# 6.9: Chapter Problems

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## Application Problems

Be sure you are familiar with the material in Essential Skills 5 (Section 10.9 "Essential Skills 5") before proceeding to the Application Problems. Problems marked with a ♦ involve multiple concepts.

1. ♦ Oxalic acid (C2H2O4) is a metabolic product of many molds. Although oxalic acid is toxic to humans if ingested, many plants and vegetables contain significant amounts of oxalic acid or oxalate salts. In solution, oxalic acid can be oxidized by air via the following chemical equation:

H2C2O4(aq) + O2(g) → H2O2(l) + 2 CO2(g)

If a plant metabolized enough oxalic acid to produce 3.2 L of CO2 on a day when the temperature was 29°C and the pressure was 752 mmHg, how many grams of oxalic acid were converted to CO2? Given that air is 21% oxygen, what volume of air was needed for the oxidation?

2. ♦ The decomposition of iron oxide is used to produce gas during the manufacture of porous, expanded materials. These materials have very low densities due to the swelling that occurs during the initial rapid heating. Consequently, they are used as additives to provide insulation in concrete, road building, and other construction materials. Iron oxide decomposes at 1150°C according to the following chemical equation:

6 Fe2O3(s) → 4 Fe3O4(s) + O2(g)

1. Explain how this reaction could cause materials containing Fe2O3 to swell on heating.
2. If you begin with 15.4 g of Fe2O3, what volume of O2 gas at STP is produced?
3. What is the volume of the same amount of O2 gas at 1200°C, assuming a constant pressure of 1.0 atm?
4. If 6.3 L of gas were produced at 1200°C and 1 atm, how many kilograms of Fe2O3 were initially used in the reaction? How many kilograms of Fe3O4 are produced?
3. ♦ A 70 kg man expends 480 kcal of energy per hour shoveling snow. The oxidation of organic nutrients such as glucose during metabolism liberates approximately 3.36 kcal of energy per gram of oxygen consumed. If air is 21% oxygen, what volume of air at STP is needed to produce enough energy for the man to clear snow from a walkway that requires 35 minutes of shoveling?

4. ♦ Calcium carbonate is an important filler in the processing industry. Its many uses include a reinforcing agent for rubber and improving the whiteness and hiding power of paints. When calcium nitrate is used as a starting material in the manufacture of fertilizers, calcium carbonate is produced according to the following chemical reaction:

Ca(NO3)2 + 2 NH3 + CO2 + H2O → CaCO3 + 2 NH4NO3

1. What volume of CO2 at STP is needed to react completely with 28.0 g of calcium nitrate?
2. What volume of ammonia at STP is needed to react with the amount of calcium nitrate?
3. If this reaction were carried out in Denver, Colorado (pressure = 630 mmHg), what volumes of CO2 and NH3 at room temperature (20°C) would be needed?
5. ♦ Calcium nitrate used in the process described in Problem 4 is produced by the reaction of fluoroapatite—Ca5[(PO4)3(F)]—with nitric acid:

Ca5[(PO4)3(F)] + 10 HNO3 → 5 Ca(NO3)2 + HF + 3 H3PO4 Ca(NO3)2 + 2 NH3 + CO2 + H2O → CaCO3 + 2 NH4NO3

1. Your lab is in Denver, Colorado, and you have a cylinder with 8.40 L of CO2 at room temperature (20°C) and 4.75 atm pressure. What would be the volume of the CO2 gas at 630 mmHg? How many grams of fluoroapatite could be converted to CaCO3 using the two reactions and this amount of CO2?
2. If 3.50 L of a 0.753 M HF solution was produced during the conversion of fluoroapatite to calcium nitrate, how many grams of calcium carbonate could you produce, assuming 100% efficiency?
3. How many liters of ammonia gas at this higher altitude and 20°C are required to convert the calcium nitrate to calcium carbonate and to neutralize all of the HF solution?
4. If the reaction of fluoroapatite with nitric acid takes place at 330 atm and 80°C, what volumes of NH3 and CO2 are needed to convert 20.5 kg of fluoroapatite to calcium carbonate?
6. Mars has an average temperature of −47°C; a surface pressure of 500 Pa; and an atmosphere that is 95% carbon dioxide, 3% nitrogen, and 2% argon by mass, with traces of other gases. What is the partial pressure (in atmospheres) of each gas in this atmosphere? A 5.0 L sample is returned to Earth and stored in a laboratory at 19°C and 1 atm. What is the volume of this sample?

7. ♦ Chlorofluorocarbons (CFCs) are inert substances that were long used as refrigerants. Because CFCs are inert, when they are released into the atmosphere they are not rapidly destroyed in the lower atmosphere. Instead, they are carried into the stratosphere, where they cause ozone depletion. A method for destroying CFC stockpiles passes the CFC through packed sodium oxalate (Na2C2O4) powder at 270°C. The reaction for Freon-12 (CF2Cl2) is as follows:

CF2Cl2(g) + 2 Na2C2O4(s) → 2 NaF(s) + 2 NaCl + C(s) + 4 CO2(g)

1. If this reaction produced 11.4 L of CO2 gas at 21°C and 752 mmHg, what mass of sodium oxalate was consumed in the reaction?
2. If you had to design a reactor to carry out the reaction at a maximum safe pressure of 10.0 atm while destroying 1.0 kg of Freon-12, what volume reactor would you need?
3. A 2.50 L reaction vessel is charged with 20.0 atm of Freon-12 and excess sodium oxalate at 20°C. The temperature is increased to 270°C, and the pressure is monitored as the reaction progresses. What is the initial pressure at 270°C? What is the final pressure when the reaction has gone to completion?
8. ♦ The exhaust from a typical six-cylinder car contains the following average compositions of CO and CO2 under different conditions (data reported as percent by volume; rpm = rotations per minute):

Species Idling (1000 rpm) Accelerating (4000 rpm) Decelerating (800 rpm)
CO 1.0 1.2 0.60
CO2 0.80 0.40 0.40
1. What are the mole fractions of CO and CO2 under each set of conditions?
2. If the engine takes in 4.70 L of air at STP mixed with fine droplets of gasoline (C8H18) with each rotation, how many grams of gasoline are burned per minute?
9. Automobile airbags inflate by the decomposition of sodium azide (NaN3), which produces sodium metal and nitrogen gas according to the following chemical equation:

2 NaN3 → 2 Na(s) + 3 N2(g)

How many grams of sodium azide are needed to inflate a 15.0 L airbag at 20°C and 760 mmHg? The density of NaN3 is 1.847 g/cm3. What is the volume of the gas produced compared to the solid reactant? Suggest a plausible reason to explain why skin burns can result from the inflation of an airbag during an automobile accident.

10. Under basic conditions, the reaction of hydrogen peroxide (H2O2) and potassium permanganate (KMnO4) produces oxygen and manganese dioxide. During a laboratory exercise, you carefully weighed out your sample of KMnO4. Unfortunately, however, you lost your data just before mixing the KMnO4 with an H2O2 solution of unknown concentration. Devise a method to determine the mass of your sample of KMnO4 using excess H2O2.

11. Carbonated beverages are pressurized with CO2. In an attempt to produce another bubbly soda beverage, an intrepid chemist attempted to use three other gases: He, N2, and Xe. Rank the four beverages in order of how fast the drink would go “flat” and explain your reasoning. Which beverage would have the shortest shelf life (i.e., how long will an unopened bottle still be good)? Explain your answer.

12. ♦ Urea is synthesized industrially by the reaction of ammonia and carbon dioxide to produce ammonium carbamate, followed by dehydration of ammonium carbamate to give urea and water. This process is shown in the following set of chemical equations:

2 NH3(g) + CO2(g) → NH2CO2NH4(s) NH2CO2NH4(s) → NH2CONH2(s) + H2O(g)

1. A 50.0 L reaction vessel is charged with 2.5 atm of ammonia and 2.5 atm of CO2 at 50°C, and the vessel is then heated to 150°C. What is the pressure in the vessel when the reaction has gone to completion? If the vessel is then cooled to 20°C, what is the pressure?
2. An aqueous solution of urea and water is drained from the reaction vessel. What is the molarity of the urea solution? Industrially, this reaction is actually carried out at pressures ranging from 130 to 260 atm and temperatures of approximately 180°C. Give a plausible reason for using these extreme conditions.
13. Explain what happens to the temperature, the volume, or the pressure of a gas during each operation and give the direction of heat flow, if any.

1. The gas is allowed to expand from V1 to V2; a heat transfer occurs to maintain a constant gas temperature.
2. The gas is allowed to expand from V2 to V3 with no concomitant heat transfer.
3. The gas is compressed from V3 to V4; a heat transfer occurs to maintain a constant gas temperature.
4. The gas is compressed from V4 to V1; no heat transfer occurs.

These four processes constitute the cycle used in refrigeration, in which a gas such as Freon is alternately compressed and allowed to expand in the piston of a compressor. Which step eventually causes the food in a refrigerator to cool? Where does the thermal energy go that was removed in the cooling process?