CHAPTER 5
EQUILIBRIA AND REACTIONS INVOLVING PROTONS
97
Expressing the equilibrium constant in terms of the partial pressures:
(db5.6)
allows the standard Gibbs energy difference to be written in terms of the equilibrium
constant:
(ΔG) rec = 0 = (ΔG)° rec + RT ln K eq
(db5.7)
y = e
x then ln y = x
For a more general situation, the chemical potential of the ith molecule can be related to
what is termed the acti9ity, a i , according to:
μ i = μ
0
i + RT ln a i
(db5.8)
The activity is a measure of the concentration of a molecule. For an ideal solution, the activity
is equal to the mole fraction. For a nonideal solution, the activity of the ith molecule is proportional to the mole fraction, x i , and the acti9ity coefficient, γ, according to:
a i = γ i x i
(db5.9)
For the cases under consideration, solutions are considered to be ideal with γ = 1. For the
reaction shown (eqn 5.3), the Gibbs energy of reaction can then be written as:
(ΔG) rec = dμ D + cμ C − bμ B + aμ A
(db5.10)
Substituting the expression for activity (eqn db5.8) yields:
(ΔG) rec = d(μ
0
D + RT ln a D ) + c(μ
0
C + RT ln a C ) − b(μ
0
B + RT ln a B ) + a(μ
0
A + RT ln a A )
(ΔG) rec = (dμ
0
D + cμ
0
C − bμ
0
B − aμ
0
A ) + RT(d ln a D + c ln a C − b ln a B − a ln a A )
(db5.11)
The standard terms can be collected and the terms depending on the activities can be
rewritten:
(ΔG)° rec = (dμ
0
D + cμ
0
C − bμ
0
B − aμ
0
A )
(db5.12)
(db5.13)
RT(d ln a D + c ln a C − b ln a B − a ln a A ) = RT
a a
a a
c d
a b
ln
C D
A B
K
e
eq
G
RT
rec
( )
=
−
°
Δ
K
P
P
eq =
B
A
9781405124362_4_005.qxd 4/30/08 19:06 Page 97
EQUILIBRIA AND REACTIONS INVOLVING PROTONS
97
Expressing the equilibrium constant in terms of the partial pressures:
(db5.6)
allows the standard Gibbs energy difference to be written in terms of the equilibrium
constant:
(ΔG) rec = 0 = (ΔG)° rec + RT ln K eq
(db5.7)
y = e
x then ln y = x
For a more general situation, the chemical potential of the ith molecule can be related to
what is termed the acti9ity, a i , according to:
μ i = μ
0
i + RT ln a i
(db5.8)
The activity is a measure of the concentration of a molecule. For an ideal solution, the activity
is equal to the mole fraction. For a nonideal solution, the activity of the ith molecule is proportional to the mole fraction, x i , and the acti9ity coefficient, γ, according to:
a i = γ i x i
(db5.9)
For the cases under consideration, solutions are considered to be ideal with γ = 1. For the
reaction shown (eqn 5.3), the Gibbs energy of reaction can then be written as:
(ΔG) rec = dμ D + cμ C − bμ B + aμ A
(db5.10)
Substituting the expression for activity (eqn db5.8) yields:
(ΔG) rec = d(μ
0
D + RT ln a D ) + c(μ
0
C + RT ln a C ) − b(μ
0
B + RT ln a B ) + a(μ
0
A + RT ln a A )
(ΔG) rec = (dμ
0
D + cμ
0
C − bμ
0
B − aμ
0
A ) + RT(d ln a D + c ln a C − b ln a B − a ln a A )
(db5.11)
The standard terms can be collected and the terms depending on the activities can be
rewritten:
(ΔG)° rec = (dμ
0
D + cμ
0
C − bμ
0
B − aμ
0
A )
(db5.12)
(db5.13)
RT(d ln a D + c ln a C − b ln a B − a ln a A ) = RT
a a
a a
c d
a b
ln
C D
A B
K
e
eq
G
RT
rec
( )
=
−
°
Δ
K
P
P
eq =
B
A
9781405124362_4_005.qxd 4/30/08 19:06 Page 97