Peter Atkins • Julio de Paula
Atkins’ Physical Chemistry
Eighth Edition
Chapter 7 – Lecture 1
Chemical Equilibrium
Sections 7.1 - 7.4 only
Copyright © 2006 by Peter Atkins and Julio de Paula
Homework Set #7
Atkins & de Paula, 8e
Chap 7
Exercises: all part (b) unless noted:
2, 3, 4, 5, 7, 9, 10, 12
Objectives:
• Further develop the concept of chemical potential, μ
• Apply μ to account for equilibrium composition of a
chemical reaction
• Establish relationship between Gibbs energy and the
equilibrium constant, K
• Establish the quantitative effects of pressure and
temperature on K
Equilibrium - state in which there are no observable changes
with time
Chemical equilibrium - achieved when:
•
rates of the forward and reverse reactions are equal and
•
concentrations of the reactants and products remain
constant
•
dynamic equilibrium
Physical equilibrium
H2O (l)
H2O (g)
Chemical equilibrium
N2O4 (g)
2NO2 (g)
colorless
red-brown
Fig 3.18 Gibbs energy tends to minimum at ΔT = 0, ΔP =0
dG = VdP - SdT
 G 
 G 
dG  
 dP  
 dT
 P  T
 T  P
 G 

 V
 P  T
 G 

  S
 T  P
“spontaneous” ⇒ G → min
Fig 7.1 Plot of Gibbs energy vs. extent of reaction, ξ
ξ pronounced zi
Reaction Gibbs energy:
 G 

dGr  
   T ,P
For equilibrium A ⇌ B
 G 


 B   A
   T ,P
Therefore
ΔGr = μB - μA
Exergonic and endergonic reactions
At constant temperature and pressure:
• ΔGrxn < 0 forward rxn spontaneous (Exergonic)
• ΔGrxn > 0 reverse rxn spontaneous (Endergonic)
• ΔGrxn = 0 rxn at equilibrium (Neither)
Fig 7.2 A strongly exergonic process can drive
a weaker endergonic process
Nonspontaneous,
but!!.....
Description of Equilibrium
For perfect gases: A ⇌ B
ΔG rxn  μB - μ A
o
 (μB
 RT ln PB )  (μoA  RT ln PA )

o
Grxn
PB
 RT ln
PA
o
 Grxn
 RT ln Q
At equilibrium: ΔGrxn = 0
o
0  Grxn
 RT ln K
o
ΔGrxn
 RT ln K
N2O4 (g)
Equilibrium constant
K=
2NO2 (g)
[NO2]2
[N2O4]
= 4.63 x 10-3 at 25 °C
Must be caps
aA + bB
K=
cC + dD
[C]c[D]d
Law of Mass Action
[A]a[B]b
Equilibrium will:
K>1
Lie to the right
Favor products
K<1
Lie to the left
Favor reactants
Fig 7.3 Plot of Gibbs energy vs. extent of reaction
Molecular interpretation
of tendency for ΔGr = 0
Hypothetical rxn A(g) → B(g)
(i) slope = ΔGr at all times
(ii) from Eqn. 5.18:
ΔGmix  nRT(x A ln x A  xB ln xB )
(iii) curve has minimum
corresponding to
equilibrium composition
Ways of Expressing Equilibrium Constants
K=
[C]c[D]d
[A]a[B]b
Law of Mass Action
Concentration of products and reactants may be expressed in
different units, so:
• Heterogeneous equilibria
• Homogeneous equilibria
Heterogenous equilibrium applies to reactions in which
reactants and products are in different phases
CaCO3 (s)
⇌ CaO (s) + CO2 (g)
[CaO][CO2]
Kc =
[CaCO3]
Kc = [CO2]
[CaCO3] = constant
[CaO] = constant
or
Kp = PCO2
The concentration of solids and pure liquids are not
included in the expression for the equilibrium constant
CaCO3 (s)
⇌ CaO (s) + CO2 (g)
PCO 2 = Kp
PCO 2 does not depend on the amount of CaCO3 or CaO
Homogenous equilibrium applies to reactions in which all
reacting species are in the same phase
N2O4 (g)
Kc =
[NO2
⇌
]2
2NO2 (g)
Kp =
[N2O4]
2
PNO
2
PN2O4
In most cases
Kc  Kp
aA (g) + bB (g)
⇌
cC (g) + dD (g)
Kp = Kc(RT)Dn
Dn = moles of gaseous products – moles of gaseous reactants
= (c + d) – (a + b)
Fig 7.4 Boltzmann distribution of populations of A and B
For endothermic reaction A → B
Assumption:
Similar densities of E-levels
Bulk of population is species A
Therefore:
A is dominant species at equilibrium
Fig 7.5 Plot of energy levels vs. population
For endothermic reaction A → B
Assumption:
Density of E-levels of B >>
density of E-levels of A
Bulk of population is species B
Therefore:
B is dominant species at equilibrium