Chapter 16

Explain why the average rate of a reaction depends on the length of the time interval over which the rate is measured.

Describe the relationship between activation energy and the rate of a reaction.

Summarize what happens during the brief existence of an activated complex.

Apply collision theory to explain why collisions between two reacting particles do not always result in the formation of a product.

Calculate the average rate of a reaction between hypothetical molecules \(A\) and \(B\) if the concentration of \(A\) changes from 1.00\(M\) to 0.50\(M\) in 2.00 s.

Explain how collision theory accounts for the effect of concentration on reaction rate.

Explain the difference between a catalyst and an inhibitor.

Describe the effect on the rate of a reaction if one of the reactants is ground to a powder rather than used as a single chunk.

Infer If increasing the temperature of a reaction by 10 K approximately doubles the reaction rate, what would be the effect of increasing the temperature by 20 K?

Research how catalysts are used in industry, in agriculture, or in the treatment of contaminated soil, waste, or water. Write a short report summarizing your findings about the role of a catalyst in one of these applications.

Write the rate law for the reaction \(a A \rightarrow b B\) if the reaction is third order in \(A\) . \([B]\) is not part of the rate law.

The rate law for the reaction \(2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}] \rightarrow 2 \mathrm{NO}_{2}(\mathrm{g})\) is first order in \(\mathrm{O}_{2}\) and third order overall. What is the rate law for the reaction?

MAIN Idea Explain what the rate law for a chemical reaction tells you about the reaction.

Apply the rate-law equations to show the difference between a first-order reaction with a single reactant and a second-order reaction with a single reactant.

Explain the function of the specific rate constant in a rate-law equation.

Explain Under what circumstance is the specific rate constant (k), not a constant. What does the size of \(k\) indicate about the rate of a reaction?

Suggest a reason why, when given the rate of a chemical reaction, it is important to know that the reaction rate is an average reaction rate.

Determine the overall reaction order for a reaction between \(A\) and \(B\) for which the rate law is rate \(=k[A]^{2}[B]^{2}\) .

Define a reaction mechanism and an intermediate

Distinguish between an intermediate and an activated complex.

Relate the size of the activation energy of an elementary step in a complex reaction to the rate of that step.

Calculate A reaction between \(A\) and \(B\) to form AB is first order in \(A\) and first order in B. The rate constant, \(k,\) equals 0.500 \(\mathrm{mol} /(\mathrm{L} \cdot \mathrm{s}) .\) What is the rate of the reaction when \([\mathrm{A}]=2.00 \times 10^{-2} M\) and \([\mathrm{B}]=1.50 \times 10^{-2} \mathrm{M?}\)

What happens to the concentrations of the reactants and products during the course of a chemical reaction?

Explain what is meant by the average rate of a reaction.

What is the role of the activated complex in a chemical reaction?

In the gas-phase reaction, \(\mathrm{I}_{2}+\mathrm{Cl}_{2} \rightarrow 2 \mathrm{ICl},\left[\mathrm{I}_{2}\right]\) changes from 0.400 \(\mathrm{M}\) at 0.00 min to 0.300 \(\mathrm{M}\) at 4.00 \(\mathrm{min.}\) Calculate the average reaction rate in moles of \(\mathrm{I} 2 \mathrm{con}\) . sumed per liter per minute.

In the gas-phase reaction, \(\mathrm{I}_{2}+\mathrm{Cl}_{2} \rightarrow 2 \mathrm{ICl},\left[\mathrm{I}_{2}\right]\) changes from 0.400 \(\mathrm{M}\) at 0.00 \(\mathrm{min}\) to 0.300 \(\mathrm{M}\) at 4.00 \(\mathrm{min.}\) Calculate the average reaction rate in moles of 12 con- sumed per liter per minute.

In a reaction \(\mathrm{Mg}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{aq}) \rightarrow \mathrm{H}_{2}(\mathrm{g})+\mathrm{MgCl}_{2}(\mathrm{aq}),\) 6.00 \(\mathrm{g}\) of Mg was present at 0.00 \(\mathrm{min}\) . After 3.00 \(\mathrm{min}\) , 4.50 gof Mg remained. Express the average rate as mol Mg consumed/min.

If a chemical reaction occurs at the rate of \(2.25 \times 10^{-2}\) moles per liter per second at 322 \(\mathrm{K}\) , what is the rate expressed in moles per liter per minute?

What role does the reactivity of the reactants play in determining the rate of a chemical reaction?

In general, what is the relationship between reaction rate and reactant concentration?

Apply collision theory to explain why increasing the concentration of a reactant usually increases the reaction rate.

Explain why a crushed solid reacts with a gas more quickly than a large chunk of the same solid.

Food Preservation Apply collision theory to explain why foods usually spoil more slowly when refrigerated than at room temperature.

Apply collision theory to explain why powdered zinc reacts to form hydrogen gas faster than large pieces of zinc when both are placed in hydrochloric acid solution.

Hydrogen peroxide decomposes to water and oxygen gas more rapidly when manganese dioxide is added. The manganese dioxide is not consumed in the reaction. Explain the role of the manganese dioxide.

In the method of initial rates used to determine the rate law for a chemical reaction, what is the significance of the word initial?

Why must the rate law for a chemical reaction be based on experimental evidence rather than the balanced equation for the reaction?

Why must the rate law for a chemical reaction be based on experimental evidence rather than the balanced equation for the reaction?

Consider the generic chemical reaction: \(A+B \rightarrow A B\) . Based on experimental data, the reaction is second order in Reactant A. If the concentration of \(\mathrm{A}\) is halved, and all other conditions remain unchanged, how does the reaction rate change?

Suppose that a generic chemical reaction has the rate law of rate \(=[A]^{2}[B]^{3}\) and that the reaction rate under a given set of conditions is \(4.5 \times 10^{-4} \mathrm{mol} /(\mathrm{L} \cdot \min ) .\) If the concentrations of both \(\mathrm{A}\) and \(\mathrm{B}\) are doubled and all other reaction conditions remain constant, how will the reaction rate change?

Use the data in Table 16.4 to calculate the value of the specific rate constant, \(k\). $$ \begin{array}{|c|c|c|} \hline \begin{array}{c} \text { Experiment } \\ \text { Number } \end{array} & \begin{array}{c} \text { Initial } \\ {\left[\mathrm{CH}_{3} \mathrm{~N}_{2} \mathrm{CH}_{3}\right]} \end{array} & \begin{array}{c} \text { Initial } \\ \text { Reaction Rate } \end{array} \\ \hline 1 & 0.012 M & 2.5 \times 10^{-6} \mathrm{~mol} /(\mathrm{L} \cdot \mathrm{s}) \\ \hline 2 & 0.024 M & 5.0 \times 10^{-6} \mathrm{~mol} /(\mathrm{L} \cdot \mathrm{s}) \\ \hline \end{array} $$

Distinguish between a complex reaction, a reaction mechanism, and an elementary step.

Suppose that a chemical reaction takes place in a two- step mechanism. Step \(1(\) fast \() A+B \rightarrow C\) Step \(2(\) slow \() C+D \rightarrow E\) Which step in the reaction mechanism is the rate- determining step? Explain.

Dinitrogen pentoxide decomposes in chloroform at a rate of \(2.48 \times 10^{-4} \mathrm{mol} /(\mathrm{L} \cdot \mathrm{min})\) at a particular tempera- ture according to the equation \(2 \mathrm{N}_{2} \mathrm{O}_{5} \rightarrow 4 \mathrm{NO}_{2}+\mathrm{O}_{2}\) The reaction is first order in \(\mathrm{N}_{2} \mathrm{O}_{5}\) . Given an initial concentration \(0.400 \mathrm{mol} / \mathrm{L},\) what is the rate constant for the reaction? What is the approximate \(\left[\mathrm{N}_{2} \mathrm{O}_{5}\right]\) after the reaction proceeds for 1.30 \(\mathrm{h} ?\)

Radioactive decay is first order in the decaying isotope. For example, strontium-90 contained in fallout from nuclear explosions decays to yttrium-90 and a beta particle. Write the rate law for the decay of strontium-90.

Evaluate the validity of this statement: You can determine the rate law for a chemical reaction by examining the mole ratio of reactants in the balanced equation. Explain your answer.

The concentration of Reactant A decreases from 0.400 mol/L at 0.00 min to 0.384 moll at 4.00 min. Calculate the average reaction rate during this time period. Express the rate in mol/(L.min).

If the concentration of a reaction product increases from 0.0882 \(\mathrm{mol} / \mathrm{L}\) to 0.1446 \(\mathrm{mol} / \mathrm{L}\) in 12.0 minutes, what is the average reaction rate during the time interval?

A two-step mechanism has been proposed for the decomposition of nitryl chloride \(\left(\mathrm{NO}_{2} \mathrm{CL}\right) .\) \begin{equation} \begin{array}{l}{\text { Step } 1 : \mathrm{NO}_{2} \mathrm{Cl}(\mathrm{g}) \rightarrow \mathrm{NO}_{2}(\mathrm{g})+\mathrm{Cl}(\mathrm{g})} \\ {\text { Step } 2 : \mathrm{NO}_{2} \mathrm{Cl}(\mathrm{g})+\mathrm{Cl}(\mathrm{g}) \rightarrow \mathrm{NO}_{2}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g})}\end{array} \end{equation} What is the overall reaction? Identify any intermediates in the reaction sequence, and explain why they are called intermediates.