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For a first order reaction A rarr P, the...

For a first order reaction `A rarr P`, the temperature `(T)` dependent rate constant `(k)` was found to follow the equation `log k = -2000(1//T) + 6.0`. The pre-exponential factor `A` and the activation energy `E_(a)`, respective, are

A

`1.0 xx 10^(6)s^(-1)` and `9.2 kJ mol^(-1)`

B

`6.0 s^(-2)` and `16.6 kJ mol^(-1)`

C

`1.0 xx 10^(6) s^(-1)` and `16.6 kJ mol^(-1)`

D

`1.0 xx 10^(6) s^(-1)` and `38.3 kJ mol^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
D
d) According to Arrhenius equation,
`k=Ae^(-Ea//RT)`
In k = In `A-(E_(a))/(RT)`
`2.303 logk = 2.303 log A - (E_(a))/(RT)`
log k `= log A-(E_(a))/(2.303RT)`
On comparing with the given equation. `logk = 6.0 - (2000) xx 1/T`
log A = 6.0, `A="Antilog"6 = 10^(6)`
`E_(a)/(2.303R)= 2000`
`E_(a) = 2000 xx 2.303 xx R`
`=2000 xx 2.303 xx 8.314 J`
=`38.29 kJ`.
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