# when do you use 0= delta G naught + RTlnK? I know how to use the equation to find K, but when is the equation above used?

Gibbs Free Energy and Equilibrium

(using text Chemistry the Central Science)

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Gibbs free energy ....

The Gibbs free energy expression for non-standard conditions

ΔG = ΔG° + RTlnQ ........... Q is the reaction quotient(*)

If a system is at equilibrium, then ΔG = 0 an Q = K

0 = ΔG° + RTlnK

ΔG° = -RTlnK

* The expression for the reaction quotient looks just like the equilibrium expression, but does not include equilibrium concentrations. Q might be based on the initial concentrations

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• ΔG° = Standard Gibb's free energy (in J mol⁻¹)

R = Gas constant = 8.314 J mol⁻¹ K⁻¹

T = Temperature (in K)

K = equilibrium constant

The expression 0 = ΔG° + R T ln(K) can be used in 2 cases:

Case 1: Rearrange to ΔG° = R T ln(K)

Calculate the standard Gibb's free energy, ΔG°, at a certain temperature when the equilibrium constant, K, is known.

Case 2: Rearrange to ln(K) = ΔG° / (R T)

Calculate the equilibrium constant, K, at a certain temperature when the standard Gibb's free energy, ΔG°, is known.

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