Q: A diver descends to a depth where the pressure is 3 atm. If the diver's lung volume at the surface (1 atm) is 6.0 L, what will be the lung volume at this depth if the diver holds their breath? (Assume constant temperature.)

$V_2 = V_1 \times \dfrac{P_1}{P_2} = 6.0\,\text{L} \times \dfrac{1}{3} = 2.0\,\text{L}$

Q: A weather report gives the barometric pressure as 30.44 in Hg. What is this pressure in psi? (1 atm = 29.92 in Hg = 14.7 psi)

$30.44\,\text{in Hg} \times \dfrac{1\,\text{atm}}{29.92\,\text{in Hg}} \times \dfrac{14.7\,\text{psi}}{1\,\text{atm}} = 14.95\,\text{psi}$

Q: A sample of gas has a volume of 2.80 L at an unknown temperature. When cooled to $0^\circ$C, its volume decreases to 2.57 L. What was the initial temperature in Kelvin?

$T_1 = T_2 \times \dfrac{V_1}{V_2} = 273\,\text{K} \times \dfrac{2.80}{2.57} = 297\,\text{K}$

Q: A 12.5-L scuba tank contains 24.2 g of He and 4.32 g of O$_2$ at 298 K. What is the mole fraction of oxygen in the tank? (Molar masses: He = 4.00 g/mol, O$_2$ = 32.00 g/mol)

$n_{He} = 6.05\,\text{mol},\ n_{O_2} = 0.135\,\text{mol};\ x_{O_2} = \dfrac{0.135}{6.05 + 0.135} = 0.022$

Q: A sample of gas has a mass of 0.311 g, a volume of 0.225 L, a temperature of 298 K, and a pressure of 886 mmHg. What is the molar mass of the gas? ($R = 0.0821\,\text{L} \cdot \text{atm} / \text{mol} \cdot \text{K}$, $1\,\text{atm} = 760\,\text{mmHg}$)

First, $P = 886/760 = 1.165\,\text{atm}$; $n = \dfrac{PV}{RT} = \dfrac{1.165 \times 0.225}{0.0821 \times 298} = 0.0107\,\text{mol}$; Molar mass $= 0.311/0.0107 = 29.0\,\text{g/mol}$

Q: A gas sample is collected over water at 293 K and a total pressure of 755.2 mmHg. The vapor pressure of water at 293 K is 17.54 mmHg. What is the partial pressure of the dry gas?

$755.2\,\text{mmHg} - 17.54\,\text{mmHg} = 737.7\,\text{mmHg}$

Question 1

According to the kinetic molecular theory, which of the following statements is TRUE about the behavior of gas particles?

Accepted Answer

Gas particles move in straight lines until they collide with something, and these collisions are elastic.

Question 2

A diver descends to a depth where the pressure is 3 atm. If the diver's lung volume at the surface (1 atm) is 6.0 L, what will be the lung volume at this depth if the diver holds their breath? (Assume constant temperature.)

Accepted Answer

$V_2 = V_1 	imes \dfrac{P_1}{P_2} = 6.0\,	ext{L} 	imes \dfrac{1}{3} = 2.0\,	ext{L}$

Question 3

Which of the following actions will increase the pressure of a gas inside a rigid, sealed container?

Accepted Answer

Adding more gas molecules to the container.

Question 4

A weather report gives the barometric pressure as 30.44 in Hg. What is this pressure in psi? (1 atm = 29.92 in Hg = 14.7 psi)

Accepted Answer

$30.44\,	ext{in Hg} 	imes \dfrac{1\,	ext{atm}}{29.92\,	ext{in Hg}} 	imes \dfrac{14.7\,	ext{psi}}{1\,	ext{atm}} = 14.95\,	ext{psi}$

Question 5

A sample of gas has a volume of 2.80 L at an unknown temperature. When cooled to $0^\circ$C, its volume decreases to 2.57 L. What was the initial temperature in Kelvin?

Accepted Answer

$T_1 = T_2 	imes \dfrac{V_1}{V_2} = 273\,	ext{K} 	imes \dfrac{2.80}{2.57} = 297\,	ext{K}$

Question 6

Which of the following best explains why a helium-filled balloon expands when moved from a cold room to a warm room?

Accepted Answer

The average kinetic energy of helium atoms increases, causing more frequent and forceful collisions with the balloon walls.

Question 7

A 12.5-L scuba tank contains 24.2 g of He and 4.32 g of O$_2$ at 298 K. What is the mole fraction of oxygen in the tank? (Molar masses: He = 4.00 g/mol, O$_2$ = 32.00 g/mol)

Accepted Answer

$n_{He} = 6.05\,	ext{mol},\ n_{O_2} = 0.135\,	ext{mol};\ x_{O_2} = \dfrac{0.135}{6.05 + 0.135} = 0.022$

Question 8

A sample of gas has a mass of 0.311 g, a volume of 0.225 L, a temperature of 298 K, and a pressure of 886 mmHg. What is the molar mass of the gas? ($R = 0.0821\,	ext{L} \cdot 	ext{atm} / 	ext{mol} \cdot 	ext{K}$, $1\,	ext{atm} = 760\,	ext{mmHg}$)

Accepted Answer

First, $P = 886/760 = 1.165\,	ext{atm}$; $n = \dfrac{PV}{RT} = \dfrac{1.165 	imes 0.225}{0.0821 	imes 298} = 0.0107\,	ext{mol}$; Molar mass $= 0.311/0.0107 = 29.0\,	ext{g/mol}$

Question 9

Which of the following gases will have the highest root mean square velocity at the same temperature?

Accepted Answer

He

Question 10

A mixture contains equal moles of He and Ne with a total pressure of 3.0 atm. What is the partial pressure of Ne?

Accepted Answer

1.5 atm

Question 11

A gas sample is collected over water at 293 K and a total pressure of 755.2 mmHg. The vapor pressure of water at 293 K is 17.54 mmHg. What is the partial pressure of the dry gas?

Accepted Answer

$755.2\,	ext{mmHg} - 17.54\,	ext{mmHg} = 737.7\,	ext{mmHg}$

Question 12

Which of the following best describes the effect of increasing altitude on atmospheric pressure?

Accepted Answer

Atmospheric pressure decreases with altitude.

Question 13

Which of the following is a correct application of Graham’s Law of Effusion?

Accepted Answer

The rate of effusion of H$_2$ is greater than that of O$_2$ because H$_2$ has a lower molar mass.

Question 14

Which of the following modifications to the ideal gas law accounts for the finite volume of gas particles?

Accepted Answer

Adding a term $b$ to the volume: $(V - nb)$

Question 15

A chemical reaction produces 0.621 mol of a gaseous product in a cylinder that initially contains 0.120 mol of gas at 2.18 L. What is the final volume after the reaction, assuming constant temperature and pressure?

Accepted Answer

$V_2 = V_1 	imes \dfrac{n_2}{n_1} = 2.18\,	ext{L} 	imes \dfrac{0.621}{0.120} = 11.3\,	ext{L}$

Question 16

Which of the following best explains why real gases deviate from ideal behavior at high pressures?

Accepted Answer

The volume of the gas particles becomes significant compared to the total volume.

Question 17

A sample of nitrogen gas has a density of 0.852 g/L at 298 K and 755 mmHg. What is the molar mass of nitrogen gas? ($R = 0.0821\,	ext{L} \cdot 	ext{atm} / 	ext{mol} \cdot 	ext{K}$, $1\,	ext{atm} = 760\,	ext{mmHg}$)

Accepted Answer

$M = \dfrac{dRT}{P} = \dfrac{0.852 	imes 0.0821 	imes 298}{0.993} = 21.0\,	ext{g/mol}$

Chapter 10: Gases – Structure, Properties, and Laws

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