)°rec−T(ΔS)°rec (5.4)
Using eqn db5.7, this expression can be revised in terms of the equilibrium
constant:
−RTlnKeq=(ΔH)°rec−T(ΔS)°rec (5.5)
Dividing both sides of the equation by RTyields the 9 an’t Hoff equation:
(5.6)
The temperature dependence of the equilibrium constant is a straight line
when plotted as a function of 1/T, with the slope giving the enthalpy and
the intercept giving the entropy. Such a graph is commonly used to yield
the enthalpy and entropy of a reaction. For an exothermic reaction, the
slope will be positive and hence an increase in the temperature will decrease
1/T, resulting in a decrease in the equilibrium constant as predicted by
Le Chatelier’s principle.
Acid–base equilibria
Consider an aqueous solution with acids, which are proton-donating
molecules, and bases, which are proton-accepting molecules. Any given
molecule may act as either an acid or a base depending upon the condi-
tions. For example, consider a molecule that is initially protonated, HA,
which acts as an acid by giving up a proton to water. After the proton
transfer, this molecule can act as a base by taking the proton back from
A−, the conjugate base:
HA +H 2 O ↔H 3 O++A− (5.7)
In an aqueous solution, the proton is never isolated and always solvated.
However, the water molecule does not undergo a change and this
ln
() ()
K
H
RT
S
eq R
=−ΔΔrec° + rec°