Solution (source code)

= Solution

At the higher <temperature> the same equilibrium rate balance gives
$$
\boxed{k'_{-1}=\frac{k'_1}{K_{318}}=\frac{1.04\times10^{-3}}{2.31}=4.50\times10^{-4}\,\mathrm{s^{-1}}.}
$$
This is a reverse <first-order rate constant>, not the net relaxation rate, which includes both elementary directions.