The relationship between equilibrium constant and free energy change is represented as

Analyze the question: You need the equation linking the equilibrium constant (K) to the standard free energy change (ΔG°).

Concept: For a reaction at equilibrium, the standard free energy change is related to K by:

ΔG° = −RT ln K

where R is the gas constant (8.314 J/mol·K), T is the absolute temperature in kelvin, and K is the equilibrium constant.

• If K > 1, ln K is positive, so ΔG° is negative and the reaction is spontaneous (products favoured).
• If K < 1, ln K is negative, so ΔG° is positive and the reaction is non-spontaneous (reactants favoured).

Checking the options:

• A. ΔG° = −nFE°: This links free energy to the standard electrode (cell) potential. It is not the relationship with K.
• B. ΔG° − RT ln K: The equals sign is missing, which is clearly a typing error. The intended form is ΔG° = −RT ln K, and it is the only option with the RT ln K relationship and the correct negative sign.
• C. ΔG° = +RT ln K: The sign is wrong. This would reverse spontaneity.
• D. ΔG° = ΔH − TΔS: This is the Gibbs-Helmholtz definition of free energy. It is not in terms of K.
• E. ΔH = TΔS: This is not a valid general relationship. It is only true at the point where ΔG = 0 in a phase change.

The option as printed is missing the "=" sign, but the sign and form of the expression are right.

Tip: Remember "minus RT ln K". A large K means a very negative ΔG°. If you can connect "big K → spontaneous → negative ΔG°", you will never pick the wrong sign. Also, ΔG° = −nFE° is for electrochemistry, and ΔG° = ΔH − TΔS is for thermodynamics.