The energy of activation of a first order reaction is $108 kJ mol^{- 1}$ and pre - exponential factor (A) is 5 × $1 0^{13} sec^{- 1}$ . At what temperature (in K ), will the reaction have a half life of 1 minute?
$[ln (2.31 \times 1 0^{- 16}) = - 36, R = 25/3 J K^{- 1} m o l^{- 1}]$

Question

The energy of activation of a first order reaction is $108 kJ mol^{- 1}$ and pre - exponential factor (A) is 5 × $1 0^{13} sec^{- 1}$ . At what temperature (in K ), will the reaction have a half life of 1 minute?

$[ln (2.31 \times 1 0^{- 16}) = - 36, R = 25/3 J K^{- 1} m o l^{- 1}]$

TestHub · Accepted Answer

For a first-order reaction: t 1/2 ​ = k 0.693 ​ Given: t 1/2 ​ = 60 s k = 60 0.693 ​ = 1.155 × 1 0 − 2 s − 1 Arrhenius equation: k = A e − E a ​ / RT 1.155 × 1 0 − 2 = 5 × 1 0 13 e − 108000/ ( RT ) e − 108000/ RT = 2.31 × 1 0 − 16 Taking ln: RT − 108000 ​ = − 36 T = 36 × ( 25/3 ) 108000 ​ T = 360 K ​

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