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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

Isolated system: dU = 0 and w = 0

Clausius inequality

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• 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

Systems Interacting with Environment

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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• Reactions at const P and T, PdV = d(PV) and TdS = d(TS)

• Gibbs free energy, G = H - TS

Gibbs Free Energy

If nonexpansion work is not possibleMaximum

nonexpansionwork

• 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

Spontaneity Criterion

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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

P = 1 bar

Solids or liquids

Ideal gases

Dependence on P

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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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• 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

Chemical Potential

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°independe

nt of T

R

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

• 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.

Extent of

reaction