Nitrogen monoxide is oxidized by to form

CHEMISTRY · Multi-part · A Level · Chemistry · Rate equations · Rate equations

Problem

Nitrogen monoxide is oxidized by O2(g)O_2(g) to form NO2(g)NO_2(g). Kinetic evidence suggests the reaction occurs by the two-step sequence shown below at 298 K298\,\text{K}: Step 1 2 NO(g)⇌N2O2(g)2\,NO(g) \rightleftharpoons N_2O_2(g)  (fast) Step 2 N2O2(g)+O2(g)→2 NO2(g)N_2O_2(g) + O_2(g) \to 2\,NO_2(g)  (slow) A chemist investigates the rate when [O2][O_2] is held constant at 0.050 M0.050\,\text{M}. Initial-rate data are listed in the table. Run [NO] (M)[NO]\,(\text{M}) Initial rate r (M⋅s−1)r\,(\text{M}\cdot\text{s}^{-1}) 1  0.010  1.5×10−41.5\times10^{-4} 2  0.020  6.0×10−46.0\times10^{-4} 3  0.050  3.8×10−33.8\times10^{-3} 4  0.100  1.5×10−21.5\times10^{-2} (a) Derive an expression for the initial rate rr in terms of the rate constant k2k_2 for Step 2, the equilibrium constant K1K_1 for Step 1, and the concentrations [NO][NO] and [O2][O_2]. (b) When [O2][O_2] is fixed, show how your result from part (a) can be rewritten in the linear form log⁡r=m log⁡[NO]+b\log r = m\,\log [NO] + b, and identify the theoretical values of the slope mm and intercept bb in terms of K1K_1, k2k_2, and [O2][O_2]. (c) Using the experimental data, construct (numerically) a log⁡r\log r versus log⁡[NO]\log [NO] plot. Determine the best-fit slope mexpm_{\text{exp}} and yy-intercept bexpb_{\text{exp}}. Show all calculations. (d) Compare mexpm_{\text{exp}} with the theoretical slope from part (b). State whether the experimental evidence supports the proposed mechanism and justify your conclusion quantitatively.

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