A chemical reaction is 20% complete in 15 min at 40 °C and in 3 min at 60 °C, then how much activation energy is required?

Question

Question

This question was previously asked in

BPSC AE Paper 3 (General Studies) 10 Nov 2022 Official Paper

Answer 1

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Concept:-

Given a chemical reaction that is 20% complete in:

Using the Arrhenius equation:
\( k = A e^{-E_a / RT}\)

The logarithmic form of the Arrhenius equation is:
\( ln(k2 / k1) = (E_a / R) (1/T1 - 1/T2)\)

Explanation:-

Determine the rate constant ratio using the times:
- k2 / k1 = 15 min / 3 min = 5
Using the temperatures T1 = 313 K, T2 = 333 K:
- 1 / 313 - 1 / 333 = (333 - 313) / (313 x 333) ≈ 0.000192
Substitute into the Arrhenius equation:
- \(ln(5) = (E_a / 1.987) x 0.000192\)
ln(5) ≈ 1.60944
\(E_a = (1.60944 / 0.000192) x 1.987 ≈ 16.4 kcal/mol\)

Therefore, the activation energy required is 16.4 kcal