19 6 Free Energy Change and Equilibrium 1

19 -6 Free Energy Change and Equilibrium 1

Free Energy Change and Equilibrium Condensation 2 Equilibrium Vaporization

Relationship of ΔG° to ΔG for Non-standard Conditions 2 N 2(g) + 3 H 2(g) ΔG = ΔH - TΔS 2 NH 3(g) ΔG° = ΔH° - TΔS° For ideal gases ΔH = ΔH° ΔG = ΔH° - TΔS 3

Relationship Between S and S° qrev = -w = RT ln Vf Vi qrev Vf = R ln ΔS = T Vi Pf Pi Vf = R ln = -R ln ΔS = Sf – Si = R ln Pi Pf Vi P P = S° - R ln S = S° - R ln 1 P° 4

N 2(g) + 3 H 2(g) SN 2 = SN 2 – Rln PN 2 2 NH 3(g) SH 2 = SH 2 – Rln PH 2 SNH 3 = SNH 3 – Rln PNH 3 ΔSrxn = 2 (SNH 3 – Rln PNH 3) – (SN 2 – Rln PN 2) – 3 (SH 2 – Rln PH 2) ΔSrxn = 2 SNH 3 – SN 2 – 3 SH 2+ Rln ΔSrxn = ΔS°rxn + Rln 5 PN 2 PH 3 2 2 PNH 3

ΔG Under Non-standard Conditions ΔG = ΔH° - TΔS ΔSrxn = ΔS°rxn + Rln ΔG = ΔH° - TΔS°rxn – TR ln PN 22 PH 3 2 2 PNH 3 2 ΔG = ΔG° + RT ln PNH 3 PN 22 PH 3 2 ΔG = ΔG° + RT ln Q 6 PN 22 PH 3 2 2 PNH 3

ΔG and the Equilibrium Constant Keq ΔG = ΔG° + RT ln Q If the reaction is at equilibrium then: ΔG = ΔG° + RT ln Keq= 0 ΔG° = -RT ln Keq 7

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. 8

Significance of the Magnitude of ΔG 9

19 -7 ΔG° and Keq as Functions of Temperature ΔG° = ΔH° -TΔS° ΔG° = -RT ln Keq -ΔG° -ΔH° TΔS° ln Keq = = + RT RT RT -ΔH° ΔS° ln Keq = + RT R 10

Van’t Hoff Equation If we evaluate this equation for a change in temperature: ln Keq 2 Keq 1 -ΔH° ΔS° = + + RT 2 R RT 1 R ln 11 Keq 2 Keq 1 1 -ΔH° 1 = R T 2 T 1

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Temperature Dependence of Keq Assume ΔH° and ΔS° do not vary significantly with temperature. -ΔH° ΔS° ln Keq = + RT R -ΔH° slope = R -ΔH° = R slope = -8. 3145 J mol-1 K-1 2. 2 104 K = -1. 8 102 k. J mol-1 13