QJEEM21Ch8577: JEE Main 2021 Chemistry - Class 12 JEEM21Ch8577 Solution: The rate constant of a reaction increases by five times on…

Question

Verified Solution • 2025–26 Session moderate

The rate constant of a reaction increases by five times on increase in temperature from 27

^\circ

C to 52

^\circ

C. The value of activation energy in kJ mol^{$-$ 1} is _________. (Rounded off to the nearest integer)

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

Accepted Answer

T₁ = (273 + 27) = 300 K, T₂ = (273 + 52) = 325 K

Given, temperature coefficient of the reaction,

{\alpha _T} = {{{K_{325}}} \over {{K_{300}}}} = 5

\log {{{K_{{T_2}}}} \over {{K_{{T_1}}}}} = {{{E_a}} \over {2.303R}} \times \left( {{{{T_2} - {T_1}} \over {{T_1}{T_2}}}} \right)

\log {{{K_{325}}} \over {{K_{300}}}} = {{{E_a}} \over {2.303 \times 8.314}}\left( {{{325 - 300} \over {300 \times 325}}} \right)

\log 5 = {{{E_a}} \over {2.303 \times 8.319}} \times {{25} \over {300 \times 325}}

E_a = 52194.78 J mol^$-$

= 52.194 kJ mol^{$-$ 1}

\simeq

52 kJ mol^{$-$ 1}

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