\(E _{ a }=11.488 KJ / mole \quad R =8.314 J / mole - K\)

so \(\ell n \left(\frac{ K _{300}}{ K _{200}}\right)=\frac{ E _{ a }}{ R }\left(\frac{1}{200}-\frac{1}{300}\right)\)

\(\ell n \left(\frac{ K _{300}}{ K _{200}}\right)=\frac{11.488 \times 1000 \times 100}{8.314 \times 200 \times 300}\)

\(=2.303\)

\(=\ell n 10\)

so \(\frac{ K _{300}}{ K _{200}}=10\)

\(K _{200}=\frac{1}{10} \times K _{300}=10^{-4}\)

\(=10 \times 10^{-5} sec ^{-1}\)