A first order reaction is 50 \% complete in {3 0} minutes ...

CBSE Class 12 Chemistry 2023 Outside Delhi Set 1 Solved Paper

Question : 28 of 35

Marks: +1, -0

A first order reaction is

50 \%

complete in

{3 0}

minutes at

300 {K}

and in 10 minutes at

320 \ { K}

. Calculate activation energy

(E_a)

for the reaction.

{[{R}=8.314\ {J}\ {K}^{-1} { mol}^{-1}\ ]}

[\text "Given ": \log 2=0.3010, \log 3=0.4771,

\log 4= 0.6021]

Solution: 👈: Video Solution

{K}_1

27°{C}

300 \ { K}={0.693}/{30 {min}}=0.0231 {min}^{-1}

{K}_2

47°{C}

320 { K}_1={0.693}/{10 \ { min}}=0.0693 \ { min}^{-1}

Using Arrhenius equation:

\log ({{K}_2}/{{ K}_1})={{Ea}}/{2.303 {R}}

({{T}_2-{T}_1}/{{T}_1 {T}_2})

\log ({0.0693}/{0.0231})={{Ea}}/{2.303 \×8.314 \× 10^{-3}\ {kj} \ {mol}^{-1} \ { K}^{-1}}({20}/{300 \×320})

{E}_{{a}}=43.85 \ {kj} \/ \ {mol}

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