The decomposition of `N_(2)O` in `N_(2)` and `O_(2)` in presence of gaseous argon follows II order kinetics having `K=5xx10^(11) e^(-29000//T)`. Find out energy of activation and rate constant at `27^(@)C`. Also evalute Arrhenius parameter.

Explanation

`:' K=Ae^(-E_(a)//RT) …(1)`
`K=5xx10^(11) e^(-29000//T) …(2)`
By comparing eqs. (1) and (2),
`A=5xx10^(11) L mol^(-1) s^(-1), E_(a)/(RT)=29000/T`
`:. E_(a)=29000xx8.314 J =241.106J mol^(-1)`
Also `K=5xx10^(11) e^(-29000//300), (T=273+27)`
`5.2xx10^(31) mol^(-1)` litre `sec^(-1)`
Note the factor A has same unit as `K` has, because `E_(a)` is in `J mol^(-1), R` in `J K^(-1) mol^(-1)` and `T` in `K`.
`K=Ae^((J mol^(-1))/(J K^(-1) mol^(-1)xxK))`