These data were collected for the reaction between hydrogen and nitric oxide at \(700^{\circ} \mathrm{C}\) : \(2 \mathrm{H}_{2}(g)+2 \mathrm{NO}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{N}_{2}(g)\) $$ \begin{array}{cllc} \text { Experiment } & {\left[\mathrm{H}_{2}\right]} & {[\mathrm{NO}]} & \text { Initial Rate }(\mathrm{M} / \mathrm{s}) \\ \hline 1 & 0.010 & 0.025 & 2.4 \times 10^{-6} \\ 2 & 0.0050 & 0.025 & 1.2 \times 10^{-6} \\ 3 & 0.010 & 0.0125 & 0.60 \times 10^{-6} \end{array} $$ (a) Determine the order of the reaction. (b) Calculate the rate constant. (c) Suggest a plausible mechanism that is consistent with the rate law. (Hint: Assume the oxygen atom is the intermediate.)

Step by step solution

01

Determine the Order of the Reaction

The order of the reaction can be determined by comparing the rate of reaction between different experiments. Comparing experiments 1 and 2, when the concentration of \(H_2\) is halved, the rate is also halved, indicating a first order dependence on \(H_2\). Comparing experiments 1 and 3, when the concentration of \(NO\) is halved, the rate is also halved, indicating a first order dependence on \(NO\). Thus, the reaction is second order: first order in \(H_2\) and first order in \(NO\). It can be written as: \(rate = k[H_2][NO]\).

02

Calculate the Rate Constant

The rate constant \(k\) can be calculated by rearranging the rate equation and inserting values from any of the experiments. For this scenario, data from experiment 1 will be used: \(k = rate / ([H_2][NO]) = 2.4 * 10^{-6} M/s / (0.010 M * 0.025 M) = 9.6 M^{-1} s^{-1}\).

03

Suggest a Plausible Mechanism

A plausible mechanism that is consistent with the rate law involves the formation of an intermediate species. As hinted in the question, assume that the Oxygen atom forms the intermediate. The proposed mechanism can be as follows: (1) \(H_2 + NO \longrightarrow H_2O + N\), (2) \(N + NO \longrightarrow N_2 + O\), (3) \(H_2 + O \longrightarrow H_2O\). The rate-determining step, which is the slowest step, should be the step that matches the rate law determined earlier. In this case, step 1 leads to a rate law that matches the determined rate law: \(rate = k [H_2][NO]\), thus it this can be considered as the rate-determining step.

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