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An elementary irreversıble gas-phase reaction, $A \rightarrow B + C$, is carried out at fixed temperature and pressure in two separate ideal reactors: $(i)$ a $10\:m^{3}$ plug flow reactor $\text{(PFR)}$, $(ii)$ a $10\:m^{3}$ continuous-stirred tank reactor $\text{(CSTR)}$. If pure $A$ is fed at $5\:m^{3}\:h^{-1}$ to the $\text{PFR}$ operating at $400\:K$, the conversion is $80\%$. If a mixture of $50\text{ mol}\%$ of $A$ and $50\text{ mol}\%$ of an inert is fed at $5\:m^{3}\:h^{-1}$ to the $\text{CSTR}$ operating at $425\:K$, the conversion is $80\%$. The universal gas constant $R = 8.314\:J\:\text{mol}^{-1}\:K^{-1}$. Assuming the Arrhenius rate law, the estimated activation energy is _____________ $kJ\:\text{mol}^{-1}$ (rounded off to one decimal place).

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