Question

If the activation energy of a reaction is 80.9 kJ mol^–1, the fraction of molecules at 700K, having enough energy to react to form products is e^–x. The value of x is ______. (Rounded off to the nearest integer) [Use R = 8.31 JK^-1 mol^-1]

Answer 1

Calculate the value of ‘x’.

According to the question,

$$\begin{gathered} {\mathrm{E}}_{\mathrm{a}}=80.9\mathrm{kJ}/\mathrm{mol} \\ \mathrm{R}=8.31{\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1} \end{gathered}$$

As we know, Fraction of molecules able to cross energy barrier$=e^{-E_2/RT}=e^{-x}$

$$\begin{gathered} \Rightarrow x=\frac{E_a}{RT}=\frac{80.9\times 1000}{8.31\times 700}=13.91 \\ \Rightarrow x\simeq 14 \end{gathered}$$

Final Answer: Hence, the correct answer is 14.