The rate constant for the decomposition of a certain substance is 2.80xx10^(-3)M^(-1)s^(-1) at 30^(@)C and 1.38xx10^(-1)m^(-1)s^(-1) at 50^(@)C. Evaluate the Arrheniusparameters of the reaction. (R=8.314xx10^(-3)kJ mol^(-1)K^(-1))

The rate constant for the decomposition of a certain substance is 2.80

1.	The rate constant for the decomposition of a certain substance is 2.80xx10^(-3)M^(-1)s^(-1) at 30^(@)C and 1.38xx10^(-1)m^(-1)s^(-1) at 50^(@)C. Evaluate the Arrheniusparameters of the reaction. (R=8.314xx10^(-3)kJ mol^(-1)K^(-1))
Answer» Solution :Energy of activation `(E_(a))` and pre-exponential FACTOR A are Arrhenius PARAMETERS. `k_(1)=2.80xx10^(-3)m^(-1)s` at `303k` `k_(2)=1.38xx10^(-2)m^(-1)s^(-1)` at `323k` As `log_(10).(k_(2))/(k_(1))=(E_(a))/(R )[(T_(2)-T_(1))/(T_(1)xxT_(2))]` `:.E_(a)=(2.303RT_(1)T_(2))/(T(T_(2)-T_(1)))log_(10).(k_(2))/(k_(1))` `=(2.303xx8.314xx10^(-3)xx303xx323)/((323-303)log_(10))((1.38xx10^(-2))/(2.80xx10^(-3)))=64.91 kJ mol^(-1)` Also `k=Ae^(-Ea//RT)` or `A=ke^(Ea//ET)=2.80xx10^(-3)e^(64.91//8.314)xx10^(-3)xx303=4.34xx10^(8)s^(-1)`