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Chapter 8: Problem 117

The bromination of acetone that occurs in acid solution is represented by this equation. \(\mathrm{CH}_{3} \mathrm{COCH}_{3}(\mathrm{aq})+\mathrm{Br}_{2}\) (aq) \(\rightarrow\) \(\mathrm{CH}_{3} \mathrm{COCH}_{2} \mathrm{Br}(\mathrm{aq})+\mathrm{H}^{+}(\mathrm{aq})+\mathrm{Br}(\mathrm{aq})\) These kinetic data were obtained from given reaction concentrations. Initial concentrations, (M) \(\begin{array}{lll}{\left[\mathrm{CH}_{3} \mathrm{COCH}_{3}\right]} & {\left[\mathrm{Br}_{2}\right]} & {\left[\mathrm{H}^{+}\right]} \\ 0.30 & 0.05 & 0.05 \\ 0.30 & 0.10 & 0.05 \\\ 0.30 & 0.10 & 0.10 \\ 0.40 & 0.05 & 0.20 \\ \text { Initial rate, disappearance of } & \end{array}\) disappearance of \(\mathrm{Br}_{2}, \mathrm{Ms}^{-1}\) \(5.7 \times 10^{-5}\) \(5.7 \times 10^{-5}\) \(1.2 \times 10^{-4}\) \(3.1 \times 10^{-4}\) Based on these data, the rate equation is: a. Rate \(=\mathrm{k}\left[\mathrm{CH}_{3} \mathrm{COCH}_{3}\right]\left[\mathrm{Br}_{2}\right]\left[\mathrm{H}^{+}\right]^{2}\) b. Rate \(=\mathrm{k}\left[\mathrm{CH}_{3} \mathrm{COCH}_{3}\right]\left[\mathrm{Br}_{2}\right]\left[\mathrm{H}^{+}\right]\) c. Rate \(=\mathrm{k}\left[\mathrm{CH}_{3} \mathrm{COCH}_{3}\right]\left[\mathrm{H}^{+}\right]\) d. Rate \(=\mathrm{k}\left[\mathrm{CH}_{3} \mathrm{COCH}_{3}\right]\left[\mathrm{Br}_{2}\right]\)

Short Answer

Expert verified
c. Rate \(=k[\mathrm{CH}_3\mathrm{COCH}_3][\mathrm{H}^+]\)

Step by step solution

01

Analyze the given data and reactions

We need to determine the order of the reaction with respect to each reactant: \([\mathrm{CH}_3\mathrm{COCH}_3]\), \([\mathrm{Br}_2]\), and \([\mathrm{H}^+]\). The reaction rate for the disappearance of \(\mathrm{Br}_2\) is given for different initial concentrations of these reactants.
02

Determine the effect of each reactant on the rate

First, examine trials where the concentration of a single reactant changes while others remain constant. This helps isolate the order with respect to that reactant.
03

Determine the order with respect to \([\mathrm{Br}_2]\)

In trials 1 and 2, the concentration of \([\mathrm{Br}_2]\) is changed from 0.05 M to 0.10 M, but the rate remains \(5.7 \times 10^{-5} \, \mathrm{Ms}^{-1}\). This indicates that the rate is independent of \([\mathrm{Br}_2]\). Thus, the order with respect to \([\mathrm{Br}_2]\) is 0.
04

Determine the order with respect to \([\mathrm{H}^+]\)

Compare trials 2 and 3, where \([\mathrm{H}^+]\) changes from 0.05 M to 0.10 M, and the rate changes from \(5.7 \times 10^{-5} \, \mathrm{Ms}^{-1}\) to \(1.2 \times 10^{-4} \, \mathrm{Ms}^{-1}\). Doubling \([\mathrm{H}^+]\) roughly doubles the rate, suggesting a first-order dependence on \([\mathrm{H}^+]\).
05

Determine the order with respect to \([\mathrm{CH}_3\mathrm{COCH}_3]\)

Compare trials 2 and 4, where \([\mathrm{CH}_3\mathrm{COCH}_3]\) increases from 0.30 M to 0.40 M while other reactant concentrations remain constant. The rate changes from \(5.7 \times 10^{-5} \, \mathrm{Ms}^{-1}\) to \(3.1 \times 10^{-4} \, \mathrm{Ms}^{-1}\). Thus, the rate increases by more than five times, indicating a first-order dependence on \([\mathrm{CH}_3\mathrm{COCH}_3]\).
06

Write the rate equation based on observations

Based on the above analysis, the rate is 0th order with respect to \([\mathrm{Br}_2]\), first order with respect to \([\mathrm{H}^+]\), and first order with respect to \([\mathrm{CH}_3\mathrm{COCH}_3]\). Thus, the rate law is: \[ \text{Rate} = k[\mathrm{CH}_3\mathrm{COCH}_3][\mathrm{H}^+] \]. This corresponds to option c.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Reaction Order
Understanding reaction order helps us predict how a change in concentration affects the rate of a chemical reaction. A reaction can be zero, first, second, or even fractional order with respect to a given reactant. This refers to the exponent of the concentration in the rate law. In the bromination of acetone, we examine each reactant one at a time to determine its impact on the reaction rate. Trials help us observe how changes in initial concentrations alter the rate:
  • If rate remains constant despite concentration change, the reaction is zero order with respect to that reactant.
  • If the rate changes proportionally to the concentration change, the reaction is first order for that reactant.
  • Higher dependencies can exist, suggesting more complex relationships.
This process reveals how sensitive a reaction is to concentration changes, guiding us towards forming a precise rate law.
Rate Law
A rate law expresses the rate of a chemical reaction as a function of the concentration of its reactants. For any given reaction, the rate law helps predict the speed at which reactants transform into products, considering different conditions. In the bromination of acetone, the rate law derived was:\[\text{Rate} = k[\text{CH}_3\text{COCH}_3][\text{H}^+]\]This tells us that the rate directly depends on the concentrations of acetone and hydrogen ions. The constant \(k\), called the rate constant, reflects the speed of the reaction. It's influenced by factors like temperature and the presence of a catalyst. Understanding the rate law allows us to:
  • Predict the effect of changing reactant concentrations.
  • Determine the necessary conditions to achieve a desired reaction speed.
  • Gain deeper insight into the reaction mechanism.
Bromination of Acetone
The bromination of acetone is a chemical reaction where bromine is added to acetone in the presence of an acid solution. This reaction is represented by the equation:\[\text{CH}_3\text{COCH}_3\,(\text{aq}) + \text{Br}_2\,(\text{aq}) \rightarrow \text{CH}_3\text{COCH}_2\text{Br}\,(\text{aq}) + \text{H}^+\,(\text{aq}) + \text{Br}^−\,(\text{aq})\]During this process, bromine is added to the acetone molecule, specifically replacing a hydrogen atom in the methyl group, making it a substitution reaction. The kinetic study of this reaction provides insights into its behavior under different conditions:
  • The reaction is zero order with respect to bromine \([\text{Br}_2]\), meaning its concentration does not affect the rate.
  • The reaction is first order in acetone \([\text{CH}_3\text{COCH}_3]\) and hydrogen ion \([\text{H}^+]\).
  • This information helps us in industrial processes where controlled reaction rates are crucial for efficiency and safety.
By understanding reactions like this, chemists can optimize conditions for desired outcomes in various applications.

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Most popular questions from this chapter

Match the following: (Here \(\mathrm{a}=\) Initial concentration of the reactant, \(\mathrm{p}=\) Initial pressure of the reactant) List I List II A. \(t \frac{1}{2}=\) constant (p) Zero order B. \(\mathrm{t} \frac{1}{2} \alpha \mathrm{a}\) (q) First order C. \(\mathrm{t} 1 / 2 \alpha \mathrm{l} / \mathrm{a}\) (r) Second order D. \(t^{1 / 2} \alpha p^{-1}\) (s) Pseudo first order

The following set of data was obtained by the method of initial rates for the reaction: $$ \begin{aligned} &\mathrm{S}_{2} \mathrm{O}_{8}^{2-}(\mathrm{aq})+3 \mathrm{I}^{-}(\mathrm{aq}) \rightarrow \\ &2 \mathrm{SO}_{4}^{2-}(\mathrm{aq})+\mathrm{I}_{3}-(\mathrm{aq}) \end{aligned} $$ What is the rate law for the reaction? $$ \begin{array}{lll} \hline\left[\mathrm{S}_{2} \mathrm{O}_{8}^{2-}\right], \mathrm{M} & {[\mathrm{I}-], \mathrm{M}} & \text { Initial rate, } \mathrm{M} \mathrm{s}^{-1} \\ \hline 0.25 & 0.10 & 9.00 \times 10^{-3} \\ 0.10 & 0.10 & 3.60 \times 10^{-3} \\ 0.20 & 0.30 & 2.16 \times 10^{-2} \\ \hline \end{array} $$ a. Rate \(=\mathrm{k}\left[\mathrm{S}_{2} \mathrm{O}_{8}^{2-}\right]\left[\mathrm{I}^{-}\right]^{2}\) b. Rate \(=\mathrm{k}\left[\mathrm{S}_{2} \mathrm{O}_{8}^{2-}\right]^{2}\left[\mathrm{I}^{-}\right]\) c. Rate \(=\mathrm{k}\left[\mathrm{S}_{2} \mathrm{O}_{8}^{2-}\right]\left[\mathrm{I}^{-}\right]\) d. Rate \(=\mathrm{k}\left[\mathrm{S}_{2} \mathrm{O}_{8}^{2-}\right]\left[\mathrm{I}^{-}\right]^{5}\)

In the following question two statements Assertion (A) and Reason (R) are given Mark. a. If \(\mathrm{A}\) and \(\mathrm{R}\) both are correct and \(\mathrm{R}\) is the correct explanation of \(\mathrm{A}\); b. If \(A\) and \(R\) both are correct but \(R\) is not the correct explanation of \(\mathrm{A}\); c. \(\mathrm{A}\) is true but \(\mathrm{R}\) is false; d. \(\mathrm{A}\) is false but \(\mathrm{R}\) is true, e. \(\mathrm{A}\) and \(\mathrm{R}\) both are false. (A): Order of reaction is an experimental property and irrespective of the fact whether the reaction is elementary or complicated, it is the sum of the powers of the concentration terms appearing in the rate law that is, experimentally observed rate law. (R): Order of reaction may change with change in experimental conditions.

The aquation of tris-(1,10-phenanthroline) iron (II) in acid solution takes place according to the equation: $$ \begin{aligned} &\mathrm{Fe}(\mathrm{phen})_{3}^{2}+3 \mathrm{H}_{3} \mathrm{O}^{+}+3 \mathrm{H}_{2} \mathrm{O} \rightarrow \\ &\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}+3 \text { (phen) } \mathrm{H}^{+} \end{aligned} $$ If the activation energy is \(126 \mathrm{~kJ} / \mathrm{mol}\) and frequency factor is \(8.62 \times 10^{17} \mathrm{~s}^{-1}\), at what temperature is the rate constant equal to \(3.63 \times 10^{-3} \mathrm{~s}^{-1}\) for the first order reaction? a. \(0^{\circ} \mathrm{C}\) b. \(50^{\circ} \mathrm{C}\) c. \(45^{\circ} \mathrm{C}\) d. \(90^{\circ} \mathrm{C}\)

In the following question two statements Assertion (A) and Reason (R) are given Mark. a. If \(\mathrm{A}\) and \(\mathrm{R}\) both are correct and \(\mathrm{R}\) is the correct explanation of \(\mathrm{A}\); b. If \(A\) and \(R\) both are correct but \(R\) is not the correct explanation of \(\mathrm{A}\); c. \(\mathrm{A}\) is true but \(\mathrm{R}\) is false; d. \(\mathrm{A}\) is false but \(\mathrm{R}\) is true, e. \(\mathrm{A}\) and \(\mathrm{R}\) both are false. (A): Hydrolysis of methyl acetate in aqueous solution is a pseudo first order reaction. (R): In this reaction concentration of \(\mathrm{H}_{2} \mathrm{O}\) remains nearly constant during the course of the reaction.
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