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A first order gas -phase reaction has...

A first order gas -phase reaction has an energy of activation of 240 kJ `mol^(-1)` . If frequency factor of the reaction is `1.6 xx 10^(13) s^(-1)` , calculate its rate constant at 600 K .

Text Solution

Verified by Experts

The correct Answer is:
Rate constant `= k= 2.01 xx 10^(-8) s^(-1)`
Given : Energy of activation ` = E_(a) 240 kJ mol^(-1) = 240 xx 10^(3) J mol^(-1)`
Frequency factor = A = `1.6 xx 10^(13) s^(-1)`
Temperature `= T= 600 K ` Rate constant = k = ?
By Arrhenius equation,
`k= A xx e^(-E_(a)//RT) :. " In " k = " In " A - (E_(a))/(RT)`
`:. 2.303 log _(10) k= 2.303 log_(10) A- (E_(a))/(RT)`
`log_(10) k = log_(10) A - (E_(a))/(2.303 RT) = log_(10) 1.6 xx 10^(13) - (240 xx 10^(3))/(2.303 xx 8.314 xx 600)`
`= 13. 204 - 20.9 = - 7.696`
`:. k= AL - 7 .696 = AL bar(8).304 = 2.01 xx 10^(-8) s^(-1)`
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