Chapter 12, Problem 75E

Experiments were conducted to study the rate of the reaction represented by this equation.^[2]

$2\text{NO}\left(g\right)+2{\text{H}}_2\left(g\right)\to {\text{N}}_2\left(g\right)+2{\text{H}}_2\text{O}\left(g\right)$

Initial concentrations and rates of reaction are given here.

Experiment

Initial Concentration

[NO] (mol/L)Initial Concentration,

[H₂] (mol/L)Initial Rate of Formation of

N₂ (mol/L min) 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.

(c) Calculate the value of the rate constant, k, for the reaction. Include units.

(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.