Chapter 13

Hydrogen iodide decomposes according to the equation, $$2 \mathrm{HI}(g) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{I}_{2}(g)$$The reaction is second order and has a rate constant equal to \(1.6 \times 10^{-3} \mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1}\) at \(750^{\circ} \mathrm{C}\). If the initial concentration of HI in a container is \(3.4 \times 10^{-2} M\), how many minutes will it take for the concentration to be reduced $$\text { to } 8.0 \times 10^{-4} \mathrm{M}$$.

The half-life of a certain first-order reaction is \(15 \mathrm{~min}-\) utes. What fraction of the original reactant concentration will remain after 2.0 hours?

Strontium-90 has a half-life of 28 years. How long will it take for all of the strontium- 90 presently on earth to be reduced to \(1 / 32\) of its present amount?

Hydrogen peroxide, which decomposes in a first-order reaction, has a half-life of 10 hours in air. How long will it take for hydrogen peroxide to decompose to \(10 \%\) of its original concentration?

\(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) decomposes in a first-order process with a half life of \(4.88 \times 10^{3} \mathrm{~s}\). If the original concentration of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) is \(0.012 \mathrm{M}\), how many seconds will it take for the \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) to reach \(0.0020 \mathrm{M}\) ?

The oxidation of \(\mathrm{NO}\) to \(\mathrm{NO}_{2}\), one of the reactions in the production of \(\mathrm{smog}\), appears to involve carbon monoxide. A possible mechanism is $$ \begin{aligned} \mathrm{CO}+\cdot \mathrm{OH} & \longrightarrow \mathrm{CO}_{2}+\mathrm{H}^{\cdot} \\ \mathrm{H} \cdot+\mathrm{O}_{2} & \longrightarrow \mathrm{HOO} \\ \mathrm{HOO} \cdot+\mathrm{NO} \longrightarrow & \mathrm{OH}+\mathrm{NO}_{2} \end{aligned} $$

A reaction has the following mechanism: $$\begin{aligned}2 \mathrm{NO} \longrightarrow & \mathrm{N}_{2} \mathrm{O}_{2} \\\\\mathrm{~N}_{2} \mathrm{O}_{2}+\mathrm{H}_{2} & \longrightarrow \mathrm{N}_{2} \mathrm{O}+\mathrm{H}_{2} \mathrm{O} \\ \mathrm{N}_{2} \mathrm{O}+\mathrm{H}_{2} \longrightarrow & \mathrm{N}_{2}+\mathrm{H}_{2} \mathrm{O}\end{aligned}$$ What is the net overall change that occurs in this reaction? Identify any intermediates in the reaction.

If the reaction $$\mathrm{NO}_{2}+\mathrm{CO} \longrightarrow \mathrm{NO}+\mathrm{CO}_{2}$$ occured by a one-step collision process, what would be the expected rate law for the reaction? The actual rate law is rate \(=k\left[\mathrm{NO}_{2}\right]^{2}\). Could the reaction actually occur by a one-step collision between \(\mathrm{NO}_{2}\) and CO? Explain.

If the reaction $$2 \mathrm{NO}_{2}(g)+\mathrm{F}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2} \mathrm{~F}(g)$$ occurred by a one-step process, what would be the expected rate law for the reaction? The actual rate law is rate \(=k\left[\mathrm{NO}_{2}\right]\left[\mathrm{F}_{2}\right]\), why is this a better rate law?

Carbon-14 dating can be used to estimate the age of formerly living materials because the uptake of carbon-14 from carbon dioxide in the atmosphere stops once the organism dies. If tissue samples from a mummy contain about \(81.0 \%\) of the carbon-14 expected in living tissue, how old is the mummy? The half- life for decay of carbon-14 is 5730 years.

For the following reactions, predict how the rate of the reaction will change as the concentration of the reactants triple. (a) \(\mathrm{SO}_{2} \mathrm{Cl}_{2} \longrightarrow \mathrm{SO}_{2}+\mathrm{Cl}_{2} \quad\) rate \(=k\left[\mathrm{SO}_{2} \mathrm{Cl}_{2}\right]\) (b) \(2 \mathrm{HI} \longrightarrow \mathrm{H}_{2}+\mathrm{I}_{2}\) rate \(=k[\mathrm{HI}]^{2}\) (c) \(\mathrm{ClOO} \longrightarrow \mathrm{Cl}+\mathrm{O}_{2} \quad\) rate \(=k\) (d) \(\mathrm{NH}_{4}^{+}(a q)+\mathrm{NO}_{2}^{-}(a q) \rightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}\) rate \(=k\left[\mathrm{NH}_{4}^{+}\right]\left[\mathrm{NO}_{2}^{-}\right]\) (e) \(2 \mathrm{H}_{2}(g)+2 \mathrm{NO}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)\) rate \(=k\left[\mathrm{H}_{2}\right][\mathrm{NO}]^{2}\)

Suppose a reaction occurs with the following mechanism: (1) \(2 A \rightleftharpoons A_{2}\) \((\) fast \()\)(2) \(A_{2}+E \longrightarrow B+C\)(slow) in which the first step is a very rapid reversible reaction that can be considered to be essentially an equilibrium (forward and reverse reactions occurring at the same rate) and the second is a slow step. (a) Write the rate law for the forward reaction in step (1). (b) Write the rate law for the reverse reaction in step (1). (c) Write the rate law for the rate-determining step. (d) What is the chemical equation for the net reaction that occurs in this chemical change? Use the results of parts (a) and (b) to rewrite the rate law of the rate- determining step in terms of the concentrations of the reactants in the overall balanced chemical equation for the reaction.

If the rate constant for a first-order reaction is doubled by heating the reaction, what happens to the rate of the reaction if the concentration is kept the same?

The following question is based on Chemistry Outside the Classroom 13.1. The reaction of hydrogen and bromine appears to follow the mechanism shown, $$\begin{aligned}\mathrm{Br}_{2} & \longrightarrow 2 \mathrm{Br}^{*} \\\\\mathrm{Br} \cdot+\mathrm{H}_{2} & \longrightarrow \mathrm{HBr}+\mathrm{H} \\\\\mathrm{H} \cdot+\mathrm{Br}_{2} & \longrightarrow \mathrm{HBr}+\mathrm{Br} \\\2 \mathrm{Br} \cdot &\longrightarrow\mathrm{Br}_{2}\end{aligned}$$ (a) Identify the initiation step in the mechanism. (b) Identify any propagation steps. (c) Identify the termination step. (d) The mechanism also contains the reaction $$\mathrm{H} \cdot+\mathrm{HBr} \longrightarrow \mathrm{H}_{2}+\mathrm{Br}$$ How does this reaction affect the rate of formation of \(\mathrm{HBr}\) ?

Show that the following two mechanisms give the same net overall reaction. Mechanism 1 \(\mathrm{OCl}^{-}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{HOCl}+\mathrm{OH}^{-}\) \(\mathrm{HOCl}+\mathrm{I}^{-} \longrightarrow \mathrm{HOI}+\mathrm{Cl}^{-}\) \(\mathrm{HOI}+\mathrm{OH}^{-} \longrightarrow \mathrm{H}_{2} \mathrm{O}+\mathrm{OI}^{-}\) Mechanism 2 \(\begin{aligned} \mathrm{OCl}^{-}+\mathrm{H}_{2} \mathrm{O} \longrightarrow & \mathrm{HOCl}+\mathrm{OH}^{-} \\ \mathrm{I}^{-}+\mathrm{HOCl} & \longrightarrow \mathrm{ICl}+\mathrm{OH}^{-} \\ \mathrm{ICl}+2 \mathrm{OH}^{-} & \longrightarrow \mathrm{OI}^{-}+\mathrm{Cl}^{-}+\mathrm{H}_{2} \mathrm{O} \end{aligned}\)

Radioactive samples are considered to become nonhazardous after 10 half-lives. If the half-life is less than 88 days, the radioactive sample can be stored through a decay-in-storage program in which the material is kept in a lead- lined cabinet for at least 10 half-lives. What percent of the initial material will remain after 10 half-lives?

Can a reaction have a negative activation energy? Explain your response.

What range of ages can \({ }^{14} \mathrm{C}\) dating reliably determine?

Can we use molality instead of molarity in constructing rate laws? Can mole fractions be used?