For the reaction, aA + bB → cC + dD, the plot of logk v/s (1)/(T)...

For the reaction, $aA + bB \to cC + dD,$ the plot of $logk$ v/s $\dfrac{1}{T}$ is given below:

For the reaction, aA + bB → cC + dD, the plot of logk v/s (1)/(T) is given below: The temperature at which the rate

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 rat5e constant of the reaction is ${10}^{- 5}{s}^{- 1}$ at $500K$ .]

Correct answer

Step-by-step solution

$logk = logA - \dfrac{Ea}{2 . 303RT}$

\left|Slope\right| = \dfrac{Ea}{2 . 303R} = 10, 000 $$ \log \left(\dfrac{{k}_{2}}{{k}_{1}}\right) = \dfrac{Ea}{2 . 303R}\left(\dfrac{1}{{T}_{1}} - \dfrac{1}{{T}_{2}}\right) $$ \log \left(\dfrac{{10}^{- 4}}{{10}^{- 5}}\right) = 10, 000\left[\dfrac{1}{500} - \dfrac{1}{{T}_{2}}\right] $$ \log \left(\dfrac{{10}^{- 4}}{{10}^{- 5}}\right) = 10, 000\left[\dfrac{1}{500} - \dfrac{1}{{T}_{2}}\right] $$ {T}_{2} = 526 . 31 ≃ 526K $Hence answer is \left(526\right)$

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