The rate constant of a first order reaction w | vedclass

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(D) Given: $T_1 = 300 \ K$,$T_2 = 310 \ K$,$k_2 = 2k_1$,$R = 8.3 \ J \cdot mol^{-1} \cdot K^{-1}$,$\log 2 = 0.3$. Using the Arrhenius equation: $\log

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$53.33$

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(D) Given: $T_1 = 300 \ K$,$T_2 = 310 \ K$,$k_2 = 2k_1$,$R = 8.3 \ J \cdot mol^{-1} \cdot K^{-1}$,$\log 2 = 0.3$. Using the Arrhenius equation: $\log \frac{k_2}{k_1} = \frac{E_a}{2.303 \ R} \left( \frac{T_2 - T_1}{T_1 T_2} ight)$ $\log 2 = \frac{E_a}{2.303 	imes 8.3} \left( \frac{310 - 300}{300 	imes 310} ight)$ $0.3 = \frac{E_a}{19.1149} 	imes \frac{10}{93000}$ $E_a = \frac{0.3 	imes 19.1149 	imes 93000}{10} \ J \cdot mol^{-1}$ $E_a = 53330.57 \ J \cdot mol^{-1} \approx 53.33 \ kJ \cdot mol^{-1}$.

The rate constant of a first order reaction was doubled when the temperature was increased from $300 \ K$ to $310 \ K$. What is its approximate activation energy (in $kJ \cdot mol^{-1}$)? ($R = 8.3 \ J \cdot mol^{-1} \cdot K^{-1}$; $\log 2 = 0.3$)

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