c
\(\ln \, = \,\ln \,A\, - \,\frac{{Ea}}{{RT}}\, = \,\ln \,A\, - \,\frac{{4606}}{T}\)

\(\ln \,\left( {\frac{k}{{{{10}^{ - 5}}}}} \right) = \left( {\frac{{Ea}}{R}} \right)\, \times \,\frac{{500 - 400}}{{500 \times 400}}\)

\(\ln \,\left( {\frac{k}{{{{10}^{ - 5}}}}} \right) = 4606 \times \frac{1}{{2000}}\, = \,2.303\, = \,\ln \,10\)

\(\ln \,\left( {\frac{k}{{{{10}^{ - 5}}}}} \right) = \,\ln \,10\)

\(k\,=\,10^{-4}\)