The rate constant of a first-order reaction i | vedclass

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(C) Given: $k_1 = 1.5 	imes 10^7 	ext{ s}^{-1}$, $T_1 = 300 	ext{ K}$, $k_2 = 3.0 	imes 10^7 	ext{ s}^{-1}$, $T_2 = 330 	ext{ K}$.Using the Arrh

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$19.02 	ext{ kJ mol}^{-1}$

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(C) Given: $k_1 = 1.5 	imes 10^7 	ext{ s}^{-1}$, $T_1 = 300 	ext{ K}$, $k_2 = 3.0 	imes 10^7 	ext{ s}^{-1}$, $T_2 = 330 	ext{ K}$.Using the Arrhenius equation: $\log \frac{k_2}{k_1} = \frac{E_a}{2.303 R} \left( \frac{T_2 - T_1}{T_1 T_2} ight)$.$\log \left( \frac{3.0 	imes 10^7}{1.5 	imes 10^7} ight) = \frac{E_a}{19.15} \left( \frac{330 - 300}{300 	imes 330} ight)$.$\log(2) = \frac{E_a}{19.15} \left( \frac{30}{99000} ight)$.$0.3010 = \frac{E_a}{19.15} 	imes \frac{1}{3300}$.$E_a = 0.3010 	imes 19.15 	imes 3300 	ext{ J mol}^{-1}$.$E_a = 19023.225 	ext{ J mol}^{-1} \approx 19.02 	ext{ kJ mol}^{-1}$.

The rate constant of a first-order reaction is $1.5 \times 10^7 \text{ s}^{-1}$ at $300 \text{ K}$ and $3.0 \times 10^7 \text{ s}^{-1}$ at $330 \text{ K}$. What is the activation energy $(E_a)$ for the reaction? $[R \times 2.303 = 19.15 \text{ J K}^{-1} \text{mol}^{-1}]$

Similar Questions

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