Question

The Gibbs free energy of a reaction is minimized when the system is at equilibrium. Which of the following conditions must hold at equilibrium?

• A. The reaction quotient is greater than the equilibrium constant.
• B. The reaction quotient is equal to the equilibrium constant.
• C. The chemical potentials of all components are equal.
• D. The Gibbs free energy is positive.

Hint:

Always remember that at equilibrium, the driving force for the reaction (Gibbs free energy change) is zero, and this only happens when \( Q = K \).

Answer 1

The Correct Option is B

At equilibrium, the Gibbs free energy change \(\Delta G\) for the reaction becomes zero.
This occurs only when the reaction quotient \( Q \) becomes equal to the equilibrium constant \( K \).
Mathematically, \[ \Delta G = \Delta G^\circ + RT \ln Q \] At equilibrium: \[ \Delta G = 0 ⇒ 0 = \Delta G^\circ + RT \ln K ⇒ Q = K \] Hence, for a system at equilibrium, the condition \( Q = K \) must be satisfied. This means the rates of the forward and reverse reactions are equal, and no net change occurs in the concentrations of reactants and products.
Therefore, the correct condition is that the reaction quotient equals the equilibrium constant.