Given below is an expression for the rate constant of a first-order reaction occurring at a certain

Question

Given below is an expression for the rate constant of a first-order reaction occurring at a certain temperature, T (K).

$$lnk = 14.34 - \frac{1.25 \times 10^{4}}{T}$$

The energy of activation in $kcal{mol}^{- 1}$ for the reaction is:

(Given: k in $s^{- 1},R = 1.987cal{mol}^{- 1}{\text{ }K}^{- 1}$ )

Accepted Answer

Sol. [Key Concept: Arrhenius equation — rate constant and activation energy] From Arrhenius equation$$\begin{matrix} & k = Ae^{\frac{- E_{a}}{RT}} \ & lnk = lnA - \frac{E_{a}}{RT} \ & \frac{E_{a}}{R} = 1.25 	imes 10^{4} \ & E_{a} = 1.25 	imes 10^{4} 	imes 1.987 \ & \ = 24.84kcal{	ext{ }mol}^{- 1} \end{matrix}$$

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