Q: A scuba diver descends to a depth where the pressure is 3 atm. If the diver inhales 2.0 L of air at this depth and then ascends to the surface (1 atm) without exhaling, what will be the volume of air in the diver's lungs at the surface? (Assume constant temperature.)

$$V_2$$ = $$V_1$$ \times \frac{$$P_1$$}{$$P_2$$} = 2.0\,\text{L} \times \frac{3.0\,\text{atm}}{1.0\,\text{atm}} = 6.0\,\text{L}$$

Q: A sample of gas occupies 4.0 L at 300 K. If the temperature is increased to 600 K at constant pressure, what is the new volume?

$$V_2$$ = $$V_1$$ \times \frac{$$T_2$$}{$$T_1$$} = 4.0\,\text{L} \times \frac{600\,\text{K}}{300\,\text{K}} = 8.0\,\text{L}$$

Q: A 0.500 mol sample of gas is at 1.00 atm and 273 K. What is its volume according to the ideal gas law?

$$V = \frac{nRT}{P} = \frac{0.500\,\text{mol} \times 0.0821\,\text{L}\cdot\text{atm}/\text{mol}\cdot\text{K} \times 273\,\text{K}}{1.00\,\text{atm}} = 11.2\,\text{L}$$

Q: A mixture of gases contains 70% nitrogen and 30% oxygen by mole. If the total pressure is 1.0 atm, what is the partial pressure of oxygen?

$$P_{O_2$} = 0.30 \times 1.0\,\text{atm} = 0.30\,\text{atm}$$

Q: A 2.0 L sample of gas at 1.0 atm and 300 K is compressed to 1.0 L and heated to 600 K. What is the final pressure?

$$P_2$$ = $$P_1$$ \times \frac{$$V_1$$}{$$V_2$$} \times \frac{$$T_2$$}{$$T_1$$} = 1.0\,\text{atm} \times \frac{2.0}{1.0} \times \frac{600}{300} = 4.0\,\text{atm}$$

Q: A 5.0 L sample of gas contains 0.20 mol at constant temperature and pressure. How many moles must be added to increase the volume to 7.5 L?

$$n_2$$ = $$n_1$$ \times \frac{$$V_2$$}{$$V_1$$} = 0.20\,\text{mol} \times \frac{7.5}{5.0} = 0.30\,\text{mol};\ \text{add}\ 0.10\,\text{mol}$$

Question 1

A scuba diver descends to a depth where the pressure is 3 atm. If the diver inhales 2.0 L of air at this depth and then ascends to the surface (1 atm) without exhaling, what will be the volume of air in the diver's lungs at the surface? (Assume constant temperature.)

Accepted Answer

$$V_2$$ = $$V_1$$ 	imes \frac{$$P_1$$}{$$P_2$$} = 2.0\,	ext{L} 	imes \frac{3.0\,	ext{atm}}{1.0\,	ext{atm}} = 6.0\,	ext{L}$$

Question 2

Which of the following best explains why gases are compressible but liquids are not?

Accepted Answer

Gas particles are far apart with a lot of empty space between them, while liquid particles are much closer together.

Question 3

A sample of gas occupies 4.0 L at 300 K. If the temperature is increased to 600 K at constant pressure, what is the new volume?

Accepted Answer

$$V_2$$ = $$V_1$$ 	imes \frac{$$T_2$$}{$$T_1$$} = 4.0\,	ext{L} 	imes \frac{600\,	ext{K}}{300\,	ext{K}} = 8.0\,	ext{L}$$

Question 4

Which of the following statements is NOT a postulate of the kinetic molecular theory of gases?

Accepted Answer

Gas particles attract each other strongly.

Question 5

A 0.500 mol sample of gas is at 1.00 atm and 273 K. What is its volume according to the ideal gas law?

Accepted Answer

$$V = \frac{nRT}{P} = \frac{0.500\,	ext{mol} 	imes 0.0821\,	ext{L}\cdot	ext{atm}/	ext{mol}\cdot	ext{K} 	imes 273\,	ext{K}}{1.00\,	ext{atm}} = 11.2\,	ext{L}$$

Question 6

A mixture of gases contains 70% nitrogen and 30% oxygen by mole. If the total pressure is 1.0 atm, what is the partial pressure of oxygen?

Accepted Answer

$$P_{O_2$} = 0.30 	imes 1.0\,	ext{atm} = 0.30\,	ext{atm}$$

Question 7

A 2.0 L sample of gas at 1.0 atm and 300 K is compressed to 1.0 L and heated to 600 K. What is the final pressure?

Accepted Answer

$$P_2$$ = $$P_1$$ 	imes \frac{$$V_1$$}{$$V_2$$} 	imes \frac{$$T_2$$}{$$T_1$$} = 1.0\,	ext{atm} 	imes \frac{2.0}{1.0} 	imes \frac{600}{300} = 4.0\,	ext{atm}$$

Question 8

Which of the following is a real-world consequence of the decrease in atmospheric pressure as altitude increases?

Accepted Answer

The partial pressure of oxygen decreases, which can lead to hypoxia (oxygen starvation).

Question 9

A 5.0 L sample of gas contains 0.20 mol at constant temperature and pressure. How many moles must be added to increase the volume to 7.5 L?

Accepted Answer

$$n_2$$ = $$n_1$$ 	imes \frac{$$V_2$$}{$$V_1$$} = 0.20\,	ext{mol} 	imes \frac{7.5}{5.0} = 0.30\,	ext{mol};\ 	ext{add}\ 0.10\,	ext{mol}$$

Question 10

Which of the following best describes why a straw longer than about 10.3 m will not work at sea level, even with a perfect vacuum inside?

Accepted Answer

Atmospheric pressure can only support a column of water up to 10.3 m high; beyond this, the pressure of the water column equals atmospheric pressure and no more liquid can be pushed up.

Question 11

A sample of hydrogen gas is collected over water at 25°C and a total pressure of 755 mm Hg. If the vapor pressure of water at 25°C is 24 mm Hg, what is the partial pressure of hydrogen gas?

Accepted Answer

$$P_{H_2$} = 755\,	ext{mm Hg} - 24\,	ext{mm Hg} = 731\,	ext{mm Hg}$$

Question 12

Which of the following is a correct conversion between units of pressure?

Accepted Answer

$$1\,	ext{atm} = 760\,	ext{mm Hg}$$

Question 13

A 1.0 L sample of gas at 2.0 atm and 300 K is allowed to expand to 2.0 L at constant temperature. What is the final pressure?

Accepted Answer

$$P_2$$ = $$P_1$$ 	imes \frac{$$V_1$$}{$$V_2$$} = 2.0\,	ext{atm} 	imes \frac{1.0}{2.0} = 1.0\,	ext{atm}$$

Question 14

Which of the following is a real-world application of the combined gas law?

Accepted Answer

Predicting how the pressure in a car tire changes when the temperature and volume of the tire change.

Question 15

A sample of gas has a volume of 500 mL at 27°C and 1.0 atm. What would its volume be at 127°C and 1.0 atm?

Accepted Answer

$$V_2$$ = $$V_1$$ 	imes \frac{$$T_2$$}{$$T_1$$} = 500\,	ext{mL} 	imes \frac{400\,	ext{K}}{300\,	ext{K}} = 667\,	ext{mL}$$

Chapter 11: Gases – Properties, Laws, and Applications

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