The decomposition of hydrocarbon follows the equation

The given equation is

k = (4.5 × 1011 s−1) e−28000 K/T (i)

Arrhenius equation is given by,

$k=\mathrm{Ae}^{-E_{\alpha} / \mathrm{R} T}$

From equation (i) and (ii), we obtain

$\frac{E_{a}}{\mathrm{R} T}=\frac{28000 \mathrm{~K}}{T}$

$\Rightarrow E_{a}=\mathrm{R} \times 28000 \mathrm{~K}$

= 8.314 J K−1 mol−1 × 28000 K

= 232792 J mol−1

= 232.792 kJ mol−1