The mechanism for the reaction described the equation

Question

Where A is CH3NC, M is any gas molecule A is an energized gas molecule and B is CH3CN. Assuming that A is governed by steady state conditions derive the rate law for the production of CH3CN in terms of A, M and the appropriate k values

Answer 1

Assuming that A* is the energized gas molecule and assuming A* is in an equilibrium state, we can proceed.

A + M ---^k1--> A* + M formation of energized intermediate

A* + M ---^k2---> A + M deactivation of energized intermediate

A* ---^k3---> B conversion of A* to B or CH₃NC* to CH₃CN

rate of formation of B = k₃[A*] and since [A*] is in steady state d[A*] / dt = 0. Thus...

d[A*] / dt = k₁[A][M] - k₂[A*][M] - k₃[A*] = 0 and solving for [A*] we have...

[A*] = k₁[A][M] / k₂[M] + k₃

Now we can substitute [A*] into the rate expression for formation of B. We do this since A* is an intermediate and as such cannot appear in the final rate equation.

rate of formation of B = k₃[A*] = k₃k₁[A][M] / k₂[M] + k₃