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Chapter 11: Problem 61

A proposed mechanism for a reaction is $$\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{Br} \longrightarrow \mathrm{C}_{4} \mathrm{H}_{9}^{+}+\mathrm{Br}^{-} \quad \text { Slow }$$ $$\mathrm{C}_{4} \mathrm{H}_{9}^{+}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{C}_{4} \mathrm{H}_{9} \mathrm{OH}_{2}^{+} \quad \text { Fast }$$ $$\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{OH}_{2}^{+}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{C}_{4} \mathrm{H}_{9} \mathrm{OH}+\mathrm{H}_{3} \mathrm{O}^{+}\quad \text { Fast }$$ Write the rate law expected for this mechanism. What is the overall balanced equation for the reaction? What are the intermediates in the proposed mechanism?

Short Answer

Expert verified
The rate law for the proposed mechanism is Rate = \(k[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{Br}]\), the overall balanced equation is: $$\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{Br} + \mathrm{H}_{2}\mathrm{O} \longrightarrow \mathrm{C}_{4}\mathrm{H}_{9}\mathrm{OH} + \mathrm{H}_{3}\mathrm{O}^{+} + \mathrm{Br}^{-}$$ And the intermediates are: 1. $$\mathrm{C}_{4}\mathrm{H}_{9}^{+}$$ 2. $$\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{OH}_{2}^{+}$$

Step by step solution

01

The rate-determining step, or slow step, is the slowest step in the mechanism, which dictates the rate law. In this case, the slow step is provided: $$\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{Br} \longrightarrow \mathrm{C}_{4} \mathrm{H}_{9}^{+}+\mathrm{Br}^{-} \quad \text { Slow }$$ #Step 2: Write the rate law for the rate-determining step#

Since the rate-determining step is the slowest step, its rate law will be the overall rate law for the mechanism. The rate of the reaction can be written as k times the concentration of the reactant in the slow step: Rate = \(k[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{Br}]\) #Step 3: Identify the overall balanced equation for the reaction#
02

To find the overall balanced equation for the reaction, we need to add all the elementary steps of the mechanism: 1. $$\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{Br} \longrightarrow \mathrm{C}_{4}\mathrm{H}_{9}^{+} + \mathrm{Br}^{-}$$ 2. $$\mathrm{C}_{4}\mathrm{H}_{9}^{+}+\mathrm{H}_{2}\mathrm{O} \longrightarrow \mathrm{C}_{4}\mathrm{H}_{9}\mathrm{OH}_{2}^{+}$$ 3. $$\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{OH}_{2}^{+}+\mathrm{H}_{2}\mathrm{O} \longrightarrow \mathrm{C}_{4}\mathrm{H}_{9}\mathrm{OH} + \mathrm{H}_{3}\mathrm{O}^{+}$$ Add them together and cancel out any intermediate species that appear on both sides of the equation: $$\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{Br} + \mathrm{H}_{2}\mathrm{O} \longrightarrow \mathrm{C}_{4}\mathrm{H}_{9}\mathrm{OH} + \mathrm{H}_{3}\mathrm{O}^{+} + \mathrm{Br}^{-}$$ #Step 4: Identify the intermediates in the mechanism#

Intermediates are species that are produced in one step and consumed in another. In this mechanism, the intermediates are: 1. $$\mathrm{C}_{4}\mathrm{H}_{9}^{+}$$: Produced in the first step and consumed in the second step. 2. $$\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{OH}_{2}^{+}$$: Produced in the second step and consumed in the third step. In conclusion, the rate law for the proposed mechanism is Rate = \(k[\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{Br}]\), the overall balanced equation is: $$\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{Br} + \mathrm{H}_{2}\mathrm{O} \longrightarrow \mathrm{C}_{4}\mathrm{H}_{9}\mathrm{OH} + \mathrm{H}_{3}\mathrm{O}^{+} + \mathrm{Br}^{-}$$ And the intermediates are: 1. $$\mathrm{C}_{4}\mathrm{H}_{9}^{+}$$ 2. $$\mathrm{C}_{4}\mathrm{H}_{9}\mathrm{OH}_{2}^{+}$$

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Most popular questions from this chapter

Define \(stability\) from both a kinetic and thermodynamic perspective. Give examples to show the differences in these concepts.

You and a coworker have developed a molecule that has shown potential as cobra antivenin (AV). This antivenin works by binding to the venom (V), thereby rendering it nontoxic. This reaction can be described by the rate law $$\text { Rate }=k[\mathrm{AV}]^{1}[\mathrm{V}]^{1}$$ You have been given the following data from your coworker: $$[\mathrm{V}]_{0}=0.20 \space\mathrm{M}$$ $$[\mathrm{AV}]_{0}=1.0 \times 10^{-4} \space\mathrm{M}$$A plot of \(\ln [\mathrm{AV}]\) versus \(t\) (s) gives a straight line with a slope of \(-0.32 \mathrm{s}^{-1} .\) What is the value of the rate constant \((k)\) for this reaction?

Each of the statements given below is false. Explain why. a. The activation energy of a reaction depends on the overall energy change \((\Delta E)\) for the reaction. b. The rate law for a reaction can be deduced from examination of the overall balanced equation for the reaction. c. Most reactions occur by one-step mechanisms.

Two isomers \((A \text { and } B)\) of a given compound dimerize as follows: $$\begin{aligned} &2 \mathrm{A} \stackrel{k_{1}}{\longrightarrow} \mathrm{A}_{2}\\\ &2 \mathrm{B} \stackrel{k_{2}}{\longrightarrow} \mathrm{B}_{2} \end{aligned}$$ Both processes are known to be second order in reactant, and \(k_{1}\) is known to be 0.250 \(\mathrm{L} / \mathrm{mol} \cdot \mathrm{s}\) at \(25^{\circ} \mathrm{C} .\) In a particular experiment \(\mathrm{A}\) and \(\mathrm{B}\) were placed in separate containers at \(25^{\circ} \mathrm{C}\) where \([\mathrm{A}]_{0}=1.00 \times 10^{-2} \mathrm{M}\) and \([\mathrm{B}]_{0}=2.50 \times 10^{-2} \mathrm{M} .\) It was found that after each reaction had progressed for 3.00 min, \([\mathrm{A}]=3.00[\mathrm{B}] .\) In this case the rate laws are defined as $$\begin{array}{l} \text { Rate }=-\frac{\Delta[\mathrm{A}]}{\Delta t}=k_{1}[\mathrm{A}]^{2} \\ \text { Rate }=-\frac{\Delta[\mathrm{B}]}{\Delta t}=k_{2}[\mathrm{B}]^{2} \end{array}$$ a. Calculate the concentration of \(\mathrm{A}_{2}\) after 3.00 min. b. Calculate the value of \(k_{2}\) c. Calculate the half-life for the experiment involving A.

The rate law for the decomposition of phosphine \(\left(\mathrm{PH}_{3}\right)\) is $$\text { Rate }=-\frac{\Delta\left[\mathrm{PH}_{3}\right]}{\Delta t}=k\left[\mathrm{PH}_{3}\right]$$ It takes \(120 .\) s for \(1.00 M\) PH \(_{3}\) to decrease to 0.250 M. How much time is required for \(2.00\space \mathrm{M} \mathrm{PH}_{3}\) to decrease to a concentration of \(0.350\space \mathrm{M} ?\)
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