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
i1
v i µ i
which leads to K, the equilibrium constant:
K
c
i1
a
v i
i,eq
where a i,eq is the equilibrium value of the activity of substance i. The equilibrium
constant is related to the standard-state Gibbs energy change of the reaction:
K e
−∆G ◦ /RT
The equilibrium constant for a reaction involving ideal gases is
K
c
i1
P i,eq
P ◦
v i
(gaseous
reaction)
The equilibrium constant for a reaction in solution is
K (γ 1 x 1 )
v 1
c
i2
(γ i m i,eq /m
◦ )
ν i
(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 expression. 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.
A D D I T I O N A L P R O B L E M S
7.66 The Haber process produces 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).
7 Chemical Equilibrium
Summary of the Chapter
For a chemical reaction at equilibrium at constant temperature and pressure,
0
∂G
∂ξ
T ,P
c
i1
v i µ i
which leads to K, the equilibrium constant:
K
c
i1
a
v i
i,eq
where a i,eq is the equilibrium value of the activity of substance i. The equilibrium
constant is related to the standard-state Gibbs energy change of the reaction:
K e
−∆G ◦ /RT
The equilibrium constant for a reaction involving ideal gases is
K
c
i1
P i,eq
P ◦
v i
(gaseous
reaction)
The equilibrium constant for a reaction in solution is
K (γ 1 x 1 )
v 1
c
i2
(γ i m i,eq /m
◦ )
ν i
(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 expression. 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.
A D D I T I O N A L P R O B L E M S
7.66 The Haber process produces 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).