The decomposition of formic acid on gold surface follows first...

${K}_{300} = {10}^{- 3}{K}_{200} = ?$

${E}_{a} = 11 . 488KJ / moleR = 8 . 314J / mole - K$

so $ℓn\left(\dfrac{{K}_{300}}{{K}_{200}}\right) = \dfrac{{E}_{a}}{R}\left(\dfrac{1}{200} - \dfrac{1}{300}\right)$

$ℓn\left(\dfrac{{K}_{300}}{{K}_{200}}\right) = \dfrac{11 . 488 \times 1000 \times 100}{8 . 314 \times 200 \times 300}$

$= 2 . 303$

$= ℓn10$

so $\dfrac{{K}_{300}}{{K}_{200}} = 10$

${K}_{200} = \dfrac{1}{10} \times {K}_{300} = {10}^{- 4}$

$= 10 \times {10}^{- 5}\sec^{- 1}$