Physical Chemistry
Lecture 26
Spontaneity, Reversibility, and
Equilibrium in Chemical Reactions
Spontaneity
At constant T and P, the criterion for
spontaneity
∆G ≤ 0
For a chemical reaction, the process is
Reactants → Products
The difference in Gibbs energy of the
standard-state products and reactants, ΔGθ,
as one measure of a reaction’s energetic
change
∆Gθ (T ) = ∑ν k ∆Gkθ, formation (T )
k
Ways to calculate ΔGθ from tables
(example: Boudouard reaction)
CO2 (g) + C (gr) → 2 CO (g)
Gibbs energies of formation
∆Gθ
= 2(−137.268 kJ ) − (−394.383 kJ ) − 0 kJ
= 119.847 kJ
From ΔHθ and ΔSθ
∆H θ
= 2(−110.525 kJ ) − (−393.509 kJ ) − (0 kJ ) = 172.459 kJ
∆S θ
= 2(197.674 J / K ) − 213.74 J / K
− 5.740 J / K
∆Gθ
= ∆H θ − T∆S θ
= 120.024 kJ
− (298.15 K )(175.87 × 10− 3 kJ / K )
= 172.459 kJ
Not quite the same


Rationalized tables
Expect some slight differences
= 175.87 J / K
Ways to calculate ΔGθ from tables
(example: Boudouard reaction)
CO2 (g) + C (gr) → 2 CO (g)
From tables of Φ0
∆H 0
= 2(−113.81kJ ) − (−393.17 kJ ) − (0 kJ ) = 165.5 kJ
∆φ0
= 2(168.4 J / K ) − (182.3 J / K ) − 2.2 J / K
∆Gθ
= ∆H 0
− T∆φ0
= 165.5 kJ
= 152.3 J / K
− (298.15 K )(152.3 × 10− 3 kJ / K )
= 120.1kJ
For some reactions, one may use Φ’, which
is a similar function based on ΔHθ(298.15K),
rather than ΔH0
∆Gθ
= ∆H θ (298.15 K ) − T∆φ '
Standard Gibbs energy
changes at 298.15 K
Reaction
H2 (g) + ½ O2 (g) → H2O (l)
O2 (g) + O (g) → O3 (g)
3/2 O2 (g) → O3 (g)
C (gr) + CO2 (g) → 2 CO (g)
ΔGθ (kilojoules)
-237.1
-68.5
+163.2
+119.8 - 120.1
CH4 (g) + ½ O2 (g) → H3COH (l)
-115.6
CH4 (g) + ½ O2 (g) → H3COH (g)
-111.2
AgCl (s) + ½ Br2 (l) → AgBr (s) + ½ Cl2 (g)
+100.8
Br (g) + Cl (g) → BrCl (g)
-189.1
SO2 (g) + O3 (g) → SO3 (g) + O2 (g)
-234.1
Equilbrium in chemical reactions
Equilibrium at constant T and P
ΔG = 0
For a chemical reaction occurring under any
conditions
∆G = G products
=
∑ν
k
= ∆Gθ
k
− Greactants
µk
=
∑ν
k
µ kθ
k
+ RT ∑ν k ln ak
k
+ RT ln ∏ aνk k
k
= ∆Gθ
+ RT ln Q
Under equilibrium conditions, this gives the relation to
the equilibrium constant, Ka
0 = ∆Gθ + RT ln K a
Equilibrium constants and
standard Gibbs energy changes
The standard Gibbs energy change and the
equilibrium constant measure the same thing
∆Gθ = − RT ln K a
Reaction
Ka
ΔGθ (kilojoules)
H2 (g) + ½ O2 (g) → H2O (l)
3.45×1041
-237.1
O2 (g) + O (g) → O3 (g)
1.00×1012
-68.5
3/2 O2 (g) → O3 (g)
2.56×10-29
+163.2
C (gr) + CO2 (g) → 2 CO (g)
0.91-1.17×10-21
+119.8 - 120.1
CH4 (g) + ½ O2 (g) → H3COH (l)
1.78×1020
-115.6
CH4 (g) + ½ O2 (g) → H3COH (g)
3.03×1019
-111.2
AgCl (s) + ½ Br2 (l) → AgBr (s) + ½ Cl2
(g)
2.19×10-18
+100.8
Br (g) + Cl (g) → BrCl (g)
1.34×1033
-189.1
SO2 (g) + O3 (g) → SO3 (g) + O2 (g)
1.03×1041
-234.1
Summary
Energy changes determine the viability of a
reaction
Standard free energy change can indicate
something about the course of reaction
ΔGθ(T) and Ka(T) are different measures of
the same quality of a chemical reaction
Calculation of ΔGθ(T) and Ka(T)


Directly from tabulations
Indirectly through tabulations of ΔHθ(T) and
ΔSθ(T)