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  4. It has been found that for a chemical reaction with rise in temperature by 9 K the rate constant gets doubled. Assuming a reaction to be occurring at 300 K, the value of activation energy is found to be kJ mol -1. [nearest integer] (Given ln 10=2.3, R =8.3 JK -1 mol -1, log 2=0.30 )

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Q. It has been found that for a chemical reaction with rise in temperature by $9\, K$ the rate constant gets doubled. Assuming a reaction to be occurring at $300\, K$, the value of activation energy is found to be ____$kJ \,mol ^{-1}$. [nearest integer]
(Given $\ln 10=2.3, R =8.3 \,JK ^{-1} \,mol ^{-1}, \log 2=0.30$ )

JEE MainJEE Main 2022Chemical Kinetics

Solution:

$\log _{10} \frac{ K _{2}}{ K _{1}}=\frac{ E _{ a }}{2.303 R }\left(\frac{1}{300}-\frac{1}{309}\right)$
$0.3=\frac{ E _{ a }}{2.303 \times 8.3}\left(\frac{9}{300 \times 309}\right)$
$E _{ a }=\frac{0.3 \times 2.303 \times 8.3 \times 300 \times 309}{9}$
$=59065.04\, J$
$E _{ a }=59.06 \,kJ$