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CHAPTER 6
CHEMICAL EQUILIBRIUM
Spontaneous process involving a reactive mixture of gases
• Two new state functions
• A: criterion for determining if a reaction mixture will evolve
towards the reactants or products at const V and T
• G: criterion for determining if a reaction mixture will
evolve towards the reactants or products at const P and T
•
Gibbs Energy and Helmholtz Energy
• Spontaneous process: S +Ssurroundings > 0
• Spontaneity and equilibrium defined using only properties
of the system rather than the combination of system and
surroundings
Clausius inequality
Isolated system: dU = 0 and w = 0
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Systems Interacting with Environment
• For isothermal processes, dT = 0, so TdS = d(TS)
• Helmholtz free energy, A = U – TS
• Maximum work a system can do on the surrounding in
an isothermal process
Helmholtz Free Energy
• At const V, dV = 0, so
0
• If nonexpansion work is not possible in the transformation,
0
• Definition of spontaneity and equilibrium
For processes
taking place at
const V and T
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Gibbs Free Energy
• Reactions at const P and T, PdV = d(PV) and TdS = d(TS)
• Gibbs free energy, G = H - TS
If nonexpansion work is not possible
Maximum
nonexpansion
work
Spontaneity Criterion
• Clausius inequality,
• A and G
• only use macroscopic variables of the system
• A: maximum work done on the surroundings at
constant T and V
• G: maximum nonexpansion work done on the
surroundings at constant T and P
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Implication on Heat Engine vs Fuel Cell
• Heat engine: conversion of heat to work at an efficiency <
100% (second law)
• Fuel cell: nonexpansion work from G, could reach 100%;
no heat is involved in the conversion
Direction of a Chemical Reaction
• At const T and P,
• The entropic contribution to GR is greater at higher temperature
• A chemical transformation is always spontaneous if HR < 0
(exothermal) and SR > 0
• A chemical transformation is never spontaneous if HR > 0
(endothermal) and SR < 0
• For all other cases, the relative magnitudes of HR and SR
determine if the chemical transformation is spontaneous.
• If a chemical reaction is not spontaneous, then the reverse process
is.
• If GR = 0, the reaction mixture is at an equilibrium, and neither
direction of change is spontaneous.
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Helmholtz Free Energy
• At constant V and T, and no nonexpansion work, dA < 0
• In a chemical transformation at constant T and V
Differential Forms of U, H, A, and G
• U and H: changes in energy for a process
• A and G: direction of the change and the maximum work
allowed
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U = U(S, V)
H = H(S, P)
A = A(T, V)
G = G(T, P)
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Maxwell Relations
• U is a state function, so
,
,
Dependence of G and A on P, V, and T
Dependence on P
P = 1 bar
Solids or liquids
Ideal gases
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∆
Dependence on T
Gibbs-Helmholtz equation
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Example 6.4
• The value of ∆
°
for Fe(g) is 370kJ/mol at 298K, and
∆
for fe(g) is 416.3 kJ/mol at the same temperature.
Assuming ∆ ° is constant in the interval 250 – 400 K,
calculate ∆ ° for Fe(g) at 400K.
°
Gibbs Energy of a Reaction Mixture
Chemical potential
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Chemical Potential
• At constant T and P,
• Transport will occur spontaneously from a region of high
chemical potential to another of low chemical potentials
(extraction, phase transition, etc)
• At equilibrium, the chemical potential of each species is
the same throughout a mixture
Gibbs Energy of a Gas in a Mixture
<
Mixing of the two subsystems
is spontaneous if not
separated by the membrane
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Calculating Gmixing
Mixing of Two Gases
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Calculating GR for a Chemical Reaction
for a pure
element in its
standard
reference state
Equilibrium Constant for a Mixture of Ideal
Gases
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Reaction Quotient of Pressures (QP)
Chemical Equilibrium
• At equilibrium, GR = 0, and QP = KP
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Variation of KP with Temperature
Gibbs-Helmholtz equation)
H°R
independe
nt of T
Equilibrium Involving Ideal Gases and
Solid or Liquid Phases
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Expressing Equilibrium Constant in Terms
of Mole Fraction
Expressing Equilibrium Constant in Terms
of Molarity
PV=nRT, so c = n/V = P/RT
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Dependence of the Extent of Reaction on
T and P
Extent
of
reaction
• If GR < 0, the reaction proceeds spontaneously as written
• If GR > 0, the reaction proceeds spontaneously in the
opposite direction
• If GR = 0, the reaction system is at equilibrium and there
is no direction of change.
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