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 the energies of activation are `40,30, and 20 KJ mol^(-1)`, the overall energy of activation is (assuming `A` to be constant for all)

Options

A. 10
B. 15
C. 30
D. 60

Answer

C

Explanation

`K=(K_1K_3)/K_2`
`:. "ln" K=ln K_1+ln K_3-ln K_2`
But `" " ln K=-E/(RT)+ ln A`
`:. -E/(RT)+ln A=-E_1/(RT)+ln A -E_3/(RT)+ ln A +E_2/(RT)-ln A`
or `E_("Total")=E_1+E_3-E_2=40+20-30=30 kJ`