GATE 2019 BT Q.14: solution and answer

GATE 2019 · BTQ.14 · 1 mark · MCQ

Which one of the following statements is CORRECT for enzyme catalyzed reactions? ( $Δ G$ is Gibbs free energy change, $K_{e q}$ is equilibrium constant)

(A)
Enzymes affect $Δ G$ , but not $K_{e q}$
(B)
Enzymes affect $K_{e q}$ , but not $Δ G$
(C)
Enzymes affect both $Δ G$ and $K_{e q}$
(D)
Enzymes do not affect $Δ G$ or $K_{e q}$

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Answer and solution

ANSWER

The correct option is (D): enzymes do not affect $Δ G$ or $K_{e q}$ .

Official answer: DSource: Official answer key, GATE 2019 BT (IIT Madras)

An enzyme is a catalyst. It lowers the activation energy $Δ G^{‡}$ of the reaction by stabilising the transition state, so the reaction reaches equilibrium faster.
The overall free energy change depends only on the free energies of the initial and final states: $Δ G = G_{products} - G_{reactants}$ . An enzyme changes neither state, so $Δ G$ is unchanged.
The equilibrium constant is fixed by the standard free energy change: $Δ G^{\circ} = - R T ln K_{e q}$ . Since $Δ G^{\circ}$ is unchanged, $K_{e q}$ is unchanged.
The enzyme speeds the forward and reverse reactions by the same factor, so the ratio $k_{f} / k_{r} = K_{e q}$ stays the same.
(A) is wrong because $Δ G$ is not changed. (B) is wrong because $K_{e q}$ is not changed, and a change in $K_{e q}$ would need a change in $Δ G^{\circ}$ . (C) is wrong because both stay the same.
(D) is correct. The enzyme alters only the rate (the activation barrier), not $Δ G$ or $K_{e q}$ .

KEY IDEA

A catalyst lowers the activation barrier and speeds the forward and reverse reactions equally. It does not change the free energy of the reactants or products, so it leaves $Δ G$ and $K_{e q}$ unchanged.

WATCH OUT FOR

Thinking that a faster reaction means a more favourable one. An enzyme changes how fast equilibrium is reached, not where equilibrium lies.

From the GATE 2019 BT paper. Every question of this paper · Download the full paper · All 6 Enzymes questions, with notes

GATE 2019 BT Q.14: solution and answer

Answer and solution

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