Question

Identify from following, the relation between standard free energy change in a reaction and equilibrium constant \(K_c\).

• A. \(△G^{\circ} = RTlnK_c\)
• B. \(-△G^{\circ} = \frac{RT}{lnK_c}\)
• C. \(△G^{\circ} = \frac{lnK_c}{RT}\)
• D. \(-△G^{\circ} = RTlnK_c\)

Hint:

Use the standard relation delta G = minus RT ln K.

Answer 1

The Correct Option is D

Step 1: Starting Point:
The free energy of a mixture is $\Delta G = \Delta G^{\circ} + RT\ln Q$.

Step 2: At Equilibrium:
The system has no tendency to change, so $\Delta G = 0$ and $Q = K_c$. Rearranging gives $\Delta G^{\circ} = -RT\ln K_c$.

Step 3: Sign Check:
A large $K_c$ means products dominate, so $\Delta G^{\circ}$ must be negative. Only option (D) has this sign and form.

Final Answer:
The correct relation is option (D). \[ \boxed{\text{(D) } -\Delta G^{\circ} = RT\ln K_c} \]