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  • If k1 and k2 are the rate constants at temperature T1 and T2 then which of the following relation holds good?<div class='qna-opti

If k1 and k2 are the rate constants at temperature T1 and T2 then which of the following relation holds good?

Option: 1

\log \frac{\mathrm{k}_{2}}{\mathrm{k}_{1}}=\frac{\mathrm{E}_{\mathrm{a}}}{2.303 \mathrm{\: R}}\left[\frac{\mathrm{T}_{1}-\mathrm{T}_{2}}{\mathrm{T}_{1}}\right]


Option: 2

\log \frac{\mathrm{k}_{2}}{\mathrm{k}_{1}}=\frac{\mathrm{E}_{\mathrm{a}}}{ \mathrm{R}}\left[\frac{\mathrm{T}_{1}-\mathrm{T}_{2}}{\mathrm{T}_{1} \mathrm{T}_{2}}\right]


Option: 3

\log \frac{\mathrm{k}_{2}}{\mathrm{k}_{1}}=\frac{\mathrm{E}_{\mathrm{a}}}{2.303 \mathrm{\, R}}\left[\frac{\mathrm{T}_{2}-\mathrm{T}_{1}}{\mathrm{T}_{1} \mathrm{T}_{2}}\right]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:


Option: 4

None of above


Answers (1)

best_answer

We have the rate constant K1 at temperature T1 and rate constant K2 at temperature T2. 

We know that the Arrhenius equation is given as follows:

\mathrm{log_{10}K_{1}\: =\: log_{10}A\: -\: \frac{E_{a}}{2.303RT_{1}}\quad\quad\quad\quad\quad............(i)}

\mathrm{log_{10}K_{2}\: =\: log_{10}A\: -\: \frac{E_{a}}{2.303RT_{2}}\quad\quad\quad\quad\quad............(ii)}

On subtracting equation (i) from (ii), we get:

\mathrm{log_{10}K_{2}\: -\: log_{10}K_{1}\: =\: \frac{E_{a}}{2.303RT_{1}}\: -\: \frac{E_{a}}{2.303RT_{2}}}

\mathrm{\: log\frac{K_{2}}{K_{1}}\: =\: \frac{Ea}{2.303R}\left [ \frac{1}{T_{1}}\: -\: \frac{1}{T_{2}} \right ]}

\mathbf{Thus,}\ \log \frac{\mathrm{k}_{2}}{\mathrm{k}_{1}}=\frac{\mathrm{E}_{\mathrm{a}}}{2.303 \mathrm{\: R}}\left[\frac{\mathrm{T}_{2}-\mathrm{T}_{1}}{\mathrm{T}_{1} \mathrm{T}_{2}}\right]
where, Ea is activation energy.

Therefore, option(3) is correct

Posted by

Irshad Anwar

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