A first order reaction is 50% complete in 40 minutes at `30^(@)` C and 20 minutes at `50^(@)` C calcualte the reaction rate constant at these temperatures and the energy of acitivation in kj/ mol

Explanation

The half life period for first order reaction is given by
`t_(1//2)=(0.693)/(k)` or `k=(0.693)/(t_(1//2))` or
and `k_(2)=(0.693)/(20 min)=0.03465 min^(-1)`
Accoriding ot Arrhenius equation
`log (k_(2))/(k_(1))=(E_(a))/(2.303 R)[(1)/(T_(1))-(1)/(T_(2))]`
log`(0.03465 min^(-1))/(0.01733 min^(-1))=(E_(a))/(2.303xx8.314 j mol^(-1) k^(-1))[(1)/(303 k)(1)/(323 k)]`
`0.3009 =(E_(a)xx20)/(2.303xx8.314 j mol^(-1)xx303xx323)`
`E_(a)=28193 j "mol"^(-1) =28.193 kj "mol"^(-1)`