A reaction takes place in theee steps: the rate constant are `k_(1), k_(2), and k_(3)`. The overall rate constant `k=(k_(1)k_(3))/(k_(2))`. If `E_(1), E_(2)`, and `E_(3)` (energy of activation) are `60, 30` and `10kJ`, respectively, the overall energy of activation is

Options

A. `40`
B. `30`
C. `400`
D. `60`

Answer

A

Explanation

`k_(1) = Ae^(-E_(a_(1))//RT)`
`k_(2) = Ae^(-E_(a_(2))//RT)`
`k_(3) = Ae^(-E_(a_(3))//RT)`
Overall rate:
`k = (k_(1)k_(3))/(k_(2))`
`:.` Overall `E_(a) = E_(a_(1)) + E_(a_(3))+E_(a_(2))`
`= 60 + 10 - 30`
`= 40 kJ`