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Question
Obtain the relationship between ∆G° of a reaction and the equilibrium constant.
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Solution
1. Gibbs energy change for a chemical reaction is given by
ΔG = ΔG° + RT ln Q …(1)
where, ΔG° is standard Gibbs energy change that is, the Gibbs energy change when the reactants and products in a reaction are in their standard states. Q is called reaction quotient. Q is analogous to that of the equilibrium constant and involves nonequilibrium concentrations or partial pressures in case of a gaseous reaction.
2. Consider the reaction, aA + bB → cC + dD
From equation (1),
ΔG = ΔG° + RT lnQC or ΔG = ΔG° + RT lnQP
= ΔG° + RT ln`(["C"]^"c"["D"]^"d")/(["A"]^"a" ["B"]^"b")` or = ΔG° + RT ln `("P"_"C"^"c" xx "P"_"D"^"d")/("P"_"A"^"a" xx "P"_"B"^"b")`
3. When the reaction reaches equilibrium, ΔG = 0 and QC and QP become KC and KP, respectively.
Thus,
∴ 0 = ΔG° + RT lnKC or 0 = ΔG° + RT lnKP
∴ ΔG° = –RT ln KC or ΔG° = –RT ln KP
∴ ΔG° = –2.303 RT log10KC or ΔG° = –2.303 RT log10KP
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