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19-6 Free Energy Change and Equilibrium

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Free Energy Change and Equilibrium

Condensation Equilibrium Vaporization

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Relationship of ΔG° to ΔG for Non-standard Conditions

2 N2(g) + 3 H2(g) 2 NH3(g)

ΔG = ΔH - TΔS ΔG° = ΔH° - TΔS°

For ideal gases ΔH = ΔH°

ΔG = ΔH° - TΔS

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Relationship Between S and S°

qrev = -w = RT lnVf

Vi

ΔS = qrev

T= R ln

Vf

Vi

ΔS = Sf – Si = R lnVf

Vi

= R lnPi

Pf

= -R lnPf

Pi

S = S° - R ln

P

P°= S° - R ln

P1

= S° - R ln P

Slide 5 of 44

N2(g) + 3 H2(g) 2 NH3(g)

SNH3 =

SNH3 – Rln PNH3

SN2 =

SN2 – Rln PN2

SH2 =

SH2 – Rln PH2

ΔSrxn = 2(SNH3 – Rln PNH3

) – (SN2 – Rln PN2

) –3(SH2 – Rln PH2

)

ΔSrxn = 2 SNH3 – SN2

–3SH2+ Rln

PN2PH2

PNH3

2

3

ΔSrxn = ΔS°rxn + RlnPN2

PH2

PNH3

2

3

Slide 6 of 44

ΔG Under Non-standard Conditions

ΔG = ΔH° - TΔS ΔSrxn = ΔS°rxn + RlnPN2

PH2

PNH3

2

2

3

ΔG = ΔH° - TΔS°rxn – TR lnPN2

PH2

PNH3

2

2

3

ΔG = ΔG° + RT lnPN2

PH2

2

PNH3

2

3

ΔG = ΔG° + RT ln Q

Slide 7 of 44

ΔG and the Equilibrium Constant Keq

ΔG = ΔG° + RT ln Q

ΔG = ΔG° + RT ln Keq= 0

If the reaction is at equilibrium then:

ΔG° = -RT ln Keq

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Criteria for Spontaneous Change

Every chemical reaction consists of both a forward and a reverse reaction.

The direction of spontaneous change is the direction in which the free energy decreases.

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Significance of the Magnitude of ΔG

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19-7 ΔG° and Keq as Functions of Temperature

ΔG° = ΔH° -TΔS° ΔG° = -RT ln Keq

ln Keq = -ΔG°

RT=

-ΔH°

RT

TΔS°

RT+

ln Keq = -ΔH°

RT

ΔS°

R+

Slide 11 of 44

Van’t Hoff Equation

If we evaluate this equation for a change in temperature:

ln = -ΔH°

RT2

ΔS°

R+

-ΔH°

RT1

ΔS°

R+-

=-ΔH°

R

1

T2

1

T1

-

Keq1

Keq2

ln Keq1

Keq2

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Temperature Dependence of Keq

ln Keq = -ΔH°

RT

ΔS°

R+

slope = -ΔH°

R

-ΔH° = R slope

= -8.3145 J mol-1 K-1 2.2104 K

= -1.8102 kJ mol-1

Assume ΔH° and ΔS° do not vary significantly with temperature.