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Chapter 14: Problem 27

Three different sets of data of \([\mathrm{A}]\) versus time are giv the following table for the reaction \(A \longrightarrow\) prod [Hint: There are several ways of arriving at answer each of the following six questions. $$\begin{array}{cccccc} \hline \text { I } & & \text { II } & & \text { III } & \\ \hline \begin{array}{c} \text { Time, } \\ \text { s } \end{array} & \text { [A], M } & \begin{array}{c} \text { Time, } \\ \text { s } \end{array} & \text { [A], M } & \begin{array}{c} \text { Time, } \\ \text { s } \end{array} & \text { [A], M } \\ \hline 0 & 1.00 & 0 & 1.00 & 0 & 1.00 \\ 25 & 0.78 & 25 & 0.75 & 25 & 0.80 \\ 50 & 0.61 & 50 & 0.50 & 50 & 0.67 \\ 75 & 0.47 & 75 & 0.25 & 75 & 0.57 \\ 100 & 0.37 & 100 & 0.00 & 100 & 0.50 \\ 150 & 0.22 & & & 150 & 0.40 \\ 200 & 0.14 & & & 200 & 0.33 \\ 250 & 0.08 & & & 250 & 0.29 \\ \hline \end{array}$$ Which of these sets of data corresponds to a (a) zero-order, (b) first-order, (c) second-order reaction?

Short Answer

Expert verified
Set I corresponds to a first-order reaction, Set II corresponds to a zero-order reaction, and Set III corresponds to a second-order reaction.

Step by step solution

01

Examine the Trends for Each Reaction Order

Start by understanding the trends for each reaction order. A zero-order reaction shows a linear decrease in concentration with time. A first-order reaction shows an exponential decay in concentration with time. A second-order reaction typically shows a rapid decrease in concentration at the beginning, which gradually slows down.
02

Identify Zero-Order Reaction

The zero-order reaction should have a linear decrease in the concentration of reactant A over time. When viewing the provided data sets, it can be seen that dataset II matches this description most closely. The concentration decreases from 1.00 M to 0.00 M over 100 seconds, indicating a linear decrease.
03

Identify First-Order Reaction

First-order reactions show exponential decay in the concentration of the reactant over time. In the given data sets, dataset I fits this description. The concentration decreases exponentially from 1.00 M to 0.08 M over 250 seconds.
04

Identify Second-Order Reaction

A second-order reaction shows a rapid decrease in concentration initially, which slows down with time. Dataset III depicts this trend. The concentration rapidly decreases from 1.00 M to 0.50 M in the first 100 seconds, then decreases slowly reaching 0.29 M at 250 seconds.

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Most popular questions from this chapter

In the reaction \(A(g) \longrightarrow 2 B(g)+C(g),\) the total pressure increases while the partial pressure of \(\mathrm{A}(\mathrm{g})\) decreases. If the initial pressure of \(\mathrm{A}(\mathrm{g})\) in a vessel of constant volume is \(1.000 \times 10^{3} \mathrm{mmHg}\) (a) What will be the total pressure when the reaction has gone to completion? (b) What will be the total gas pressure when the partial pressure of \(\mathrm{A}(\mathrm{g})\) has fallen to \(8.00 \times 10^{2} \mathrm{mmHg} ?\)

A kinetic study of the reaction \(A \longrightarrow\) products yields the data: \(t=0 \mathrm{s},[\mathrm{A}]=2.00 \mathrm{M} ; 500 \mathrm{s}, 1.00 \mathrm{M}; 1500 \mathrm{s}, 0.50 \mathrm{M} ; 3500 \mathrm{s}, 0.25 \mathrm{M} .\) Without performing detailed calculations, determine the order of this reaction and indicate your method of reasoning.

One of the following statements is true and the other is false regarding the first-order reaction 2A \(\longrightarrow \mathrm{B}+\mathrm{C}\). Identify the true statement and the false one, and explain your reasoning. (a) The rate of the reaction decreases as more and more of \(\mathrm{B}\) and \(\mathrm{C}\) form. (b) The time required for one-half of substance \(A\) to react is directly proportional to the quantity of A present initially.

For the reaction \(\mathrm{A}+2 \mathrm{B} \longrightarrow \mathrm{C}+\mathrm{D},\) the rate law is rate of reaction \(=k[\mathrm{A}][\mathrm{B}]\) (a) Show that the following mechanism is consistent with the stoichiometry of the overall reaction and with the rate law. $$\begin{array}{l} \mathrm{A}+\mathrm{B} \longrightarrow \mathrm{I} \quad(\text { slow }) \\ \mathrm{I}+\mathrm{B} \longrightarrow \mathrm{C}+\mathrm{D} \quad(\text { fast }) \end{array}$$ (b) Show that the following mechanism is consistent with the stoichiometry of the overall reaction, but not with the rate law. $$\begin{array}{c} 2 \mathrm{B} \stackrel{k_{1}}{\mathrm{k}_{1}} \mathrm{B}_{2} \text { (fast) } \\\ \mathrm{A}+\mathrm{B}_{2} \stackrel{k_{2}}{\longrightarrow} \mathrm{C}+\mathrm{D} \text { (slow) } \end{array}$$

The reaction \(A \longrightarrow\) products is second order. The initial rate of decomposition of \(A\) when \([\mathrm{A}]_{0}=0.50 \mathrm{M}\) is \((\mathrm{a})\) the same as the initial rate for any other value of \([\mathrm{A}]_{0} ;\) (b) half as great as when \([\mathrm{A}]_{0}=1.00 \mathrm{M} ;(\mathrm{c})\) five times as great as when \([\mathrm{A}]_{0}=[\mathrm{A}]_{0}=0.25 \mathrm{M}.\)
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