Ozone is believed to decay according to the following mechanism k1 is forward re

Question

Ozone is believed to decay according to the following mechanism
                             k1 is forward reaction (---->)
O3+M<------> O2 +O+M
                            k-1 reverse reaction( <----)

                        k2
O3+O-----> 2O2

a) write expression for rate of formation of O2
b) Write expression for rate of change of [O] atoms per change of time
c) apply steady state approximation to O atoms. Use the resulting expression to simplify the rate of formation of O2 in part (a) so it does not include [O].

answers I have come up with, need help to double check they are correct.
a) d[O2]/dt=(k1)(O3)(M)- (k-1)(O2)(O)(M) + (2k2)(O3)(O)

b) d[O]/dt= (k1)(O3)(M) - (k-1)(O3)(O)(M) - (k2)(O3)(O)

c) d[O2]/dt= (3k2)(O3)(O) not sure about this one, a) and b) I feel fairly confident about, c) not so much.  

Explanation / Answer

rate of formation of O2 = K1[O3][M] - K-1[O2][O][M] +2k2[O3][O]

b] rate of change of [o] atoms per change in time =

K1[O3][M] - K-1[O2][O][M] -k2[O3][O]

c]so from part b we equate it to =0

to get the conc of [O] and replace in part a so that it doesniot contain the [o]

[O] = k1[O3][M] /[k-1[O2][M] +k2[O3]]

now we replce it in part a to get the final result

the concept regarding the steady state is that at steady state the conc is not changing w.r.t time and the cncept behind writing the equations is that simple we need to see which reaction results in the decay of the compound we need and which reaction leads to its formation and after this we simply need to ad up all this to see the net change in the conc of the compound w.r.t time .

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