Consider A to B and C to D reactions activation energy calculation using Arrhenius equation
Q. Consider A → B and C → D are two reactions. If the rate constant (k1) of the A → B reaction can be expressed by the following equation

log10 k = 14.34 − $\dfrac{1.5 \times 10^{4}}{T/K}$

and activation energy of C → D reaction (Ea2) is $\dfrac{1}{5}$ th of the A → B reaction (Ea1), then the value of (Ea2) is _____ kJ mol−1. (Nearest Integer)
Correct Answer: 57

Explanation

Arrhenius equation in logarithmic form is:

$$ \log_{10} k = \log_{10} A - \frac{E_a}{2.303RT} $$

Comparing this standard equation with the given equation:

$$ \log_{10} k = 14.34 - \frac{1.5 \times 10^{4}}{T} $$

From comparison:

$$ \frac{E_{a1}}{2.303R} = 1.5 \times 10^{4} $$

Using value of gas constant:

$$ R = 8.314\ \text{J mol}^{-1}\text{K}^{-1} $$

Substitute value of R:

$$ E_{a1} = 2.303 \times 8.314 \times 1.5 \times 10^{4} $$

$$ E_{a1} = 287000\ \text{J mol}^{-1} $$

$$ E_{a1} = 287\ \text{kJ mol}^{-1} $$

Given that activation energy of C → D reaction is one-fifth of A → B reaction:

$$ E_{a2} = \frac{1}{5} \times 287 $$

$$ E_{a2} = 57.4\ \text{kJ mol}^{-1} $$

Nearest integer value of activation energy is 57 kJ mol−1.

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