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Chapter 12: Q17E (page 703)

Regular flights of supersonic aircraft in the stratosphere are of concern because such aircraft produce nitric oxide, NO, as a by-product in the exhaust of their engines. Nitric oxide reacts with ozone, and it has been suggested that this could contribute to depletion of the ozone layer. The reaction \({\bf{NO + }}{{\bf{O}}_{\bf{3}}} \to {\bf{N}}{{\bf{O}}_{\bf{2}}}{\bf{ + }}{{\bf{O}}_{\bf{2}}}\) is first order with respect to both NO and \({{\bf{O}}_{\bf{3}}}\) with a rate constant of \({\bf{2}}{\bf{.20 \times 1}}{{\bf{0}}^{\bf{7}}}{\bf{mol}}{{\bf{L}}^{{\bf{ - 1}}}}{{\bf{s}}^{{\bf{ - 1}}}}\). What is the instantaneous rate of disappearance of NO when \(\left( {{\bf{NO}}} \right){\bf{ = 3}}{\bf{.3 \times 1}}{{\bf{0}}^{{\bf{ - 6}}}}{\bf{ M}}\) and \({\bf{(}}{{\bf{O}}_{\bf{3}}}{\bf{) = 5}}{\bf{.9 \times 1}}{{\bf{0}}^{{\bf{ - 7}}}}{\bf{ M}}\)?

Short Answer

Expert verified

The rate of disappearance of NO is \({\bf{4}}{\bf{.3 \times 1}}{{\bf{0}}^{{\bf{ - 5}}}}{\bf{Mol}}{{\bf{L}}^{{\bf{ - 1}}}}{{\bf{s}}^{{\bf{ - 1}}}}\).

Step by step solution

01

rate law 

The rate law for a chemical reaction is an expression that provides a relationship between the rate of the reaction and the concentration of the reactants participating in it.

Given reaction

\({\bf{NO + }}{{\bf{O}}_{\bf{3}}} \to {\bf{N}}{{\bf{O}}_{\bf{2}}}{\bf{ + }}{{\bf{O}}_{\bf{2}}}\)

The rate law or rate of disappearance of NO can be represented as

\({\bf{rate = k(NO)(}}{{\bf{O}}_{\bf{3}}}{\bf{)}}\)

02

Rate of reaction

Given the concentration value of NO is \({\bf{3}}{\bf{.3 \times 1}}{{\bf{0}}^{{\bf{ - 6}}}}\)M and \({{\bf{O}}_{\bf{3}}}\)is \({\bf{5}}{\bf{.9 \times 1}}{{\bf{0}}^{{\bf{ - 7}}}}{\bf{M}}\). The value of rate constant k is \({\bf{2}}{\bf{.20 \times 1}}{{\bf{0}}^{\bf{7}}}{\bf{M}}\) .

The rate of disappearance of NO can be calculated as;

\(\begin{aligned}{}{\bf{Rate}}\,{\bf{ = k(NO)(O}}{}_{\bf{3}}{\bf{)}}\\{\bf{ = 2}}{\bf{.2 \times 1}}{{\bf{0}}^{\bf{7}}}{\bf{LMo}}{{\bf{l}}^{{\bf{ - 1}}}}{{\bf{s}}^{{\bf{ - 1}}}}{\bf{(3}}{\bf{.3 \times 1}}{{\bf{0}}^{{\bf{ - 6}}}}{\bf{M)(5}}{\bf{.9 \times 1}}{{\bf{0}}^{{\bf{ - 7}}}}{\bf{M)}}\\{\bf{ = 4}}{\bf{.3 \times 1}}{{\bf{0}}^{{\bf{ - 5}}}}{\bf{Mol}}{{\bf{L}}^{{\bf{ - 1}}}}{{\bf{s}}^{{\bf{ - 1}}}}\end{aligned}\)

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Most popular questions from this chapter

Chemical reactions occur when reactants collide. What are two factors that may prevent a collision from producing a chemical reaction?

Consider this scenario and answer the following questions: Chlorine atoms resulting from decomposition of chlorofluoromethanes, such as \({\bf{CC}}{{\bf{l}}_{\bf{2}}}{{\bf{F}}_{\bf{2}}}\), catalyse the decomposition of ozone in the atmosphere. One simplified mechanism for the decomposition is:

\(\begin{aligned}{}{{\bf{O}}_{\bf{3}}}\overset{sunlight}{\rightarrow}{}{{\bf{O}}_{\bf{2}}}{\rm{ }} + {\rm{ }}{\bf{O}}\\{{\bf{O}}_{\bf{3}}}{\rm{ }} + {\rm{ }}{\bf{Cl}}\to {{\bf{O}}_{\bf{2}}}{\rm{ }} + {\rm{ }}{\bf{ClO}}\\{\bf{ClO}}{\rm{ }} + {\rm{ }}{\bf{O}}\to {\bf{Cl}}{\rm{ }} + {\rm{ }}{{\bf{O}}_{\bf{2}}}\end{aligned}\)

(a) Explain why chlorine atoms are catalysts in the gas-phase transformation:

\({\bf{2}}{{\bf{O}}_{\bf{3}}}\mathop {}\limits^{}\to {\bf{3}}{{\bf{O}}_{\bf{2}}}\)

(b) Nitric oxide is also involved in the decomposition of ozone by the mechanism: Is NO a catalyst for the decomposition? Explain your answer.

\(\begin{aligned}{}{{\bf{O}}_{\bf{3}}}\overset{sunlight}{\rightarrow}{\rm{ }}{{\bf{O}}_{\bf{2}}}{\rm{ }} + {\rm{ }}{\bf{O}}\\{{\bf{O}}_{\bf{3}}}{\rm{ }} + {\rm{ }}{\bf{NO}}\rightarrow {\bf{N}}{{\bf{O}}_{\bf{2}}}{\rm{ }} + {\rm{ }}{{\bf{O}}_{\bf{2}}}\\{\bf{N}}{{\bf{O}}_{\bf{2}}}{\rm{ }} + {\rm{ }}{\bf{O}}\rightarrow {\bf{NO}}{\rm{ }} + {\rm{ }}{{\bf{O}}_{\bf{2}}}\end{aligned}\)

Usethe data provided to graphically determine the order and rate constant of the following reaction: \({\bf{S}}{{\bf{O}}_{\bf{2}}}{\bf{C}}{{\bf{l}}_{\bf{2}}} \to {\bf{S}}{{\bf{O}}_{\bf{2}}}{\bf{ + C}}{{\bf{l}}_{\bf{2}}}\)

Time(hr)

0

5.00*\({\bf{1}}{{\bf{0}}^{\bf{3}}}\)

1.00*\({\bf{1}}{{\bf{0}}^{\bf{4}}}\)

1.50*\({\bf{1}}{{\bf{0}}^{\bf{4}}}\)

2.50*\({\bf{1}}{{\bf{0}}^{\bf{4}}}\)

3.00*104

4.00*104

\({\bf{(S}}{{\bf{O}}_{\bf{2}}}{\bf{C}}{{\bf{l}}_{\bf{2}}}{\bf{)}}\)(M)

0.100

0.0896

0.0802

0.0719

0.0577

0.0517

0.0415

Describe how graphical methods can be used to determine the order of a reaction and its rate constant from a series of data that includes the concentration of A at varying times.

Based on the diagrams in Exercise 12.83, which of the reactions has the fastest rate? Which has the slowest rate?
See all solutions

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