It has been found that for a chemical reaction with rise in temperature by 9 K the rate constant gets doubled. Assuming a reaction to be occurring at 300 K , the value of activation energy is found to

Question

It has been found that for a chemical reaction with rise in temperature by 9 K the rate constant gets doubled. Assuming a reaction to be occurring at 300 K , the value of activation energy is found to be kJmol - 1 . [nearest integer] (Given ln 10 = 2 . 3 , R = 8 . 3 J K - 1 mol - 1 , log 2 = 0 . 30 )

TestHub · Accepted Answer

Arrhenius equation for the rate constant of a reaction in terms of energy of activation at two different temperatures is given by

$\log (\frac{K_{2}}{K_{1}}) = \frac{E_{a}}{2.3 R} [\frac{1}{T_{1}} - \frac{1}{T_{2}}]$

Rise in temperature $= 9 K$

Initial temperature $= 300 K$

$\log (\frac{K_{309}}{K_{300}}) = \frac{E_{a}}{2.3 R} [\frac{1}{300} - \frac{1}{309}]$

$\log 2 = \frac{E_{a}}{2.3 R} [\frac{9}{300 \times 309}]$

$E_{a} = \frac{2.3 \times 0.30 \times 300 \times 309}{9}$

$E_{a} = 58.988 \times 10^{3} J = 58.988 kJ = 59 kJ$

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