[XGen]

I found the following problem online while I was looking for steady-state approximation problems, and after I did it I found I didn't have an answer key. Could anyone tell me if my answers/thinking are correct?

Given the mechanism:
        k₁
PdL₂   PdL + L
        k_-1

               k₂
PdL + ArX   PdLArX

1. Use the steady-state approximation to solve for the concentration of the intermediate
species [PdL].
2. Write the rate law for the formation of the oxidative addition product PdLArX.



We can start by realizing the rate of formation for PdL can be represented as k₁[PdL₂], and the rates of consumption as k₂[ArX][PdL] and k_-1[PdL][L].

From this, we can write d[PdL]/dt = k₁[PdL₂] - k₂[ArX][PdL] - k_-1[PdL][L] = 0, as this is the assumption for steady-state, that the concentrations of the intermediates do not change. After manipulation, [PdL] = k₁[PdL₂]/(k₂[ArX] + k_-1[L]).

For the second part, we begin by realizing that the rate of formation for PdLArX can be written as k₂[PdL][ArX]. Substituting the result in from the first part, d[PdLArX]/dt = k₁k₂[PdL₂][ArX]/(k₂[ArX] + k_-1[L]).

Thanks for your time!