12.6 Exercise 8 — General Chemistry

Experiments were conducted to study the rate of the reaction represented by this equation.This question is taken from the Chemistry Advanced Placement Examination and is used with the permission of the Educational Testing Service.
$\text{2NO} \left(g\right) + 2 \text{H}_{2} \left(g\right) \rightarrow \text{N}_{2} \left(g\right) + 2 \text{H}_{2} \text{O} \left(g\right)$

Initial concentrations and rates of reaction are given here.

Experiment	Initial Concentration [NO] (mol L⁻¹)	Initial Concentration, [H₂] (mol L⁻¹)	Initial Rate of Formation of N₂ (mol L⁻¹ min⁻¹)
1	0.0060	0.0010	1.8 $\times$ 10⁻⁴
2	0.0060	0.0020	3.6 $\times$ 10⁻⁴
3	0.0010	0.0060	0.30 $\times$ 10⁻⁴
4	0.0020	0.0060	1.2 $\times$ 10⁻⁴

Consider the following questions:

(a) Determine the order for each of the reactants, NO and H₂, from the data given and show your reasoning.

(b) Write the overall rate law for the reaction.

(d) For experiment 2, calculate the concentration of NO remaining when exactly one-half of the original amount of H₂ had been consumed.

(e) The following sequence of elementary steps is a proposed mechanism for the reaction.

Step 1: $\text{NO} + \text{NO} \rightleftharpoons \text{N}_{2} \text{O}_{2}$

Step 2: $\text{N}_{2} \text{O}_{2} + \text{H}_{2} \rightleftharpoons \text{H}_{2} \text{O} + \text{N}_{2} \text{O}$

Step 3: $\text{N}_{2} \text{O} + \text{H}_{2} \rightleftharpoons \text{N}_{2} + \text{H}_{2} \text{O}$

Based on the data presented, which of these is the rate determining step? Show that the mechanism is consistent with the observed rate law for the reaction and the overall stoichiometry of the reaction.

OpenStax Chemistry 2e, 12.6 Reaction Mechanisms, exercise 8

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