Activation energy of parallel reaction

[adi1998]

Well,I know that the activation energy of a parallel reaction can be determined by the arrhenius
equation as (e1k1+e2k2)/(k1+k2) where e1,k1 and e2,k2 are the activation energies and rate constants for the two reacations.now consider the reaction A》B,and A》C since at every instant the reacted amount of A(in moles) is the sum of amounts of B and C produced,assume that in time dA moles of A react.the energy of activation required will be e1*dB+e2*dC=e*dAwhere dB and dC moles of B and C are formed and the total energy of activation being e.Using the rate law definition now yields the same result.Is this proof also valid?I understand that these are all crude approximations(temperature changes may affect the result etc)

 

[Bystander]

Is this proof also valid?

Proof of what? What in particular are you trying to accomplish?

 

[adi1998]

I am talking about the expression for the overall activation energy
,given by e=(e1k1+e2k2)/(k1+k2).