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Chapter 14: Problem 78

In solution, chemical species as simple as \(\mathrm{H}^{+}\)and \(\mathrm{OH}^{-}\)can serve as catalysts for reactions. Imagine you could measure the \(\left[\mathrm{H}^{+}\right.\)] of a solution containing an acid- catalyzed reaction as it occurs. Assume the reactants and products themselves are neither acids nor bases. Sketch the \(\left[\mathrm{H}^{+}\right]\)concentration profile you would measure as a function of time for the reaction, assuming \(t=0\) is when you add a drop of acid to the reaction.

Short Answer

Expert verified
The \(\mathrm{H}^{+}\) concentration profile as a function of time can be sketched as follows: 1. At \(t=0\), there is a sharp increase in the concentration of \(\mathrm{H}^{+}\) ions when the acid is added. 2. After the initial increase, the concentration of \(\mathrm{H}^{+}\) ions decreases as the reaction progresses. 3. As the concentration of \(\mathrm{H}^{+}\) ions decreases, the reaction rate slows down, and the concentration profile becomes less steep. 4. When the reaction reaches equilibrium, the \(\mathrm{H}^{+}\) concentration profile levels off and becomes constant. The resulting graph should resemble a curve that starts with a sharp increase and gradually decreases until it reaches a constant value.

Step by step solution

01

1. Identify initial situation

At \(t=0\), a drop of acid is added to the reaction. This means that initially, there is a large increase in the concentration of \(\mathrm{H}^{+}\) ions in the solution.
02

2. Reaction rate is proportional to the concentration of the catalyst (\(\mathrm{H}^+\) ions)

As the reaction progresses, the rate of the reaction will be proportional to the concentration of the catalyst, \(\mathrm{H}^{+}\) ions, in the solution. This means that as the concentration of \(\mathrm{H}^{+}\) ions decreases, the reaction rate will also decrease.
03

3. Acid catalyst is not consumed in the reaction

The \(\mathrm{H}^{+}\) ions serve as a catalyst, which means that they are not consumed in the reaction and help to speed up the reaction without being used up themselves. However, as the reactants are converted into products, the concentration of reactants will decrease, and the reaction rate will slow down.
04

4. Acid-catalyzed reaction reaches equilibrium

As the reaction progresses, it will reach an equilibrium state where the rate of the forward reaction is equal to the rate of the reverse reaction. At equilibrium, the catalyst concentration will become constant, and the \(\mathrm{H}^{+}\) concentration profile will level off.
05

5. Sketch the \(\mathrm{H}^{+}\) concentration profile as a function of time

To sketch the \(\mathrm{H}^{+}\) concentration profile: 1. Start with a sharp increase in the concentration of \(\mathrm{H}^{+}\) ions at \(t=0\) when the acid is added. 2. After the initial increase, the concentration of \(\mathrm{H}^{+}\) ions begins to decrease as the reaction progresses. 3. As the concentration of \(\mathrm{H}^{+}\) ions decreases, the reaction rate slows down, and the concentration profile becomes less steep. 4. When the reaction reaches equilibrium, the \(\mathrm{H}^{+}\) concentration profile levels off and becomes constant. The resulting graph should resemble a curve that starts with a sharp increase and gradually decreases until it reaches a constant value.

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Key Concepts

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

Reaction Kinetics
Reaction kinetics is the study of the speed at which chemical reactions occur and the factors affecting this speed. In an acid-catalyzed reaction, the egin{itemize}
  • catalyst, often ( [ H^+ ] ), increases the rate of reaction
  • it provides an alternative pathway with a lower activation energy
  • the rate of reaction usually depends on the concentration of the reactants and catalysts
    • As reactants convert to products, the concentration of the ( [ H^+ ] ) ion can change, which in turn affects the reaction speed. Initially, when a drop of acid is added to a solution, a peak in the ( [ H^+ ] ) concentration occurs, rapidly increasing the reaction rate. As the concentration of ( [ H^+ ] ) decreases over time, the speed of the reaction also diminishes, demonstrating the principle of reaction kinetics where a higher concentration leads to a faster reaction.
    Equilibrium State
    The equilibrium state in a chemical reaction is reached when the forward and reverse reactions proceed at equal rates. In an acid-catalyzed reaction:
    • initially, the forward reaction is dominant, consuming reactants at a fast pace
    • over time, as products form, they begin reacting to form reactants again, starting the reverse reaction
    • eventually, both reactions are equal, reaching dynamic equilibrium
    This state is characterized by a flat line on the concentration profile graph, where the concentration of all species, including the catalyst ( H^+ ), remain constant. Achieving equilibrium does not mean the reaction has stopped. Instead, product and reactant formation occur continuously at the same rate, maintaining constant concentrations.
    Concentration Profile
    The concentration profile of a reactant or product shows its concentration as a function of time during a chemical reaction. For a catalyst like ( H^+ ) in an acid-catalyzed reaction:
    • the profile typically shows a sharp increase then a gradual decrease
    • initially, this increase occurs when the acid is added, raising ( [ H^+ ] )
    • as the reaction proceeds, ( [ H^+ ] ) decreases as reactants are converted, before stabilizing
    The graph eventually levels off, indicating that the solution has reached equilibrium. Understanding and analyzing the concentration profile is essential for predicting how long a reaction will proceed and when equilibrium is achieved.
    Acid-Base Catalysis
    Acid-base catalysis involves the acceleration of chemical reactions through the addition of an acid or a base. These catalysts:
    • help to lower the activation energy
    • are not consumed by the reaction itself
    • increase reaction speed without being removed in the process
    In the exercise scenario, the ( [ H^+ ] ) ions from the acid act as the catalyst, making the reaction happen more efficiently without altering the final amount of products or reactants. Such catalysis is crucial in many industrial and biological processes, influencing the rate and path of many reactions. It showcases how altering the environment through acids or bases can significantly shift reaction dynamics, showcasing the power of acid-base catalysis in chemistry.

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    Most popular questions from this chapter

    Enzymes are often described as following the two-step mechanism: $$ \begin{aligned} &\mathrm{E}+\mathrm{S} \rightleftharpoons \mathrm{ES} \quad \text { (fast) } \\\ &\mathrm{ES} \longrightarrow \mathrm{E}+\mathrm{P} \quad \text { (slow) } \end{aligned} $$ where \(\mathrm{E}=\) enzyme, \(\mathrm{S}=\) substrate, \(\mathrm{ES}=\) enzyme-substrate complex, and \(\mathrm{P}=\) product. (a) If an enzyme follows this mechanism, what rate law is expected for the reaction? (b) Molecules that can bind to the active site of an enzyme but are not converted into product are called enzyme inhibitors. Write an additional elementary step to add into the preceding mechanism to account for the reaction of \(E\) with \(I\), an inhibitor.

    Consider the hypothetical reaction \(2 \mathrm{~A}+\mathrm{B} \longrightarrow 2 \mathrm{C}+\mathrm{D}\). The following two-step mechanism is proposed for the reaction: Step 1: \(\mathrm{A}+\mathrm{B} \longrightarrow \mathrm{C}+\mathrm{X}\) Step 2: A \(+\mathrm{X} \longrightarrow \mathrm{C}+\mathrm{D}\) \(\mathrm{X}\) is an unstable intermediate. (a) What is the predicted rate law expression if Step 1 is rate determining? (b) What is the predicted rate law expression if Step 2 is rate determining? (c) Your result for part (b) might be considered surprising for which of the following reasons: (i) The concentration of a product is in the rate law. (ii) There is a negative reaction order in the rate law. (iii) Both reasons (i) and (ii). (iv) Neither reasons (i) nor (ii).

    The following kinetic data are collected for the initial rates of a reaction \(2 \mathrm{X}+\mathrm{Z} \longrightarrow\) products: $$ \begin{array}{llll} \hline \text { Experiment } & {[\mathrm{X}]_{0}(M)} & {[\mathrm{Z}]_{0}(M)} & \text { Rate }(M / \mathrm{s}) \\ \hline 1 & 0.25 & 0.25 & 4.0 \times 10^{1} \\ 2 & 0.50 & 0.50 & 3.2 \times 10^{2} \\ 3 & 0.50 & 0.75 & 7.2 \times 10^{2} \\ \hline \end{array} $$ (a) What is the rate law for this reaction? (b) What is the value of the rate constant with proper units? (c) What is the reaction rate when the initial concentration of \(X\) is \(0.75 M\) and that of \(Z\) is \(1.25 M ?\)

    You perform a series of experiments for the reaction \(A \longrightarrow B+C\) and find that the rate law has the form rate \(=k[\mathrm{~A}]^{x}\). Determine the value of \(x\) in each of the following cases: (a) There is no rate change when \([\mathrm{A}]_{0}\) is tripled. (b) The rate increases by a factor of 9 when \([\mathrm{A}]_{0}\) is tripled. (c) When \([\mathrm{A}]_{0}\) is doubled, the rate increases by a factor of 8 .

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