For a reaction taking place in three steps, the rate constant are `k_(1), k_(2)` and `k_(3)` and overall rate constant is `k=(k_(1)k_(3))/(k_(2)`. If the energies of activation `E_(1)`, `E_(2)` and `E_(3)` are 60, 30 and 10 kJ `mol^(-1)` respectively, then the overall energy of activation is:

Options

A. 30 kJ `mol^(-1)`
B. 40 kJ `mol^(-1)`
C. `60 kJ mol^(-1)`
D. `100 kJ mol^(-1)`

Answer

B

Explanation

According to the available information.
`k_(1) = A_(1)e^((-Ea)//Rt)`
`k_(2) = A_(2)e^((-Ea)//RT)`
`k_(3) = A_(3)e^((-Ea)//RT)`
`k = (k_(1)k_(3))/(k_(2)) - [E_(a1)+E_(a3) - E_(a2)]`
`=(k_(3)k_(2))/(k_(2)) = (A_(1)A_(3))/(A_(2))e`
`=E_(a) ("total") = E_(a1)+E_(a3)-E_(a2)`
`=60 + 10-30=40 kJ mol^(-1)`