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Two Reactions \mathrm{P_1} and \mathrm{P_2} have identical po exponential factors. The activation energy of \mathrm{P_1} is more than \mathrm{P_2} by \mathrm{30 \mathrm{kJmol}^{-1}}.If \mathrm{K_1} and \mathrm{K_2} are rate constants for reactions \mathrm{P_1} and \mathrm{P_2}, respectively at 300 k then \mathrm{\ln \left(\frac{k_2}{k_1}\right)} is equal to

Option: 1

8


Option: 2

6


Option: 3

4


Option: 4

12


Answers (1)

best_answer

By Arrhenius Equation 

\mathrm{\begin{aligned} k & =A e^{-E a_1 / R T} \\ k_1 & =A e^{-E a_1 / R T} \\ k_2 & =A e^{-E a_2 / R T} \\ \ln \left(\frac{k_1}{k_2}\right) & =e^{\left(E a_1-E a_2\right) / R T} \\ \ln \left(\frac{k_2}{k_1}\right) & =\frac{E a_1-E a_2}{R T}=\frac{30 \times 1000}{8.314 \times 300} \\ \ln \left(\frac{k_2}{k_1}\right) & =12 \end{aligned}}

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Ritika Jonwal

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