Answer
$E_a=269.3\ kJ/mol$
Work Step by Step
From the Arrhenius equation:
$ln(k_2/k_1)=-E_a/R(1/T_2-1/T_1)$
$ln(1.02\times10^{-3}\ s^{-1}/1.10\times10^{-4}\ s^{-1})=-E_a/8.314\ J/mol.K(1/783\ K-1/743\ K)$
$E_a=269.3\ kJ/mol$
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