Question

For the reaction, $aA+bB\to cC+dD,$ the plot of $\log K$ vs $1/T$ is given below:

The temperature at which the rate constant of the reaction is
${10}^{-4}{s}^{-1}$ is ________ $K.$ (Rounded off to the nearest integer)

[Given: The rate constant of the reaction is ${10}^{-5}{s}^{-1}$ at $500K.]$

Answer 1

From Arrhenius equation,
$lo{g}_{10}K=lo{g}_{10}A-\frac{E_a}{2.303RT}$

$\text{Slope}=-\frac{E_a}{2.303R}=-10000$

$lo{g}_{10}\frac{K_1}{K_2}=-\frac{E_a}{2.303R}(\frac{1}{T_1}-\frac{1}{T_2})$

$lo{g}_{10}\frac{{10}^{-4}}{{10}^{-5}}=-10000(\frac{1}{T}-\frac{1}{500})$

$1=10000(\frac{1}{500}-\frac{1}{T})$

$\frac{1}{10000}=\frac{1}{500}-\frac{1}{T}$

$\frac{1}{T}=\frac{1}{500}-\frac{1}{10000}$

$\frac{1}{T}=\frac{20-1}{10000}=\frac{19}{10000}$

$T=\frac{10000}{19}$

$\therefore T=526K$