Activation energy of a chemical reaction can be determined by _____.

The correct answer is Option (2) → determining the rate constant at two temperatures

The temperature dependence of the rate constant is given by the Arrhenius equation:

    \( \displaystyle k = A\,e^{-E_a/RT} \qquad \text{or} \qquad \ln k = -\frac{E_a}{RT} + \ln A \)

It contains two unknowns, the activation energy E_a and the factor A, so one value of k is not enough. If k₁ and k₂ are measured at two temperatures, T₁ and T₂, the two equations are subtracted, ln A cancels, and E_a is left as the only unknown.

So the activation energy is found by determining the rate constant at two temperatures (or, more accurately, from the slope −E_a/R of a plot of ln k against 1/T).

Why the other options are incorrect

• Option (1) determining the rate constant at standard temperature — Incorrect. A single value of k at one temperature contains both A and E_a, and the two cannot be separated from it.

• Option (3) determining the probability of collision — Incorrect. The probability (steric) factor tells what fraction of collisions have the proper orientation; it is part of A and says nothing about E_a.

• Option (4) using catalyst — Incorrect. A catalyst provides a path of lower activation energy and so changes the rate; it does not measure E_a.

NCERT (2026-27 edition):
Temperature Dependence of the Rate of a Reaction – “… At temperature T₁, equation (3.19) is

    \( \displaystyle \ln k_1 = -\frac{E_a}{RT_1} + \ln A \)   (3.20)

At temperature T₂, equation (3.19) is

    \( \displaystyle \ln k_2 = -\frac{E_a}{RT_2} + \ln A \)   (3.21)

(since A is constant for a given reaction)

k₁ and k₂ are the values of rate constants at temperatures T₁ and T₂ respectively.”