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The rate constant for a reaction at 5...

The rate constant for a reaction at `500^(@) C " is " 1.6 xx 10^(3) M^(-1) s^(-1)` . What is the frequency factor of the reaction if its energy of activation is 56 kJ `mol^(-1)`

Text Solution

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The correct Answer is:
Frequency factor `=A= 9. 727 xx 10^(6) S^(-1)`
Given : `k = 1.6 xx 10^(3) M ^(-1) s^(-1) , T = 273 + 500 = 773 K`
Energy of activation = `E_(a) = 56 kJ mol^(-1) = 56000 J mol^(-1)`
Frequency factor = A= ?
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) A = log_(10) k + (E_(a))/(2.303 RT)`
`= log_(10) 1.6 xx 10^(3) + (56000)/(2.303 xx 8.314 xx 773) = 3.204 + 3.784 = 6.988`
`:. A = AL 6.988= 9.727 xx 10^(6) s^(-1)`
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