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(B) Given,$T_1 = 27 + 273 = 300 \ K$ and $T_2 = 37 + 273 = 310 \ K$. The temperature coefficient of a reaction is defined as the ratio of rate constan

Vedclass · Accepted Answer

$53.5$

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(B) Given,$T_1 = 27 + 273 = 300 \ K$ and $T_2 = 37 + 273 = 310 \ K$. The temperature coefficient of a reaction is defined as the ratio of rate constants at temperatures differing by $10 \ K$,which is typically $2$. Let $K_1 = k$ and $K_2 = 2k$. Using the Arrhenius equation: $\log \frac{K_2}{K_1} = \frac{E_a}{2.303 \ R} \left( \frac{T_2 - T_1}{T_1 \ T_2} ight)$. Substituting the values: $\log 2 = \frac{E_a}{2.303 	imes 8.314 	imes 10^{-3}} 	imes \left( \frac{310 - 300}{310 	imes 300} ight)$. $0.3010 = \frac{E_a}{0.019147} 	imes \frac{10}{93000}$. $E_a = \frac{0.3010 	imes 0.019147 	imes 93000}{10} \approx 53.5 \ kJ \cdot mol^{-1}$.

If the definition of the temperature coefficient of the reaction holds good for a reaction between $27^{\circ} C$ and $37^{\circ} C$,the activation energy for the reaction in $kJ \cdot mol^{-1}$ is

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