Application Problems

Please be sure you are familiar with the topics discussed in Essential Skills 4 (Section 5.6 "Essential Skills 4") before proceeding to the Application Problems. Problems marked with a ♦ involve multiple concepts.

1. Palm trees grow on the coast of southern England even though the latitude is the same as that of Winnipeg, Canada. What is a plausible explanation for this phenomenon? (Hint: the Gulf Stream current is a factor.)

2. During intense exercise, your body cannot provide enough oxygen to allow the complete combustion of glucose to carbon dioxide. Under these conditions, an alternative means of obtaining energy from glucose is used in which glucose (C₆H₁₂O₆) is converted to lactic acid (C₃H₅O₃H). The equation for this reaction is as follows:

   C₆H₁₂O₆ → 2C₃H₅O₃H

   

   1. Calculate the energy yield for this reaction per mole of glucose.
   2. How does this energy yield compare with that obtained per mole of glucose for the combustion reaction?
   3. Muscles become sore after intense exercise. Propose a chemical explanation for this.

3. ♦ During the late spring, icebergs in the North Atlantic pose a hazard to shipping. To avoid them, ships travel routes that are about 30% longer. Many attempts have been made to destroy icebergs, including using explosives, torpedoes, and bombs. How much heat must be generated to melt 15% of a 1.9 × 10⁸ kg iceberg? How many kilograms of TNT (trinitrotoluene, C₇H₅N₃O₆) would be needed to provide enough energy to melt the ice? (The ΔH for explosive decomposition of TNT is −1035.8 kJ/mol.)

4. Many biochemical processes occur through sequences of reactions called pathways. The total energy released by many of these pathways is much more than the energy a cell could handle if it were all released in a single step. For example, the combustion of glucose in a single step would release enough energy to kill a cell. By using a series of smaller steps that release less energy per reaction, however, the cell can extract the maximum energy from glucose without being destroyed. Referring to Equation 5.30, calculate how many grams of glucose would need to be metabolized to raise the temperature of a liver cell from an average body temperature of 37°C to 100°C, if the cell has a volume of 5000 μm³. Although the cell is only 69% water, assume that the density of the cell is 1.00 and that its C_s is the same as that of water.

5. ♦ During smelting, naturally occurring metal oxides are reduced by carbon at high temperature. For copper(II) oxide, this process includes the following series of chemical equations:

   CuO(s) + C(s) → Cu(l) + CO(g) 2C(s) + O₂(g) → 2CO(g) CuO(l) + CO(g) → Cu(s) + CO₂(g)

   The final products are CO₂ and Cu. The discovery of this process led to the increasing use of ores as sources of metals in ancient cultures. In fact, between 3000 BC and 2000 BC, the smelting of copper was well established, and beads made from copper are some of the earliest known metal artifacts.

   1. Write a balanced chemical equation for the overall reaction of CuO, C, and O₂ to give only CO₂ and Cu.
   2. Using Hess’s law and the data in Chapter 25 "Appendix A: Standard Thermodynamic Quantities for Chemical Substances at 25°C", calculate ΔH_rxn for the smelting of CuO ore to give Cu and CO₂.
   3. Assuming complete reaction, how much heat was released if 23 g of Cu metal was produced from its ore?

6. ♦ The earliest known Egyptian artifacts made from tin metal date back to approximately 1400 BC. If the smelting process for SnO₂ occurs via the reaction sequence

   SnO₂(s) + 2C(s) → Sn(s) + 2CO(g) SnO₂(s) + 2CO(g) → Sn(s) + 2CO₂(g)

   what is ΔH_rxn for the conversion of SnO₂ to Sn (s, white) by this smelting process? How much heat was released or required if 28 g of Sn metal was produced from its ore, assuming complete reaction?

7. ♦ An average American consumes approximately 10⁶ kJ of energy per day. The average life expectancy of an American is 77.9 years.

   1. How much coal would need to be burned to provide enough energy to meet a person’s energy demands if the efficiency of energy production from coal is 38%?
   2. If the coal contains 0.6% by mass FeS₂, how many kilograms of sulfuric acid are produced during the time in part (a)?

8. Several theories propose that life on Earth evolved in the absence of oxygen. One theory is that primitive organisms used fermentation processes, in which sugars are decomposed in an oxygen-free environment, to obtain energy. Many kinds of fermentation processes are possible, including the conversion of glucose to lactic acid (a), to CO₂ and ethanol (b), and to ethanol and acetic acid (c):

   1. C₆H₁₂O₆(s) → 2C₃H₆O₃(s)
   2. C₆H₁₂O₆(s) → 2C₂H₅OH(l) + 2CO₂(g)
   3. C₆H₁₂O₆(s) + H₂O(l) → C₂H₅OH(l) + CH₃CO₂H(l) + 2H₂(g) + 2CO₂(g)

   Reaction (a) occurs in rapidly exercising muscle cells, reaction (b) occurs in yeast, and reaction (c) occurs in intestinal bacteria. Using Chapter 25 "Appendix A: Standard Thermodynamic Quantities for Chemical Substances at 25°C", calculate which reaction gives the greatest energy yield (most negative$\Delta H_{\text{rxn}}^o$) per mole of glucose.

9. A 70 kg person expends 85 Cal/h watching television. If the person eats 8 cups of popcorn that contains 55 Cal per cup, how many kilojoules of energy from the popcorn will have been burned during a 2 h movie? After the movie, the person goes outside to play tennis and burns approximately 500 Cal/h. How long will that person have to play tennis to work off all the residual energy from the popcorn?

10. ♦ Photosynthesis in higher plants is a complex process in which glucose is synthesized from atmospheric carbon dioxide and water in a sequence of reactions that uses light as an energy source. The overall reaction is as follows:

    $${\text{6CO}}_{\text{2}}\text{(g)}+{\text{6H}}_{\text{2}}\text{O(l)}\stackrel{\text{light}}{\to }{\text{C}}_{\text{6}}{\text{H}}_{\text{12}}{\text{O}}_{\text{6}}\text{(s)}+{\text{6O}}_{\text{2}}\text{(g)}$$

    Glucose may then be used to produce the complex carbohydrates, such as cellulose, that constitute plant tissues.

    1. Is the reaction endothermic or exothermic?
    2. How many grams of glucose are produced per kilogram of carbon dioxide?
    3. A 2.5 lb sweet potato is approximately 73% water by mass. If the remaining mass is made up of carbohydrates derived from glucose, how much carbon dioxide was needed to grow this sweet potato?
    4. How many kilojoules of energy are stored in the potato?
    5. Which releases more energy—digestion of the potato or combustion of the potato?

11. Adipose (fat) tissue consists of cellular protoplasm, which is mostly water, and fat globules. Nearly all the energy stored in adipose tissue comes from the chemical energy of its fat globules, totaling approximately 3500 Cal per pound of tissue. How many kilojoules of energy are stored in 10 g of adipose tissue? How many 50 g brownies would you need to consume to generate 10 lb of fat? (Refer to Table 5.5 "Approximate Compositions and Fuel Values of Some Common Foods" for the necessary caloric data.)

12. If a moderate running pace of 5 min/km expends energy at a rate of about 400 kJ/km, how many 8 oz apples would a person have to eat to have enough energy to run 5 mi? How many 4 oz hamburgers? (Refer to Table 5.5 "Approximate Compositions and Fuel Values of Some Common Foods" for the necessary caloric data.)

13. Proteins contain approximately 4 Cal/g, carbohydrates approximately 4 Cal/g, and fat approximately 9 Cal/g. How many kilojoules of energy are available from the consumption of one serving (8 oz) of each food in the table? (Data are shown per serving.)

    Food	Protein (g)	Fat (g)	Carbohydrates (g)
    sour cream	7	48	10
    banana	2	1	35
    cheeseburger	60	31	40
    green peas	8	1	21

14. When you eat a bowl of cereal with 500 g of milk, how many Calories must your body burn to warm the milk from 4°C to a normal body temperature of 37°C? (Assume milk has the same specific heat as water.) How many Calories are burned warming the same amount of milk in a 32°C bowl of oatmeal from 32°C to normal body temperature? In some countries that experience starvation conditions, it has been found that infants don’t starve even though the milk from their mothers doesn’t contain the number of Calories thought necessary to sustain them. Propose an explanation for this.

15. If a person’s fever is caused by an increase in the temperature of water inside the body, how much additional energy is needed if a 70 kg person with a normal body temperature of 37°C runs a temperature of 39.5°C? (A person’s body is approximately 79% water.) The old adage “feed a fever” may contain some truth in this case. How many 4 oz hamburgers would the person need to consume to cause this change? (Refer to Table 5.5 "Approximate Compositions and Fuel Values of Some Common Foods" for the necessary caloric data.)

16. Approximately 810 kJ of energy is needed to evaporate water from the leaves of a 9.2 m tree in one day. What mass of water is evaporated from the tree?