Ideal Gases

1. (a) Which, if either, contains a greater number of molecules, a mole of hydrogen (H2) or a mole of oxygen (O2)? (b) Which one has more mass? Give reasons for your answers.

2. (a) Which, if either, contains a greater number of molecules, a mole of neon (Ne) or a mole of argon (Ar)? (b) Which one has more mass? Give reasons for your answers.

3. Above the liquid in a can of hair spray is a gas at a relatively high pressure. The label on the can includes the warning “Do not store at high temperatures.” Use the ideal gas law and explain why the warning is given.

4. Assuming that air behaves like an ideal gas, explain what happens to the pressure in a tightly sealed house when the electric furnace turns on for a while.

5. Atmospheric pressure decreases with increasing altitude. With this fact in mind, explain why helium-filled weather balloons are underinflated when they are launched from earth.

6. A commonly used packing material consists of “bubbles” of air trapped between bonded layers of plastic (bubble packing). Using the ideal gas law, explain why this packing material offers less protection on cold days than on warm days.

7. The chlorophyll-a molecule, C55H72MgN4O5, is important in photosynthesis. (a) Using a periodic table, determine its molar mass. (b) What is the mass (in grams) of 3.00 moles of chlorophyll-a molecules?

8. The artificial sweetener NutraSweet is a chemical called aspartame (C14H18N2O5). (a) Using a periodic table, determine its molar mass. (b) What is the mass (in grams) of 3.00 moles of an aspartame molecule?

9. A Goodyear blimp typically contains 5400 m3 of helium (He) at an absolute pressure of 1.1 × 105 Pa. The temperature of the helium is 280 K. What is the mass (in kg) of the helium in the blimp?

10. In a portable oxygen system, the oxygen (O2) is contained in a cylinder whose volume is 0.0028 m3. A full cylinder has an absolute pressure of 1.5 × 107 Pa when the temperature is 296 K. Find the mass (in kg) of oxygen in the cylinder.

11. At the start of a trip, a driver adjusts the absolute pressure in her tires to be 2.81 × 105 Pa when the outdoor temperature is 284 K. At the end of the trip she measures the pressure to be 3.01 × 105 Pa. Ignoring the expansion of the tires, find the air temperature inside the tires at the end of the trip.

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 young male adult takes in about 5.0 × 10-4 m3 of fresh air during a normal breath. Fresh air contains approximately 21% oxygen (O2). Assuming that the pressure in the lungs is 1.0 × 105 Pa and air is an ideal gas at a temperature of 310 K, find the number of oxygen molecules in a normal breath.

14. A young male adult takes in about 5.0 × 10-4 m3 of fresh air during a normal breath. Fresh air contains approximately 21% oxygen (O2). Assuming that the pressure in the lungs is 1.0 × 105 Pa and air is an ideal gas at a temperature of 310 K, find the number of oxygen molecules in a normal breath.

Challenge Problem

15. On the sunlit surface of Venus, the atmospheric pressure is 9.0 × 106 Pa, and the temperature is 740 K. On the earth's surface the atmospheric pressure is 1.0 × 105 Pa, 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.

16. On the sunlit surface of Venus, the atmospheric pressure is 9.0 × 106 Pa, and the temperature is 740 K. On the earth's surface the atmospheric pressure is 1.0 × 105 Pa, 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.