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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
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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
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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+
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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.
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