Question

Let’s assume you are a student of Arrhenius. He asked you to calculate $E_a$ for a reaction so that he can study a reaction on which he is working for a long time. He told you the rate constants of the reaction at 500 K and 700 K are $0.02s^{-1}and0.07s^{-1}$ respectively. Calculate the value of $E_a$.

• A. 18231 J
• B. 12831 J
• C. 18431 J
• D. 19231 J

Answer 1

The correct option is A 18231 J

I know you want to help Arrhenius here.
Now let’s use his own equation to help him.

We know the Arrhenius equation and we also derived the equation at different temperatures.

$log\frac{k_2}{k_1}=\frac{E_a}{2.303R}\left[\frac{T_2-T_1}{T_1{T}_2}\right]$

Now put the values of rate constants and temperatures.

$log\frac{0.07}{0.02}=\left(\frac{E_a}{2.303\times 8.314J{K}^{-1}JK-1mo{l}^{-1}}\right)\left[\frac{700-500}{700\times 500}\right]$

$0.544=E_a\times 5.714\times \frac{{10}^{-4}}{19.15}$
$E_a=\frac{0.544\times 19.15}{5.714\times {10}^{-4}}=18230.8J$

So Activation energy required is approximately 18231 J.