Suppose the decomposition of ozone proceeds by the following mechanism:step elementary reaction rate constant1 O3(g) → O2(g) + O(g) k12 O3(g) + O(g) → 2O2(g) k2Suppose also k1≫k2. That is, the first step is much faster than the second.Write the balanced chemical equation for the overall chemical reaction: Write the experimentally-observable rate law for the overall chemical reaction. =ratek Note: your answer should not contain the concentrations of any intermediates.Express the rate constant k for the overall chemical reaction in terms of k1, k2, and (if necessary) the rate constants k-1 and k-2 for the reverse of the two elementary reactions in the mechanism. =k
Question
Suppose the decomposition of ozone proceeds by the following mechanism:step elementary reaction rate constant1 O3(g) → O2(g) + O(g) k12 O3(g) + O(g) → 2O2(g) k2Suppose also k1≫k2. That is, the first step is much faster than the second.Write the balanced chemical equation for the overall chemical reaction: Write the experimentally-observable rate law for the overall chemical reaction. =ratek Note: your answer should not contain the concentrations of any intermediates.Express the rate constant k for the overall chemical reaction in terms of k1, k2, and (if necessary) the rate constants k-1 and k-2 for the reverse of the two elementary reactions in the mechanism. =k
Solution
The balanced chemical equation for the overall chemical reaction is:
2O3(g) → 3O2(g)
The experimentally-observable rate law for the overall chemical reaction is:
rate = k[O3]^2
This is because the overall reaction is second order with respect to O3.
The rate constant k for the overall chemical reaction cannot be expressed simply in terms of k1 and k2. This is because the rate constant for the overall reaction depends on the mechanism of the reaction, which includes the relative rates of the elementary steps and possible reverse reactions. However, if we assume that the first step is at equilibrium (because it is much faster than the second step), then we can express the rate constant for the overall reaction as:
k = k1 * k2 / (k-1 + k2)
where k-1 is the rate constant for the reverse of the first elementary reaction. This expression assumes that the reverse of the second elementary reaction is negligible, which may or may not be a good assumption depending on the specific system.
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