A reaction takes place in three rate determining steps having rate constants `K_(1), K_(2), K_(3)` respectively. The overall rate constant `K=(K_(1)K_(3))/K_(2)`. If energy of activations for the three steps are respectively `10, 20, 40 kJ`. The overall energy of activation is:

Options

A. `30 kJ`
B. `20 kJ`
C. `10 kJ`
D. `70 kJ`

Answer

a

Explanation

`K_(1)=A_(1)e^(-E_(a_(1))//RT)`
`K_(2)=A_(2)e^(-E_(a_(2))//RT)`
`K_(3)=A_(3)e^(-E_(a_(3))//RT)`
`:. K=(K_(1)K_(3))/(K_(2))=(A_(1)A_(3))/(A_(2)). E^((-[E_(a_(1))+E_(a_(3))-E_(a_(2)))]//RT)`
`=A' e^(-[10+40-20]//RT)`
`=A'e^(-30//RT)`