Problems

Note to Instructors: Most of the homework problems in this chapter are available for assignment via an on-line homework management program such as WileyPLUS or WebAssign, and those marked with the icon are presented in a guided tutorial format that provides enhanced interactivity. See Preface for additional details.
Note: The pressures referred to in these problems are absolute pressures, unless indicated otherwise.
ssm Solution is in the Student Solutions Manual.
This icon represents a biomedical application.
Section 14.1 Molecular Mass, the Mole, and Avogadro’s Number

| 1 | ssm Hemoglobin has a molecular mass of 64 500 u. Find the mass (in kg) of one molecule of hemoglobin.

| 2 | The active ingredient in the allergy medication Claritin contains carbon (C), hydrogen (H), chlorine (Cl), nitrogen (N), and oxygen (O). Its molecular formula is C22H23ClN2O2. The standard adult dosage utilizes molecules of this species. Determine the mass (in grams) of the active ingredient in the standard dosage.

| 3 | The artificial sweetener NutraSweet is a chemical called aspartame (C14H18N2O5). What is (a) its molecular mass (in atomic mass units) and (b) the mass (in kg) of an aspartame molecule?

| 4 | Manufacturers of headache remedies routinely claim that their own brands are more potent pain relievers than the competing brands. Their way of making the comparison is to compare the number of molecules in the standard dosage. Tylenol uses 325 mg of acetaminophen (C8H9NO2) as the standard dose, while Advil uses of ibuprofen (C13H18O2). Find the number of molecules of pain reliever in the standard doses of (a) Tylenol and (b) Advil.

| 5 | ssm A mass of 135 g of a certain element is known to contain . What is the element?

* | 6 | A runner weighs 580 N (about 130 lb), and 71% of this weight is water. (a) How many moles of water are in the runner’s body? (b) How many water molecules (H2O) are there?

* | 7 | ssm A cylindrical glass of water (H2O) has a radius of 4.50 cm and a height of 12.0 cm. The density of water is 1.00 g/cm3. How many moles of water molecules are contained in the glass?

* | 8 | A sample of ethyl alcohol (C2H5OH) has a density of 806 kg/m3 and a volume of m3. (a) Determine the mass (in kg) of a molecule of ethyl alcohol, and (b) find the number of molecules in the liquid. Section 14.2 The Ideal Gas Law

| 9 | ssm A bicycle tire whose volume is has a temperature of 296 K and an absolute pressure of . A cyclist brings the pressure up to without changing the temperature or volume. How many moles of air must have been pumped into the tire?

| 10 | It takes 0.16 g of helium (He) to fill a balloon. How many grams of nitrogen (N2) would be required to fill the balloon to the same pressure, volume, and temperature?

| 11 | An ideal gas at 15.5 °C and a pressure of occupies a volume of 2.81 m3. (a) How many moles of gas are present? (b) If the volume is raised to 4.16 m3 and the temperature raised to 28.2 °C, what will be the pressure of the gas?

| 12 | Oxygen for hospital patients is kept in special tanks, where the oxygen has a pressure of 65.0 atmospheres and a temperature of 288 K. The tanks are stored in a separate room, and the oxygen is pumped to the patient’s room, where it is administered at a pressure of 1.00 atmosphere and a temperature of 297 K. What volume does 1.00 m3 of oxygen in the tanks occupy at the conditions in the patient’s room?

| 13 | A Goodyear blimp typically contains 5400 m3 of helium (He) at an absolute pressure of . The temperature of the helium is 280 K. What is the mass (in kg) of the helium in the blimp?

| 14 | A clown at a birthday party has brought along a helium cylinder, with which he intends to fill balloons. When full, each balloon contains 0.034 m3 of helium at an absolute pressure of . The cylinder contains helium at an absolute pressure of and has a volume of 0.0031 m3. The temperature of the helium in the tank and in the balloons is the same and remains constant. What is the maximum number of balloons that can be filled?

| 15 | ssm In a diesel engine, the piston compresses air at 305 K to a volume that is one-sixteenth of the original volume and a pressure that is 48.5 times the original pressure. What is the temperature of the air after the compression?

| 16 | A 0.030-m3 container is initially evacuated. Then, 4.0 g of water is placed in the container and, after some time, all the water evaporates. If the temperature of the water vapor is 388 K, what is its pressure?

| 17 | On the sunlit surface of Venus, the atmospheric pressure is , and the temperature is 740 K. On the earth’s surface the atmospheric pressure is , while the surface temperature can reach 320 K. These data imply that Venus has a “thicker” atmosphere at its surface than does the earth, which means that the number of molecules per unit volume (N/V) is greater on the surface of Venus than on the earth. Find the ratio (N/V)Venus/(N/V)Earth.

| 18 | What is the density (in kg/m3) of nitrogen gas at a pressure of 2.0 atmospheres and a temperature of 310 K?

* | 19 | ssm wwwThe drawing shows two thermally insulated tanks. They are connected by a valve that is initially closed. Each tank contains neon gas at the pressure, temperature, and volume indicated in the drawing. When the valve is opened, the contents of the two tanks mix, and the pressure becomes constant throughout. (a) What is the final temperature? Ignore any change in temperature of the tanks themselves. (Hint: The heat gained by the gas in one tank is equal to that lost by the other.) (b) What is the final pressure?

* | 20 | Multiple-Concept Example 4 reviews the principles that play roles in this problem. A primitive diving bell consists of a cylindrical tank with one end open and one end closed. The tank is lowered into a freshwater lake, open end downward. Water rises into the tank, compressing the trapped air, whose temperature remains constant during the descent. The tank is brought to a halt when the distance between the surface of the water in the tank and the surface of the lake is 40.0 m. Atmospheric pressure at the surface of the lake is . Find the fraction of the tank’s volume that is filled with air.

* | 21 | Refer to Interactive Solution 14.21 at for help with problems like this one. An apartment has a living room whose dimensions are . Assume that the air in the room is composed of 79% nitrogen (N2) and 21% oxygen (O2). At a temperature of 22 °C and a pressure of , what is the mass (in grams) of the air?

* | 22 | Multiple-Concept Example 4 deals with the concepts used in this problem. Conceptual Example 3 is also pertinent. A bubble, located 0.200 m beneath the surface in a glass of beer, rises to the top. The air pressure at the top is . Assume that the density of beer is the same as that of fresh water. If the temperature and number of moles of CO2 remain constant as the bubble rises, find the ratio of its volume at the top to that at the bottom.

* | 23 | ssm The relative humidity is 55% on a day when the temperature is 30.0 °C. Using the graph that accompanies Problem 68 in Chapter 12, determine the number of moles of water vapor per cubic meter of air.

* | 24 | Interactive Solution 14.24 at offers one approach to this problem. One assumption of the ideal gas law is that the atoms or molecules themselves occupy a negligible volume. Verify that this assumption is reasonable by considering gaseous xenon (Xe). Xenon has an atomic radius of . For STP conditions, calculate the percentage of the total volume occupied by the atoms.

** | 25 | The mass of a hot-air balloon and its occupants is 320 kg (excluding the hot air inside the balloon). The air outside the balloon has a pressure of and a density of 1.29 kg/m3. To lift off, the air inside the balloon is heated. The volume of the heated balloon is 650 m3. The pressure of the heated air remains the same as that of the outside air. To what temperature (in kelvins) must the air be heated so that the balloon just lifts off? The molecular mass of air is 29 u.

** | 26 | A gas fills the right portion of a horizontal cylinder whose radius is 5.00 cm. The initial pressure of the gas is . A frictionless movable piston separates the gas from the left portion of the cylinder, which is evacuated and contains an ideal spring, as the drawing shows. The piston is initially held in place by a pin. The spring is initially unstrained, and the length of the gas-filled portion is 20.0 cm. When the pin is removed and the gas is allowed to expand, the length of the gas-filled chamber doubles. The initial and final temperatures are equal. Determine the spring constant of the spring.

** | 27 | ssm A cylindrical glass beaker of height 1.520 m rests on a table. The bottom half of the beaker is filled with a gas, and the top half is filled with liquid mercury that is exposed to the atmosphere. The gas and mercury do not mix because they are separated by a frictionless, movable piston of negligible mass and thickness. The initial temperature is 273 K. The temperature is increased until a value is reached when one-half of the mercury has spilled out. Ignore the thermal expansion of the glass and mercury, and find this temperature.
Section 14.3 Kinetic Theory of Gases

| 28 | Consult Multiple-Concept Example 6 to review the principles involved in this problem. Near the surface of Venus, the rms speed of carbon dioxide molecules (CO2) is 650 m /s. What is the temperature (in kelvins) of the atmosphere at that point?

| 29 | ssm The average value of the squared speed does not equal the square of the average speed . To verify this fact, consider three particles with the following speeds: , , and . Calculate (a) and (b) .

| 30 | If the translational rms speed of the water vapor molecules (H2O) in air is 648 m/s, what is the translational rms speed of the carbon dioxide molecules (CO2) in the same air? Both gases are at the same temperature.

| 31 | Two gas cylinders are identical. One contains the monatomic gas argon (Ar), and the other contains an equal mass of the monatomic gas krypton (Kr). The pressures in the cylinders are the same, but the temperatures are different. Determine the ratio of the average kinetic energy of a krypton atom to the average kinetic energy of an argon atom.

| 32 | Refer to Multiple-Concept Example 6 for insight into the concepts used in this problem. An oxygen molecule is moving near the earth’s surface. Another oxygen molecule is moving in the ionosphere (the uppermost part of the earth’s atmosphere) where the Kelvin temperature is three times greater. Determine the ratio of the translational rms speed in the ionosphere to that near the earth’s surface.

| 33 | Consult Interactive Solution 14.33 at to see how this problem can be solved. Very fine smoke particles are suspended in air. The translational rms speed of a smoke particle is , and the temperature is 301 K. Find the mass of a particle.

| 34 | Each molecule in a gas has an average kinetic energy. What is the total average kinetic energy of all the molecules in 3.0 mol of a gas whose temperature is 320 K?

* | 35 | ssm www Compressed air can be pumped underground into huge caverns as a form of energy storage. The volume of a cavern is , and the pressure of the air in it is . Assume that air is a diatomic ideal gas whose internal energy U is given by If one home uses 30.0 kW · h of energy per day, how many homes could this internal energy serve for one day?

* | 36 | Helium (He), a monatomic gas, fills a 0.010-m3 container. The pressure of the gas is . How long would a 0.25-hp engine have to run to produce an amount of energy equal to the internal energy of this gas?

** | 37 | ssm www In a TV, electrons with a speed of strike the screen from behind, causing it to glow. The electrons come to a halt after striking the screen. Each electron has a mass of , and there are electrons per second hitting the screen over an area of m2. What is the pressure that the electrons exert on the screen?

** | 38 | In 10.0 s, 200 bullets strike and embed themselves in a wall. The bullets strike the wall perpendicularly. Each bullet has a mass of and a speed of 1200 m/s. (a) What is the average change in momentum per second for the bullets? (b) Determine the average force exerted on the wall. (c) Assuming the bullets are spread out over an area of , obtain the average pressure they exert on this region of the wall.
Section 14.4 Diffusion

| 39 | Insects do not have lungs as we do, nor do they breathe through their mouths. Instead, they have a system of tiny tubes, called tracheae, through which oxygen diffuses into their bodies. The tracheae begin at the surface of the insect’s body and penetrate into the interior. Suppose that a trachea is 1.9 mm long with a cross-sectional area of . The concentration of oxygen in the air outside the insect is 0.28 kg/m3, and the diffusion constant is . If the mass per second of oxygen diffusing through a trachea is , find the oxygen concentration at the interior end of the tube.

| 40 | Review Conceptual Example 7 before starting this problem. Ammonia, which has a strong smell, is diffusing through air contained in a tube of length L and cross-sectional area . The diffusion constant for ammonia in air is . In a certain time, of ammonia diffuses through the air when the difference in ammonia concentration between the ends of the tube is . Find the speed at which ammonia diffuses through the air—that is, the length of the tube divided by the time to travel this length.

| 41 | ssmThe diffusion constant of for the alcohol ethanol in water is . A cylinder has a cross-sectional area of 4.00 cm2 and a length of 2.00 cm. A difference in ethanol concentration of 1.50 kg/m3 is maintained between the ends of the cylinder. In one hour, what mass of ethanol diffuses through the cylinder?

| 42 | The diffusion constant for the amino acid glycine in water is . In a 2.0-cm-long tube with a cross-sectional area of , the mass rate of diffusion is , because the glycine concentration is maintained at a value of at one end of the tube and at a lower value at the other end. What is the lower concentration?

| 43 | ssm www Carbon tetrachloride (CCl4) is diffusing through benzene (C6H6), as the drawing illustrates. The concentration of CCl4 at the left end of the tube is maintained at , and the diffusion constant is . The CCl4 enters the tube at a mass rate of . Using these data and those shown in the drawing, find (a) the mass of CCl4 per second that passes point A and (b) the concentration of CCl4 at point A.

* | 44 | Review Conceptual Example 7 as background for this problem. It is possible to convert Fick’s law into a form that is useful when the concentration is zero at one end of the diffusion channel ( in Figure 14-16a). (a) Noting that AL is the volume V of the channel and that m/V is the average concentration of solute in the channel, show that Fick’s law becomes . This form of Fick’s law can be used to estimate the time required for the first solute molecules to traverse the channel. (b) A bottle of perfume is opened in a room where convection currents are absent. Assuming that the diffusion constant for perfume in air is , estimate the minimum time required for the perfume to be smelled 2.5 cm away.

** | 45 | The drawing shows a container that is partially filled with 2.0 grams of water. The temperature is maintained at a constant 20 °C. The space above the liquid contains air that is completely saturated with water vapor. A tube of length 0.15 m and cross-sectional area connects the water vapor at one end to air that remains completely dry at the other end. The diffusion constant for water vapor in air is . How long does it take for the water in the container to evaporate completely? (Hint: Refer to Problem 68 in Chapter 12 to find the pressure of the water vapor.)

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