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, areA. `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)`

For a first order reaction `A rarr P`, the temperature `(T)` dependent

1.	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, areA. `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)`
Answer» Correct Answer - 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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