## 14.9 End-of-Chapter Material

### Application Problems

Problems marked with a ♦ involve multiple concepts.

1. Atmospheric chemistry in the region below the clouds of Venus appears to be dominated by reactions of sulfur and carbon-containing compounds. Included in representative elementary reactions are the following:

SO2 + CO → SO + CO2 SO + CO → S + CO2 SO + SO2 → S + SO3

For each elementary reaction, write an expression for the net rate of reaction in terms of the concentrations of reactants and products.

2. In acid, nitriles hydrolyze to produce a carboxylic acid and ammonium ion. For example, acetonitrile, a substance used to extract fatty acids from fish liver oils, is hydrolyzed to acetic acid via the following reaction:

Express the reaction rate in terms of changes in the concentrations of each reactant and each product with time.

3. ♦ Ozone production occurs at lower altitudes according to the elementary reaction O + O2 → O3, with an estimated rate of ozone production of 4.86 × 1031 molecules·s−1 worldwide. What is the overall reaction order? If the reaction rate of loss of O3 due to absorption of UV light (Equation 3.36) is 0.89 × 1031 molecules·s−1, and 0.06 × 1031 molecules·s−1 of ozone is transported to other atmospheric regions, is ozone being produced faster than it is being destroyed? Measurements show that ozone concentrations are not increasing rapidly. What conclusion can you draw from these data?

4. ♦ The water in a fishery became polluted when toxic waste was dumped into its pond, causing the fish population to substantially decline. The percentage of fish that survived is recorded in the following table.

 Day 1 2 3 4 5 % survival 79 55 38 31 19

What is the reaction order of live fish → dead fish? What is the rate constant? If the fish continue to die at this rate, how many fish will be alive after 10 days?

5. Until 200 yr ago, manufactured iron contained charcoal produced from freshly cut wood that was added during the smelting process. As a result of this practice, older samples of iron can be dated accurately using the carbon-14 method. An archaeologist found a cast iron specimen that she believed dated to the period between 480 and 221 BC in Hunan, China. Radiocarbon dating of the sample indicated a 24% reduction in carbon-14 content. Was the archaeologist correct?

6. ♦ Because of its short half-life, 32P-labeled compounds must be shipped as quickly as possible so that they can be used as radioactive tags in biological studies. A 50 g sample that contained 0.60% 32P by mass was shipped at 11 a.m. on Monday morning. The package was delivered to a chemist via an overnight delivery service such that it arrived the next day.

1. What would be the mass of 32P remaining in the sample if he received the package on Tuesday afternoon but was unable to use it until 9 a.m. on Wednesday?
2. What would be the mass of 32P present in the sample if the shipper had not delivered the sample until Friday afternoon and then it sat on a loading dock until 9 a.m. on Monday morning?
3. The late shipment was used immediately on Monday morning, but the biological samples were not analyzed until Thursday at 5 p.m. What percentage of the sample still consists of 32P?
7. ♦ Tritium (3H) is a radioactive isotope that is commonly used to follow biochemical reactions.

1. Using the data in Table 14.6 "Half-Lives and Applications of Some Radioactive Isotopes", calculate the radioactive decay constant (k) for tritium.
2. Use the value of k to determine the mass of tritium that is still present in a 5.00 g sample of NaB3H4 that is 17.57 yr old.
8. ♦ L-Aspartic acid is an amino acid found in fossil bone. It can convert to a geometrically different form (D-aspartic acid) at 20°C, with a half-life corresponding to the conversion of L → D of 14,000–20,000 yr. If the temperature of an archaeological site is constant, then the extent of the conversion can be used to date fossils. In one such case, archaeologists dated the arrival of humans on the North American continent to be 20,000 yr ago, but the conversion of L-aspartic acid to D-aspartic acid in human fossils indicated that Paleo-Indians were living in California at least 48,000 yr ago. What would be the relative concentrations of the L- and D-forms that produced this result? Carbon-14 has a half-life of approximately 5730 yr. What percentage of the carbon-14 originally present would have been found in the bones?

The technique described is frequently used in conjunction with radiocarbon dating. In cases where the results from the two techniques are in gross disagreement, what information can you get by comparing the two results?

9. ♦ Peroxides are able to initiate the radical polymerization of alkenes. Polyethylene, for example, is a high-molecular-weight polymer used as a film in packaging, as kitchenware, and as tubing. It is produced by heating ethylene at high pressure in the presence of oxygen or peroxide. It is formed by the following radical process:

$RO : OR → Δ 2 RO ⋅$ $RO ⋅ + CH 2 =CH 2 → RO − CH 2 − CH 2 ⋅$ RO―CH2―CH2· + CH2=CH2 → RO―CH2―CH2―CH2―CH2·
1. Label the steps that correspond to initiation and propagation.
2. Show all available chain-terminating steps.
3. The polymerization of styrene (C6H5CH=CH2) occurs by a similar process to produce polystyrene, which is used as a packaging material. Draw the structure of the polymer that results from five propagation cycles.
10. Lucite and Plexiglas are transparent polymers used as a glass substitute when a plastic material is preferred for safety. The compound used to synthesize Lucite and Plexiglas is methyl methacrylate, which is shown here. During the polymerization reaction, light produces a radical initiator from hydrogen peroxide (H2O2 → 2HO·). Show the mechanism for the polymerization, being sure to include the initiation and propagation steps.

11. ♦ At higher altitudes ozone is converted to O2 by the reaction O + O3 → 2O2, with a rate constant at 220 K of 6.8 × 10−16 cm3·molecule−1·s−1.

1. What is the overall reaction order?
2. What is Ea for this reaction if A = 8 × 10−12 cm3·molecule−1·s−1?

If Cl is present, the rate constant at 220 K becomes 3.7 × 10−11 cm3·molecule−1 · s−1, with A = 4.7 × 10−11 cm3·molecule−1·s−1.

3. Calculate Ea for the depletion of ozone in the presence of Cl.
4. Show an energy-level diagram for these two processes, clearly labeling reactants, products, and activation energies.
5. If you were an environmental scientist using these data to explain the effects of Cl on ozone concentration, what would be your conclusions?
12. ♦ Nitric acid is produced commercially by the catalytic oxidation of ammonia by air over platinum gauze at approximately 900°C. The following reactions occur:

Why is platinum gauze rather than platinum wire used for the initial reaction? The reaction 4NH3(g) + 3O2(g) → 2N2(g) + 6H2O(g) has ΔH° = −316.6 kJ/mol. What would occur if the catalyst were not present? If the gas leaving the catalyst is not free of NH3, the following reaction takes place: 6NO(g) + 4NH3(g) → 5N2(g) + 6H2O(g). If this occurs, what will be the overall reaction?

13. Figure 14.27 "Hydrogenation of Ethylene on a Heterogeneous Catalyst" illustrates the mechanism for the reduction of ethylene on a platinum surface to produce ethane. Industrially important silanes are synthesized using a related mechanism and are used to increase adhesion between layers of glass fiber and between layers of silicone rubber. Predict the products of the following reactions:

14. ♦ In catalysis, if a molecule forms strong bonds to the catalyst, then the catalyst may become poisoned. Experiments on various catalysts showed the following results:

1. Fe, Ru, and Os form weak bonds with N2; however, O2, alkynes, alkenes, CO, H2, and CO2 interact more strongly.
2. CO2 and H2 form weak bonds with a Co or Ni surface.
3. Rh, Pd, Ir, and Pt form weak bonds with H2 but do not bond with CO2.
4. Cu, Ag, and Au form weak bonds with CO and ethylene.
1. Explain why Fe was chosen as a catalyst to convert nitrogen and hydrogen to ammonia. Why is Fe more suitable than Ru or Os?
2. Because alkenes generally interact more strongly with metal surfaces than does H2, what catalyst would you choose for hydrogenation of an alkene such as ethylene?
3. Although platinum is used in catalytic converters for automobile exhaust, it was not found to be a particularly effective catalyst for the reaction of H2 with a mixture of carbon monoxide and carbon dioxide to produce methane. Why?
4. If you were interested in developing a catalyst to reversibly bind ethylene, which of the catalysts listed here would you choose?
15. Nonstoichiometric metal oxides can be effective catalysts for oxidation–reduction reactions. One such catalyst is Ni1−xO, found to be effective for converting CO to CO2 when oxygen is present. Why is it so effective?

16. The chemical reactions in an organism can be controlled by regulating the activity of certain enzymes. Efficient regulation results in an enzyme being active only when it is needed. For example, if a cell needed histidine, the nine enzymes needed to synthesize histidine would all be active. If the cell had adequate histidine, however, those enzymes would be inactive. The following diagram illustrates a situation in which three amino acids (D, F, H) are all synthesized from a common species, A. The numbers above the arrows refer to the enzymes that catalyze each step. Which enzymes would need to be regulated to produce D? F? H?

17. ♦ Because phosphorus-32 is incorporated into deoxyribonucleic acid (DNA), it can be used to detect DNA fragments. Consequently, it is used extensively in biological research, including the Human Genome Project, whose goal was to determine the complete sequence of human DNA. If you were to start with a 20 g sample of phosphorus that contained 10% 32P by mass, converted it into DNA via several chemical steps that had an overall yield of 75% and took 25 days, and then incorporated it into bacteria and allowed them to grow for 5 more days, what mass of 32P would be available for analysis at the end of this time?

18. The enzyme urease contains two atoms of nickel and catalyzes the hydrolysis of urea by the following reaction:

H2NC(O)NH2 + H2O → 2NH3 + CO2

Urease is one of the most powerful catalysts known. It lowers the activation energy for the hydrolysis of urea from 137 kJ/mol to only 37 kJ/mol. Calculate the ratio of the reaction rate of the catalyzed reaction to the reaction rate of the uncatalyzed reaction at 37°C. Assume that the frequency factor is the same for both reactions.

19. As noted in Section 14.8 "Catalysis", the reaction rate for the hydrogenation of ethylene to give ethane can be increased by heterogeneous catalysts such as Pt or Ni:

$H 2 (g) + H 2 C=CH 2 (g) → Pt,Ni H 3 C–CH 3 (g)$

The activation energy for the uncatalyzed reaction is large (188 kJ/mol), so the reaction is very slow at room temperature. In the presence of finely divided metallic Ni, the activation energy is only 84 kJ/mol. Calculate the ratio of the reaction rate of the catalyzed reaction to the reaction rate of the uncatalyzed reaction at 75°C.

1. rate = kf[SO2][CO] − kr[SO][CO2]; rate = kf[SO][CO] − kr[S][CO2]; rate = kf[SO][SO2] − kr[S][SO3]

2. The reaction is second order: first order in O and first order in O3. Ozone is being produced faster than it is being destroyed. If ozone concentrations are not increasing, then either some other reaction must be consuming some of the ozone produced in this reaction or the ozone-producing reaction does not operate at this rate continuously.

3. Yes; the object is about 2300 yr old.

1. k = 0.05626 yr−1
2. 0.487 g of 3H
1. second order, first order in O and first order in O3;
2. 17 kJ/mol;
3. 0.44 kJ/mol;
4.

5. Cl is a potent catalyst for ozone destruction because there is a large decrease in Ea when Cl is present.
4. Ni1−xO is a nonstoichiometric oxide that contains a fraction of Ni(I) sites. These can react with oxygen to form a Ni(III)-oxide site, which is reduced by CO to give Ni(I) and CO2.

5. 0.35 g of 32P

6. 4.1 × 1015