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(C) Given: $T_1 = 27 + 273 = 300 \, K$,$T_2 = 52 + 273 = 325 \, K$,$K_2 = 5K_1$,$R = 8.314 \, J \, K^{-1} \, mol^{-1}$.Using the Arrhenius equation: $

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$52$

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(C) Given: $T_1 = 27 + 273 = 300 \, K$,$T_2 = 52 + 273 = 325 \, K$,$K_2 = 5K_1$,$R = 8.314 \, J \, K^{-1} \, mol^{-1}$.Using the Arrhenius equation: $\ln \frac{K_2}{K_1} = \frac{E_a}{R} \left[ \frac{T_2 - T_1}{T_1 T_2} ight]$.$\ln(5) = \frac{E_a}{8.314} \left[ \frac{325 - 300}{300 	imes 325} ight]$.$1.6094 = \frac{E_a}{8.314} \left[ \frac{25}{97500} ight]$.$1.6094 = \frac{E_a}{8.314} 	imes 0.0002564$.$E_a = \frac{1.6094 	imes 8.314}{0.0002564} \approx 52194 \, J \, mol^{-1} = 52.194 \, kJ \, mol^{-1}$.Rounding to the nearest integer,we get $52 \, kJ \, mol^{-1}$.

The rate constant of a reaction increases by five times on increase in temperature from $27^{\circ} C$ to $52^{\circ} C$. The value of activation energy in $kJ \, mol^{-1}$ is $....$ . (Rounded-off to the nearest integer) $[R = 8.314 \, J \, K^{-1} \, mol^{-1}]$

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