A first order reaction is 50% complete in 30 minutes at `27^(@)C` and in 10 minutes at `47^(@)C`. The reaction rate constant at `27^(@)C` and the energy of activation of the reaction are respectively

Answer

`E_(a) = 43.85 kJ mol^(-1)`

Explanation

`k_(1)` at `27^(@)C(300 K) = (0.693)/(30 min) = 0.0231 min^(-1)`
`k_(2)` at `47^(@)C(320 K) = (0.693)/(10 min) = 0.0693 min^(-1)`
Uisng Arrhenius equation:
`log.(k_(2))/(k_(1)) = (E_(a))/(2.303R)((T_(2)-T_(1))/(T_(1)T_(2)))`,
`log.(0.0693)/(0.0231) = (E_(a))/(2.303 xx 8.314 xx 10^(-3) kJ mol^(-1) K^(-1))`
`((20)/(300 xx 320))`
`E_(a) = 43.85 kJ mol^(-1)`