The rate coefficient $$(k)$$  for a particular reactions is $$1.3 \times {10^{ - 4}}{M^{ - 1}}{s^{ - 1}}$$    at $${100^ \circ }C,$$  and $$1.3 \times {10^{ - 3}}{M^{ - 1}}{s^{ - 1}}$$    at $${150^ \circ }C.$$  What is the energy of activation $$\left( {{E_a}} \right)$$  ( in $$kJ$$  ) for this reaction? ( $$R = $$  molar gas constant $$ = 8.314\,J{K^{ - 1}}mo{l^{ - 1}}$$     )

Solution :
$$\eqalign{ & {\text{According to Arrhenius equation}} \cr & \log \frac{{{k_2}}}{{{k_1}}} = \frac{{{E_a}}}{{2.303\,R}}\left( {\frac{1}{{{T_1}}} - \frac{1}{{{T_2}}}} \right) \cr & \log \frac{{1.3 \times {{10}^{ - 3}}}}{{1.3 \times {{10}^{ - 4}}}} \cr & = \frac{{{E_a}}}{{2.303 \times 8.314}}\left[ {\frac{1}{{373}} - \frac{1}{{423}}} \right] \cr & 1 = \frac{{{E_a}}}{{2.303 \times 8.314}}\left[ {\frac{1}{{373}} - \frac{1}{{423}}} \right] \cr & {E_a} = 60\,kJ/mol \cr} $$