Q: A sample of gas occupies 10.0 L at 2.00 atm and 300 K. What is the mass of the gas if its molar mass is 44.0 g/mol? (Use $$R = 0.08206\,\text{L} \cdot \text{atm} / \text{mol} \cdot \text{K})$$

$$n = \frac{PV}{RT} = \frac{(2.00)(10.0)}{0.08206 \times 300} = 0.812\,\text{mol};\ \text{mass} = 0.812 \times 44.0 = 35.7\,\text{g}$$

Q: A sample of methane gas ($$CH_4) $$effuses through a porous membrane in 64 seconds. How long would it take for an equal amount of sulfur hexafluoride ($$SF_6) to $$effuse under the same conditions? (Molar masses: $$CH_4 = 16.0$ g/mol, SF_6$ = 146.0 g/$$mol)

$$t_{SF_6$} = t_{CH_4$} \times \sqrt{\frac{M_{SF_6$}}{M_{CH_4$}}} = 64 \times \sqrt{\frac{146.0}{16.0}} = 64 \times 3.02 = 193\,\text{s}$$

Q: A 1.00 g sample of an unknown gas occupies 0.500 L at 1.00 atm and 273 K. What is the molar mass of the gas?

$$n = \frac{PV}{RT} = \frac{(1.00)(0.500)}{0.08206 \times 273} = 0.0223\,\text{mol};\ M = \frac{1.00}{0.0223} = 44.8\,\text{g/mol}$$

Q: A gas is collected over water at 25°C. The total pressure is 755 mmHg, and the vapor pressure of water at 25°C is 24 mmHg. What is the partial pressure of the dry gas?

$$P_{\text{gas}} = P_{\text{total}} - P$$_{\text{H}$$_2O} = 755 - 24 = 731\,\text{mmHg}$$

Question 1

A weather balloon is filled with 5.00 L of helium gas at 1.00 atm and 300 K. If the balloon rises to an altitude where the pressure is 0.500 atm and the temperature is 250 K, what will be the new volume of the balloon, assuming ideal gas behavior?

Accepted Answer

$$V_2$$ = \frac{$$P_1$$ $$V_1$$ $$T_2$$}{$$T_1$$ $$P_2$$} = \frac{(1.00\,	ext{atm})(5.00\,	ext{L})(250\,	ext{K})}{(300\,	ext{K})(0.500\,	ext{atm})} = 8.33\,	ext{L}$$

Question 2

Which of the following best explains why a diver ascending too quickly from deep water is at risk of decompression sickness ('the bends')?

Accepted Answer

The rapid decrease in pressure causes dissolved gases (mainly nitrogen) in the blood to come out of solution and form bubbles.

Question 3

A sample of gas occupies 10.0 L at 2.00 atm and 300 K. What is the mass of the gas if its molar mass is 44.0 g/mol? (Use $$R = 0.08206\,	ext{L} \cdot 	ext{atm} / 	ext{mol} \cdot 	ext{K})$$

Accepted Answer

$$n = \frac{PV}{RT} = \frac{(2.00)(10.0)}{0.08206 	imes 300} = 0.812\,	ext{mol};\ 	ext{mass} = 0.812 	imes 44.0 = 35.7\,	ext{g}$$

Question 4

Which statement about the kinetic molecular theory of gases is INCORRECT?

Accepted Answer

Gas particles lose energy when they collide with each other or the walls of the container.

Question 5

A 2.00 L flask contains a mixture of nitrogen, oxygen, and argon gases at a total pressure of 1.00 atm. If the partial pressures are $$P_{N_2$} = 0.70$$ atm and $$P_{O_2$} = 0.20$$ atm, what is the partial pressure of argon?

Accepted Answer

$$P_{Ar} = P_{total} - P_{N_2$} - P_{O_2$} = 1.00 - 0.70 - 0.20 = 0.10\,	ext{atm}$$

Question 6

Which of the following gases will have the highest root mean square velocity ($$u_{rms}) at 298 K$$?

Accepted Answer

Hydrogen ($$H_2)$$

Question 7

A sample of methane gas ($$CH_4) $$effuses through a porous membrane in 64 seconds. How long would it take for an equal amount of sulfur hexafluoride ($$SF_6) to $$effuse under the same conditions? (Molar masses: $$CH_4 = 16.0$ g/mol, SF_6$ = 146.0 g/$$mol)

Accepted Answer

$$t_{SF_6$} = t_{CH_4$} 	imes \sqrt{\frac{M_{SF_6$}}{M_{CH_4$}}} = 64 	imes \sqrt{\frac{146.0}{16.0}} = 64 	imes 3.02 = 193\,	ext{s}$$

Question 8

Which of the following best describes the effect of increasing temperature on the pressure of a fixed amount of gas in a rigid container?

Accepted Answer

The pressure increases because the gas particles move faster and collide with the walls more frequently and with greater force.

Question 9

A 1.00 g sample of an unknown gas occupies 0.500 L at 1.00 atm and 273 K. What is the molar mass of the gas?

Accepted Answer

$$n = \frac{PV}{RT} = \frac{(1.00)(0.500)}{0.08206 	imes 273} = 0.0223\,	ext{mol};\ M = \frac{1.00}{0.0223} = 44.8\,	ext{g/mol}$$

Question 10

Which of the following statements about real gases is TRUE?

Accepted Answer

At high pressures, the volume occupied by gas particles becomes significant compared to the container volume.

Question 11

A gas is collected over water at 25°C. The total pressure is 755 mmHg, and the vapor pressure of water at 25°C is 24 mmHg. What is the partial pressure of the dry gas?

Accepted Answer

$$P_{	ext{gas}} = P_{	ext{total}} - P$$_{	ext{H}$$_2O} = 755 - 24 = 731\,	ext{mmHg}$$

Question 12

Which of the following best explains why helium is used in deep-sea diving gas mixtures instead of nitrogen?

Accepted Answer

Helium is less soluble in blood than nitrogen, reducing the risk of nitrogen narcosis and decompression sickness.

Question 13

Which of the following equations correctly relates the density ($$d) of an $$ideal gas to its molar mass ($$M$$), pressure ($$P$$), and temperature ($$T$$)?

Accepted Answer

$$d = \frac{PM}{RT}$$

Question 14

A rigid 10.0 L container holds 2.00 mol of $$O_2$$ gas at 300 K. What is the pressure inside the container? ($$R = 0.08206\,	ext{L} \cdot 	ext{atm} / 	ext{mol} \cdot 	ext{K})$$

Accepted Answer

$$P = \frac{nRT}{V} = \frac{2.00 	imes 0.08206 	imes 300}{10.0} = 4.92\,	ext{atm}$$

Question 15

Which of the following is a correct statement of Avogadro's Law?

Accepted Answer

At constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of gas.

Question 16

Which of the following best describes the effect of intermolecular forces on real gas behavior at low temperatures?

Accepted Answer

Intermolecular attractions cause the pressure to be lower than predicted by the ideal gas law.

Question 17

A mixture contains 2.0 mol $$N_2$$, 1.0 mol $$O_2$$, and 1.0 mol $$CO_2 in a 10.0 L $$container at 300 K. What is the mole fraction of $$O_2 in $$the mixture?

Accepted Answer

$$\chi_{O_2$} = \frac{n_{O_2$}}{n_{total}} = \frac{1.0}{2.0 + 1.0 + 1.0} = \frac{1.0}{4.0} = 0.25$$

Question 18

Which of the following is the correct van der Waals equation for real gases?

Accepted Answer

$$(P + a\frac{n^2$}{V^2$})(V - nb) = nRT$$

Chapter 10: Gases

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