The rate constants of a reaction at 500 K and 700 K are 0.02 s−1 and…

The correct answer is Option (1) → 18230.8 J mol⁻¹

The Arrhenius equation relates the rate constant to temperature. Taking the rate constants at two temperatures gives:

    \( \displaystyle \log\frac{k_2}{k_1}=\frac{E_a}{2.303R}\left(\frac{T_2-T_1}{T_1T_2}\right) \)

Here \( k_1 = 0.02\ \mathrm{s^{-1}} \) at \( T_1 = 500\ \mathrm{K} \), \( k_2 = 0.07\ \mathrm{s^{-1}} \) at \( T_2 = 700\ \mathrm{K} \), and \( R = 8.314\ \mathrm{J\,K^{-1}\,mol^{-1}} \).

    \( \displaystyle \frac{k_2}{k_1}=\frac{0.07}{0.02}=\frac{7}{2} \)

    \( \displaystyle \log\frac{7}{2}=\log 7-\log 2=0.8451-0.3010=0.5441 \)

    \( \displaystyle \frac{T_2-T_1}{T_1T_2}=\frac{200}{500\times700}=\frac{1}{1750}\ \mathrm{K^{-1}} \)

    \( \displaystyle E_a=0.5441\times2.303\times8.314\times1750 \)

    \( \displaystyle E_a\approx18231\ \mathrm{J\,mol^{-1}} \)

So \( E_a \) = 18230.8 J mol⁻¹ (18.23 kJ mol⁻¹).

Note 1: This question is from NCERT (2026-27). NTA sets numerical questions from NCERT too, so do not ignore NCERT while practising numericals.

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

Note 2: The same/similar question has been asked in different years by NTA as per the details given below: