When considering the relationship among standard free energy change, equilibrium constants, and standard cell potential, the equation δg∘=−rtlnk is

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used to find the standard cell potential given the standard free energy change

used to find the standard cell potential given the equilibrium constant

used to find the equilibrium constant given the standard cell potential

used to find the equilibrium constant given the standard free energy change

ΔG° = - RTLnK is used to find the standard cell  potential given the equilibrium constant

Explanation:

for an ideal disolution:

⇒ ΔG = RT∑ni LnXi

∴ ΔG = ( μi - μi*)ni

∴ μ : chemical potential

∴ μ*: chem. potential of the pure component at T and P.

⇒ ΔG = μi - μi* = RT LnXi

for a equilibrium reaction:

⇒ ∑ νi*μi = 0

⇒ ΔGr = ΔG°+ RT Ln Kx = 0

⇒ ΔG° = - RT LnKx

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