Physical Chemistry Third Edition

348 7 Chemical Equilibrium

Summary of the Chapter

For a chemical reaction at equilibrium at constant temperature and pressure,

0 

(

∂G

∂ξ

)

T,P



∑c

i 1

viμi

which leads toK, the equilibrium constant:

K

∏c

i 1

avi,ieq

whereai,eqis the equilibrium value of the activity of substancei. The equilibrium

constant is related to the standard-state Gibbs energy change of the reaction:

Ke−∆G

◦/RT

The equilibrium constant for a reaction involving ideal gases is

K

∏c

i 1

(

Pi,eq

P◦

)vi

(gaseous

reaction)

The equilibrium constant for a reaction in solution is

K(γ 1 x 1 )v^1

∏c

i 2

(γimi,eq/m◦)νi

(solution

reaction)

where the solvent is designated as substance number 1. For dilute solution, the(γ 1 x 1 )v^1

factor is approximately equal to unity and can be omitted from the equilibrium expres-

sion. The Gibbs–Helmholtz equation for the temperature dependence of an equilibrium

constant is

(

∂ln(K)

∂T

)

P



∆H◦

RT^2

The principle of Le Châtelier asserts that in general a system will react to lessen the

effect of a stress on an intensive variable, if it can do so. This effect was illustrated

by considering the shift in equilibrium by changing the temperature or the pressure

on a system and by adding a reactant or product to the system. The application of

the thermodynamics of chemical equilibrium to biological processes was illustrated

through a discussion of the coupling of chemical reactions and active transport.

ADDITIONAL PROBLEMS

7.66 TheHaber processproduces gaseous ammonia directly
from hydrogen gas and nitrogen gas. This process is named
for Fritz Haber, 1868–1934, a German chemist who
received the 1919 Nobel Prize in chemistry for developing

a catalyst and a set of conditions that made this process

commercially feasible. The catalyst used is a mixture of

iron oxide and potassium aluminate. The reaction is

N 2 (g)+3H 2 (g)
2NH 3 (g).