Question

A first order gas phase reaction has activation energy of 240 KJ mol`¹.If the per-exponential factor is 1.6×10¹³ s`¹.what is the rate constant of the reaction at 600 K?​

Answer 1

Solution:-

$Arrhenius \: \: equation$

$k = A \: {e}^{ - Ea/RT} is \: written \: as$

$log_{10} \frac{A}{k} = \frac{ E_{a}}{2.303RT}$

$E_{a} = 240KJ \: {mol}^{ - 1}$

$= 240 \times {10}^{3} J \: {mol}^{ - 1}$

$T = 600 K, \: A = 1.6 \times {10}^{13} \: {s}^{ - 1}$

Hence,

$log_{10} \: \: \frac{A}{k}$

$= \frac{240 \times {10}^{3} J \: {mol}^{ - 1} }{2.303 \times 8.314J \: {mol}^{ - 1} {K}^{ - 1} \times 600 K}$

$\frac{A}{k} = antilog \: 20.89$

$= 7.78 \times {10}^{20}$

And

$k = \frac{A}{7.78 \times {10}^{20} }$

$= \frac{1.6 \times {10}^{13} {s}^{ - 1} }{7.78 \times {10}^{20} }$

$= 2.05 \times {10}^{ - 8} {s}^{ - 1}$