A possible mechanism for the decomposition of Ozone is: O_3 == O_2 + O with forw

Question

A possible mechanism for the decomposition of Ozone is: O_3 == O_2 + O with forward and reverse rate constants k_1 and k_1 O + O_3 -rightarrow 2 O_2 with rate constant k_2 Using the steady-state approximation for O, which of the following rate laws is consistent with the proposed mechanism? a. d[O_2]/dt = 3 k_1 k_2[O_3]/(k_1[O_2] + k_2[O_3]) b. d[O_2]/dt = 2 k_1 k_2[O_3]^2/(k_1 + k_2) c. d[O_2]/dt = 3 k_1 k_2[O_3]^2/(k_1 [O_2] + k_2[O_3]) d. d[O_2]/dt = 3 k_1 k_2[O_3]/(k_1 [O_2] + k_2[O_3]^2) e. none of the above

Explanation / Answer

answer

option b

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e steady-state approximation applies to [O] (but see the question below).

Then d[O] dt = 0 = k1[O3] k! 1[O][O2] k2[O][O3].

solving for [O],

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

Rate = 1 /2 * d[O3] /dt ,

d[O3] /dt = k1[O3] + k! 1[O][O2] k2[O][O3].

substituting for [O] from above,

d[O3]/ dt = = k1[O3] + k1[O3](k! 1[O2] k2[O3]) / k! 1[O2] + k2[O3]

= k1[O3](k! 1[O2] + k2[O3]) + k1[O3](k! 1[O2] k2[O3]) / k! 1[O2] + k2[O3]

=2k1k2[O3] 2 / k! 1[O2] + k2[O3] .

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