Suppose the decomposition of dinitrogen monoxide proceeds by the following mechanism:step elementary reaction rate constant1 N2O(g) → N2(g) + O(g) k12 N2O(g) + O(g) → N2(g) + O2(g) k2Suppose also k1≪k2. That is, the first step is much slower 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 dinitrogen monoxide proceeds by the following mechanism:step elementary reaction rate constant1 N2O(g) → N2(g) + O(g) k12 N2O(g) + O(g) → N2(g) + O2(g) k2Suppose also k1≪k2. That is, the first step is much slower 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:
2N2O(g) → 2N2(g) + O2(g)
The experimentally-observable rate law for the overall chemical reaction is:
rate = k[N2O]^2
This is because the slow step (rate-determining step) is the first step, and it involves one molecule of N2O. The second step is fast and involves another molecule of N2O and the O produced in the first step. Since the O is an intermediate, it is not included in the rate law.
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 is:
k = k1 * k2 / (k-1 + k2)
This is because the overall rate constant is determined by the rate constants of the individual steps and their reverse reactions. However, since k1 is much smaller than k2, we can simplify this to:
k = k1
This is because the rate of the overall reaction is determined by the slowest step, which is the first step in this case.
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