Problem 114
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 \(=k\left[\mathrm{H}_{2}\right][\mathrm{NO}]^{2}\)
Problem 116
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.
Problem 120
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?
Problem 125
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 \(\mathrm{HBr}\) ?
Problem 126
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 \(\begin{aligned} \mathrm{OCl}^{-}+\mathrm{H}_{2} \mathrm{O} \longrightarrow & \mathrm{HOCl}+\mathrm{OH}^{-} \\ \mathrm{I}^{-}+\mathrm{HOCl} & \longrightarrow \mathrm{ICl}+\mathrm{OH}^{-} \\ \mathrm{ICl}+2 \mathrm{OH}^{-} & \longrightarrow \mathrm{OI}^{-}+\mathrm{Cl}^{-}+\mathrm{H}_{2} \mathrm{O} \end{aligned}\)
Problem 128
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?
Problem 136
Can a reaction have a negative activation energy? Explain your response.
Problem 138
What range of ages can \({ }^{14} \mathrm{C}\) dating reliably determine?
Problem 144
Can we use molality instead of molarity in constructing rate laws? Can mole fractions be used?
