b
\(\log \,\frac{{{k_2}}}{{{k_1}}}\,\, = \,\,\frac{{{E_a}}}{{2.303R}}\,\left[ {\frac{1}{{{T_1}}}\,\, - \,\,\frac{1}{{{T_2}}}} \right],\,\,{T_1}\, = \,\,293\,K,\,\,\,{T_2}\, = \,\,313\,\,K\)

\(\log \,\frac{4}{1}\,\, = \,\,\frac{{{E_a}}}{{2.303\,\, \times \,\,(8.314\,\,J\,\,mo{l^{ - 1}}\,{K^{ - 1}})}}\,\left[ {\frac{1}{{293}}\,\, - \,\,\frac{1}{{313}}} \right]\)

\(\log \,4\,\, = \,\,\frac{{{E_a}}}{{2.303\, \times \,\,(8.314\,\,J\,mo{l^{ - 1}}\,{K^{ - 1}})}}\, \times \,\frac{{20}}{{293\,\, \times \,\,313}}\)

\(0.6021\,\, = \,\,\frac{{{E_a}}}{{2.303\,\, \times \,\,(8.314\,\,J\,\,mo{l^{ - 1}}\,{K^{ - 1}})}}\, \times \,\frac{{20}}{{293\,\, \times \,\,313}}\)

\({E_a}\, = \,\,\,\frac{{0.6021\,\, \times \,\,2.303\,\, \times \,\,8.314\,\, \times \,\,293\,\, \times \,\,313(J\,mo{l^{ - 1}})}}{{20}}\,\)

\({E_a}\, = \,\,5.2863\,\, \times \,\,{10^4}\,J\,mo{l^{ - 1}}\, = \,\,52.863\,\,kJ\,mo{l^{ - 1}}\)