The activation energy for a reaction at a temperature T K was found t…

The correct answer is Option (1) → \(10^{-1}\)

The Arrhenius equation relates the rate constant k to the activation energy E_a:

    \( k = A\,e^{-E_a/RT} \)

Here A is the Arrhenius factor (frequency factor), and e^−E_a/RT is the fraction of molecules with kinetic energy equal to or greater than E_a. So the ratio k/A is just this exponential term. Taking common logarithms:

    \( \displaystyle \log\frac{k}{A} = -\frac{E_a}{2.303\,RT} \)

Substituting E_a = 2.303 RT J mol⁻¹:

    \( \displaystyle \log\frac{k}{A} = -\frac{2.303\,RT}{2.303\,RT} = -1 \)

    \( \displaystyle \frac{k}{A} = 10^{-1} \)

So the ratio of the rate constant to the Arrhenius factor is 10⁻¹.

Shortcut: E_a = 2.303 RT means E_a/RT = ln 10, so e^−E_a/RT = 1/10 directly.

NCERT (2026-27 edition):
Temperature Dependence of the Rate of a Reaction – …