Question

For the reaction, $aA+bB\to cC+dD$, the plot of $logkvs\frac{1}{T}$ 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 ${10}^{-5}{s}^{-1}at500K.]$

• A. 526.0
• B. 526.00
• C. 526

Answer 1

Answer: (A), (B), (C)

Arrhenius equation,
$k=A{e}^{-E_a/RT}$

$logk=logA-\frac{E_a}{2.303R}\times \frac{1}{T}$

From given graph : Slope = $-10000=\frac{-E_a}{2.303R}$

Expression for rate constant at two different temperature is given by
$log\frac{k_2}{k_1}=\frac{E_a}{2.303R}[\frac{1}{T_1}-\frac{1}{T_2}]$

$log\frac{{10}^{-4}}{{10}^{-5}}=10000[\frac{1}{500}-\frac{1}{T_2}]$

$\Rightarrow 1=20-\frac{10000}{T_2}$

$\Rightarrow T_2=\frac{10000}{19}=526.3\approx 526K$