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Chapter 14: Problem 86

NO catalyzes the decomposition of \(\mathrm{N}_{2} \mathrm{O},\) possibly by the following mechanism: $$ \begin{aligned} \mathrm{NO}(g)+\mathrm{N}_{2} \mathrm{O}(g) & \longrightarrow \mathrm{N}_{2}(g)+\mathrm{NO}_{2}(g) \\ 2 \mathrm{NO}_{2}(g) & \longrightarrow 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \end{aligned} $$ (a) What is the chemical equation for the overall reaction? Show how the two steps can be added to give the overall equation. (b) Why is NO considered a catalyst and not an intermediate? (c) If experiments show that during the decomposition of \(\mathrm{N}_{2} \mathrm{O}, \mathrm{NO}_{2}\) does not accumulate in measurable quantities, does this rule out the proposed mechanism? If you think not, suggest what might be going on.

Short Answer

Expert verified
The overall reaction equation for the decomposition of N2O is N2O(g) → N2(g) + O2(g). NO is considered a catalyst, as it is involved in the reaction but not consumed by the end. The low accumulation of NO2 does not rule out the proposed mechanism but supports it, as NO2 could be rapidly reacting, keeping its concentration low.

Step by step solution

01

Determine the overall reaction equation

To find the overall chemical equation, we need to add both steps of the given mechanism and simplify. Given steps: 1. NO(g) + N2O(g) → N2(g) + NO2(g) 2. 2NO2(g) → 2NO(g) + O2(g) Add both equations together: NO(g) + N2O(g) + 2NO2(g) → N2(g) + NO2(g) + 2NO(g) + O2(g) Now cancel out the species appearing on both sides: N2O(g) → N2(g) + O2(g)
02

Determine if NO is a catalyst or an intermediate

A catalyst is a substance that is involved in a reaction and helps speed up the reaction, but is not consumed in the process. An intermediate is a species that is formed and consumed during the overall reaction. Since NO appears in both steps, but not in the overall reaction equation: N2O(g) → N2(g) + O2(g) NO is considered a catalyst, not an intermediate, because it is involved in the reaction but is not consumed by the end of the process.
03

Discuss whether the experimental evidence rules out the proposed mechanism or not

The experimental evidence shows that NO2 does not accumulate in measurable quantities during the decomposition of N2O, which is consistent with this proposed mechanism since NO2 is an intermediate. This observation does not rule out the proposed mechanism but supports it. It is possible that the reaction occurs rapidly, so the concentration of NO2 remains low with little to no accumulation.

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Most popular questions from this chapter

For each of the following gas-phase reactions, write the rate expression in terms of the appearance of each product and disappearance of each reactant: (a) \(2 \mathrm{H}_{2} \mathrm{O}(g) \longrightarrow 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)\) (b) \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)\) (c) \(2 \mathrm{NO}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)\) (d) \(\mathrm{N}_{2}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{H}_{4}(g)\)

What is the molecularity of each of the following elementary reactions? Write the rate law for each. (a) \(2 \mathrm{NO}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{2}(g)\)

The following is a quote from an article in the August 18,1998 , issue of The New York Times about the breakdown of cellulose and starch: "A drop of 18 degrees Fahrenheit [from \(77^{\circ} \mathrm{F}\) to \(\left.59^{\circ} \mathrm{F}\right]\) lowers the reaction rate six times; a 36 -degree drop [from \(77^{\circ} \mathrm{F}\) to \(\left.41^{\circ} \mathrm{F}\right]\) produces a fortyfold decrease in the rate." (a) Calculate activation energies for the breakdown process based on the two estimates of the effect of temperature on rate. Are the values consistent? (b) Assuming the value of \(E_{a}\) calculated from the 36 -degree drop and that the rate of breakdown is first order with a half-life at \(25^{\circ} \mathrm{C}\) of 2.7 years, calculate the half-life for breakdown at a temperature of \(-15^{\circ} \mathrm{C}\).

What is the molecularity of each of the following elementary reactions? Write the rate law for each. (a) \(\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{Cl}(g)\) (b) \(\mathrm{OCl}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{HOCl}(a q)+\mathrm{OH}^{-}(a q)\) (c) \(\mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{NOCl}_{2}(g)\)

The following data were collected for the rate of disappearance of \(\mathrm{NO}\) in the reaction \(2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)\) : $$ \begin{array}{llll} \hline \text { Experiment } & {[\mathrm{NO}](M)} & {\left[\mathrm{O}_{2}\right](M)} & \text { Initial Rate }(M / s) \\ \hline 1 & 0.0126 & 0.0125 & 1.41 \times 10^{-2} \\ 2 & 0.0252 & 0.0125 & 5.64 \times 10^{-2} \\ 3 & 0.0252 & 0.0250 & 1.13 \times 10^{-1} \end{array} $$ (a) What is the rate law for the reaction? (b) What are the units of the rate constant? (c) What is the average value of the rate constant calculated from the three data sets? (d) What is the rate of disappearance of \(\mathrm{NO}\) when \([\mathrm{NO}]=0.0750 \mathrm{M}\) and \(\left[\mathrm{O}_{2}\right]=0.0100 \mathrm{M} ?(\mathrm{e})\) What is the rate of disappearance of \(\mathrm{O}_{2}\) at the concentrations given in part ( \(\mathrm{d}\) )?
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