JEE Main · 2023 · 15 Apr 2023 · Shift 1 · Chemical Kinetics

For a reversible reaction

A ⇌ B

, the

Δ H_{forward}

reaction

= 20 kJ mol^{- 1}

. The activation energy of the uncatalysed forward reaction is

300 kJ mol^{- 1}

. When the reaction is catalysed keeping the reactant concentration same, the rate of the catalysed forward reaction at

2 7^{\circ} C

is found to be same as that of the uncatalysed reaction at

32 7^{\circ} C

. The activation energy of the catalysed backward reaction is ______

kJ mol^{- 1}

Answer: 130

Solution

Equal rates at the same reactant concentration mean equal rate constants, so from the Arrhenius expression with a common pre-exponential factor the quantity

E_{a} / T

must match for the two cases. Comparing the catalysed forward reaction at

300 K

with the uncatalysed forward reaction at

600 K

gives

\frac{E _{a} ( cat , f )}{300} = \frac{300}{600}

, so

E_{a} (cat, f) = 150 kJ mo l^{- 1}

. For this path the reaction enthalpy equals the forward activation energy minus the backward one, so

20 = 150 - E_{a} (cat, b)

. The activation energy of the catalysed backward reaction is

130 kJ mo l^{- 1}

JEE Main · 2023 · 15 Apr 2023 · Shift 1 · Integer answer

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JEE Main · 2023 · 15 Apr 2023 · Shift 1 · Chemical Kinetics

Solution

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