The correct relationship between free energy change in a reaction and the corresponding equilibrium constant Kc is :

Thermodynamics PYQ — JEE Main 2003 · Shift 0 · Q5 with Solution

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Correct answer: C

Use the standard thermodynamic relation

For a reaction at equilibrium, the standard free energy change and equilibrium constant are related by:
$\Delta G^\circ = -RT \ln K$
Here, since the equilibrium constant is given as $K_c$ , we write:
$\Delta G^\circ = -RT \ln K_c$
Rearrange the equation

Moving the minus sign to the left side:
$-\Delta G^\circ = RT \ln K_c$
Match with the options
- A: $-\Delta G = RT \ln K_c$
  Incorrect, because it should involve $\Delta G^\circ$ , not $\Delta G$ .
- B: $\Delta G^o = RT \ln K_c$
  Incorrect, sign is wrong.
- C: $-\Delta G^o = RT \ln K_c$
  Correct.
- D: $\Delta G = RT \ln K_c$
  Incorrect, both the sign and use of $\Delta G$ instead of $\Delta G^\circ$ are wrong.
Final answer

The correct relationship is:
$-\Delta G^\circ = RT \ln K_c$
Hence, the correct option is C.