The overall equation of ozone formation is 2O3--->3O2 Ozone is believed to decay
ID: 800021 • Letter: T
Question
The overall equation of ozone formation is 2O3--->3O2
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) Can you please show me the math used to obtain this part? I am close but I am ending up with a k1 in the final answer, that should not be there. I got the answer from teacher but am confused how he got his answer. d[O2]/dt= (3k2 [O3]^2 [M]) / ([k-1] [O2][M]+ k2 [O3])
Explanation / Answer
(1) O3 + M <=> O2 + O + M
(2) O3 + O => 2 O2
(a) O2 is formed in steps 1 and 2 and consumed in step -1
d[O2]/dt = k1[O3][M] - k-1[O2][O][M] + 2k2[O3][O]
(b) O is formed in step 1 and consumed in steps -1 and 2
d[O]/dt = k1[O3][M] - k-1[O2][O][M] - k2[O3][O]
(c) Applying steady state approximation:
d[O]/dt = k1[O3][M] - k-1[O2][O][M] - k2[O3][O] = 0
[O] = k1[O3][M]/(k-1[O2][M] + k2[O3])
d[O2]/dt = k1[O3][M] - k-1[O2][O][M] + 2k2[O3][O]
= k1[O3][M] - k-1[O2][M] x k1[O3][M]/(k-1[O2][M] + k2[O3]) + 2k2[O3] x k1[O3][M]/(k-1[O2][M] + k2[O3])
= k1k-1[O2][O3][M]^2 + k1k2[O3]^2[M] - k1k-1[O2][O3][M]^2 + 2k1k2[O3]^2[M]/(k-1[O2][M] + k2[O3])
= 3k1k2[O3]^2[M]/(k-1[O2][M] + k2[O3])
(There should be an extra k1 in the answer to part (c). Your teacher probably missed it out.)
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