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.