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Given the following reactions and the corresponding rate laws, in which of the reactions might the elementary reaction and the overall reaction be the same?\(\begin{aligned}{\rm{(a) C}}{{\rm{l}}_2}{\rm{ + CO }} \to {\rm{ C}}{{\rm{l}}_2}{\rm{CO}}\\{\rm{rate = }}k{{\rm{(C}}{{\rm{l}}_2}{\rm{)}}^{\frac{3}{2}}}{\rm{(CO)}}\\{\rm{(b) PC}}{{\rm{l}}_3}{\rm{ + C}}{{\rm{l}}_{\rm{2}}}{\rm{ }} \to {\rm{ PC}}{{\rm{l}}_{\rm{5}}}\\{\rm{rate = }}k{\rm{(PC}}{{\rm{l}}_{\rm{3}}}{\rm{) (C}}{{\rm{l}}_{\rm{2}}}{\rm{)}}\\{\rm{(c) 2NO + }}{{\rm{H}}_{\rm{2}}}{\rm{ }} \to {\rm{ }}{{\rm{N}}_{\rm{2}}}{\rm{ + }}{{\rm{H}}_{\rm{2}}}{\rm{O}}\\{\rm{rate = }}k{\rm{(NO)(}}{{\rm{H}}_{\rm{2}}}{\rm{)}}\\{\rm{(d) 2NO + }}{{\rm{O}}_{\rm{2}}}{\rm{ }} \to {\rm{ 2N}}{{\rm{O}}_{\rm{2}}}\\{\rm{rate = }}k{{\rm{(NO)}}^{\rm{2}}}{\rm{(}}{{\rm{O}}_{\rm{2}}}{\rm{)}}\\{\rm{(e) NO + }}{{\rm{O}}_{\rm{3}}}{\rm{ }} \to {\rm{ N}}{{\rm{O}}_{\rm{2}}}{\rm{ + }}{{\rm{O}}_{\rm{2}}}\\{\rm{rate = }}k{\rm{(NO)(}}{{\rm{O}}_{\rm{3}}}{\rm{)}}\end{aligned}\)

Short Answer

Expert verified

The reactions given below may have the same elementary reaction and overall reaction.\(\begin{aligned}{\rm{(b) PC}}{{\rm{l}}_3}{\rm{ + C}}{{\rm{l}}_{\rm{2}}}{\rm{ }} \to {\rm{ PC}}{{\rm{l}}_{\rm{5}}}\\{\rm{rate = }}k{\rm{(PC}}{{\rm{l}}_{\rm{3}}}{\rm{) (C}}{{\rm{l}}_{\rm{2}}}{\rm{)}}\\{\rm{(d) 2NO + }}{{\rm{O}}_{\rm{2}}}{\rm{ }} \to {\rm{ 2N}}{{\rm{O}}_{\rm{2}}}\\{\rm{rate = }}k{{\rm{(NO)}}^{\rm{2}}}{\rm{(}}{{\rm{O}}_{\rm{2}}}{\rm{)}}\\{\rm{(e) NO + }}{{\rm{O}}_{\rm{3}}}{\rm{ }} \to {\rm{ N}}{{\rm{O}}_{\rm{2}}}{\rm{ + }}{{\rm{O}}_{\rm{2}}}\\{\rm{rate = }}k{\rm{(NO)(}}{{\rm{O}}_{\rm{3}}}{\rm{)}}\end{aligned}\)

Step by step solution

01

Definition of Elementary Reaction

Chemical reactions generally occur in steps. Every step which occurs in the reaction mechanism is called the elementary reaction. For example, the decomposition of ozone occurs in a two-step mechanism.\(\begin{aligned}{{\rm{O}}_{\rm{3}}}{\rm{(g) }} \to {\rm{ }}{{\rm{O}}_{\rm{2}}}{\rm{(g) + O}}\\{\rm{O + }}{{\rm{O}}_{\rm{3}}}{\rm{(g) }} \to {\rm{ 2}}{{\rm{O}}_{\rm{2}}}{\rm{(g)}}\end{aligned}\)The elementary steps combine to give the overall reaction, for the above decomposition of ozone, the overall reaction would be,\({\rm{2}}{{\rm{O}}_{\rm{3}}}{\rm{(g) }} \to {\rm{ 3}}{{\rm{O}}_{\rm{2}}}{\rm{(g)}}\)An elementary reaction can also be an overall reaction.

02

Reactions that may have the same Elementary Reaction and Overall Reaction

The below reactions have mechanisms involving a single bimolecular elementary reaction with the same overall reaction with a supporting rate equation for the reaction.\(\begin{aligned}{\rm{(b) PC}}{{\rm{l}}_3}{\rm{ + C}}{{\rm{l}}_{\rm{2}}}{\rm{ }} \to {\rm{ PC}}{{\rm{l}}_{\rm{5}}}\\{\rm{rate = }}k{\rm{(PC}}{{\rm{l}}_{\rm{3}}}{\rm{) (C}}{{\rm{l}}_{\rm{2}}}{\rm{)}}\end{aligned}\)\(\begin{aligned}{\rm{(e) NO + }}{{\rm{O}}_{\rm{3}}}{\rm{ }} \to {\rm{ N}}{{\rm{O}}_{\rm{2}}}{\rm{ + }}{{\rm{O}}_{\rm{2}}}\\{\rm{rate = }}k{\rm{(NO)(}}{{\rm{O}}_{\rm{3}}}{\rm{)}}\end{aligned}\)The below reaction has a termolecular elementary reaction with the same overall reaction with a supporting rate equation for the reaction.\(\begin{aligned}{\rm{(d) 2NO + }}{{\rm{O}}_{\rm{2}}}{\rm{ }} \to {\rm{ 2N}}{{\rm{O}}_{\rm{2}}}\\{\rm{rate = }}k{{\rm{(NO)}}^{\rm{2}}}{\rm{(}}{{\rm{O}}_{\rm{2}}}{\rm{)}}\end{aligned}\)

03

Reactions that may not have the same Elementary Reaction and Overall Reaction

In the below reaction, the overall reaction cannot be an elementary reaction as from the given rate equation, it is highly doubtful to calculate the concentration with power raised to \(\frac{3}{2}\).\(\begin{aligned}{\rm{(a) C}}{{\rm{l}}_2}{\rm{ + CO }} \to {\rm{ C}}{{\rm{l}}_2}{\rm{CO}}\\{\rm{rate = }}k{{\rm{(C}}{{\rm{l}}_2}{\rm{)}}^{\frac{3}{2}}}{\rm{(CO)}}\end{aligned}\)In the below reaction, the overall reaction cannot be an elementary reaction as the given rate equation is different and should have been \({\rm{rate = }}k{{\rm{(NO)}}^2}{\rm{(}}{{\rm{H}}_{\rm{2}}}{\rm{)}}\)for both elementary and overall reaction to be the same. \(\begin{aligned}{\rm{(c) 2NO + }}{{\rm{H}}_{\rm{2}}}{\rm{ }} \to {\rm{ }}{{\rm{N}}_{\rm{2}}}{\rm{ + }}{{\rm{H}}_{\rm{2}}}{\rm{O}}\\{\rm{rate = }}k{\rm{(NO)(}}{{\rm{H}}_{\rm{2}}}{\rm{)}}\end{aligned}\)Thus, equations (b), (d), (e) may have the same elementary and overall reaction.

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Most popular questions from this chapter

Use the PhET Reactions & Rates interactive simulation to simulate a system. On the 鈥淪ingle collision鈥 tab of the simulation applet, enable the 鈥淓nergy view鈥 by clicking the 鈥+鈥 icon. Select the first A + BC鉄禔B + C reaction (A is yellow, B is purple, and C is navy blue). Using the 鈥渟traight shot鈥 default option, try launching the A atom with varying amounts of energy. What changes when the Total Energy line at launch is below the transition state of the Potential Energy line? Why? What happens when it is above the transition state? Why?

Does the following data fit a second-order rate law?

Trial

Time(s)

(A) (M)

1

5

0.952

2

10

0.625

3

15

0.465

4

20

0.370

5

25

0.308

6

35

0.230

In the nuclear industry, chlorine trifluoride is used to prepare uranium hexafluoride, a volatile compound of uranium used in the separation of uranium isotopes. Chlorine trifluoride is prepared by the reaction \({\bf{C}}{{\bf{l}}_{\bf{2}}}{\bf{(g) + 3}}{{\bf{F}}_{\bf{2}}}{\bf{(g)}} \to {\bf{2Cl}}{{\bf{F}}_{\bf{3}}}{\bf{(g)}}\). Write the equation that relates the rate expressions for this reaction in terms of the disappearance of \({\bf{C}}{{\bf{l}}_{\bf{2}}}\) and \({{\bf{F}}_{\bf{2}}}\) and the formation of \({\bf{Cl}}{{\bf{F}}_{\bf{3}}}\).

What is the half-life for the decomposition of \({{\bf{O}}_{\bf{3}}}\) when the concentration of \({{\bf{O}}_{\bf{3}}}\)is \({\bf{2}}{\bf{.35 \times 1}}{{\bf{0}}^{{\bf{ - 6}}}}\)M? The rate constant for this second-order reaction is 50.4 L/mol/h.

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

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