For a first order reaction A to 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) , respectively , are

For a first order reaction A to P , the temperature (T) dependent rate

1.	For a first order reaction A to 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) , respectively , are
Answer» `1.0 xx 10^(6) s^(-1)` and `9.2 K J mol^(-1)` `6.0 s^(-1)` and `16.6 kJ mol^(-1)` `1.0 xx 10^(6) s^(-1)` and `16.6 kJ mol^(-1)` `1.0 xx 10^(6) s^(-1)` and `38.3 kJ mol^(-1)` Solution :From Arrhenius EQUATION k = `Ae^(-E_(a)//RT)` LN k = ln A `- (E_(a))/(RT)` `2.303` log k = `2.303` log `A - (E_(a))/(RT)` log k `= (-E_(a))/(2.303R) xx (1)/(T) + ` log A `"" … (i)` log k = `-(2000) (1)/(T) + 6 "" … (ii)` On comparing equation (i) and (ii) `(-E_(a))/(2.303R) = -2000` `E_(a) = 2.303 xx 8.314 xx 2000 = 38.29 kJ` M and log `A = 6 implies A = 10^(6)`