Question

The decomposition of hydrocarbon follows the equation
$k = (4.5 \times 10^{11} s^{-1})e^{-28000 \ K/T }$
$Calculate\ E_a$.

Answer 1

The given equation is
$k = (4.5 \times 10^{11} s^{-1})e^{-28000 \ K/T }$ ..... (i)
Arrhenius equation is given by,
$k = Ae^{-\frac {E_a}{RT}}$ ...... (ii)
From equation (i) and (ii), we obtain
$\frac {E_a}{RT} =\frac { 28000\ k}{T}$
$E_a = R \times 28000 \ K$
$E_a = 8.314 \ J K^{-1} mol^{-1} \times 28000\ K$
$E_a = 232792 \ J \ mol^{-1}$
$E_a = 232.792\ kJ \ mol^{-1}$