Q: A scuba diver fills a tank with 12.0 L of air at 300 K and 200 atm. If the diver uses half the air at a constant temperature and the remaining air is released at 1.0 atm, what volume will the released air occupy at 300 K?

$$V = \frac{nRT}{P} = \frac{(0.5 \times 200 \text{ atm} \times 12.0 \text{ L})}{1.0 \text{ atm}} = 1200 \text{ L}$$

Q: A sample of gas occupies 10.0 L at 2.00 atm and 300 K. What will be its volume at 1.00 atm and 300 K?

$$V_2$$ = $$V_1$$ \frac{$$P_1$$}{$$P_2$$} = 10.0 \text{ L} \times \frac{2.00}{1.00} = 20.0 \text{ L}$$

Q: A 2.00 L flask contains a mixture of O$$_2$$ and N$$_2 at a $$total pressure of 1.50 atm. If the mole fraction of O$$_2 is 0.40$$, what is the partial pressure of O$$_2$$?

$$P_{O_2$} = X_{O_2$} \times P_{\text{total}} = 0.40 \times 1.50 \text{ atm} = 0.60 \text{ atm}$$

Q: A sample of hydrogen gas is collected over water at 25$$^\circC $$and a total pressure of 755 mmHg. If the vapor pressure of water at this temperature is 24 mmHg, what is the partial pressure of the hydrogen gas?

$$P_{H_2$} = 755 \text{ mmHg} - 24 \text{ mmHg} = 731 \text{ mmHg}$$

Q: Which of the following best describes Graham’s Law of Effusion?

$$\frac{\text{Rate}_1}{\text{Rate}_2} = \sqrt{\frac{M_2$}{M_1$}}$$

Q: A 5.00 g sample of an unknown gas occupies 2.50 L at 1.00 atm and 300 K. What is the molar mass of the gas?

$$M = \frac{mRT}{PV} = \frac{5.00 \times 0.08206 \times 300}{1.00 \times 2.50} = 49.2 \text{ g/mol}$$

Question 1

A scuba diver fills a tank with 12.0 L of air at 300 K and 200 atm. If the diver uses half the air at a constant temperature and the remaining air is released at 1.0 atm, what volume will the released air occupy at 300 K?

Accepted Answer

$$V = \frac{nRT}{P} = \frac{(0.5 	imes 200 	ext{ atm} 	imes 12.0 	ext{ L})}{1.0 	ext{ atm}} = 1200 	ext{ L}$$

Question 2

Which of the following best explains why helium balloons rise in air?

Accepted Answer

Helium has a lower density than air due to its lower molar mass.

Question 3

A sample of gas occupies 10.0 L at 2.00 atm and 300 K. What will be its volume at 1.00 atm and 300 K?

Accepted Answer

$$V_2$$ = $$V_1$$ \frac{$$P_1$$}{$$P_2$$} = 10.0 	ext{ L} 	imes \frac{2.00}{1.00} = 20.0 	ext{ L}$$

Question 4

Which postulate of the kinetic molecular theory explains why the pressure of a gas increases with temperature?

Accepted Answer

The average kinetic energy of gas particles is directly proportional to the temperature in kelvins.

Question 5

A 2.00 L flask contains a mixture of O$$_2$$ and N$$_2 at a $$total pressure of 1.50 atm. If the mole fraction of O$$_2 is 0.40$$, what is the partial pressure of O$$_2$$?

Accepted Answer

$$P_{O_2$} = X_{O_2$} 	imes P_{	ext{total}} = 0.40 	imes 1.50 	ext{ atm} = 0.60 	ext{ atm}$$

Question 6

Which of the following statements about real gases is correct?

Accepted Answer

At high pressures, the molar volume of a real gas is larger than predicted by the ideal gas law.

Question 7

A sample of hydrogen gas is collected over water at 25$$^\circC $$and a total pressure of 755 mmHg. If the vapor pressure of water at this temperature is 24 mmHg, what is the partial pressure of the hydrogen gas?

Accepted Answer

$$P_{H_2$} = 755 	ext{ mmHg} - 24 	ext{ mmHg} = 731 	ext{ mmHg}$$

Question 8

Which of the following best describes Graham’s Law of Effusion?

Accepted Answer

$$\frac{	ext{Rate}_1}{	ext{Rate}_2} = \sqrt{\frac{M_2$}{M_1$}}$$

Question 9

A 5.00 g sample of an unknown gas occupies 2.50 L at 1.00 atm and 300 K. What is the molar mass of the gas?

Accepted Answer

$$M = \frac{mRT}{PV} = \frac{5.00 	imes 0.08206 	imes 300}{1.00 	imes 2.50} = 49.2 	ext{ g/mol}$$

Question 10

Which of the following is NOT an assumption of the kinetic molecular theory for ideal gases?

Accepted Answer

Gas molecules are attracted to each other.

Question 11

A 1.00 mol sample of methane gas and a 1.00 mol sample of xenon gas are each placed in identical 22.4 L containers at STP. Which statement is true?

Accepted Answer

Both gases exert the same pressure and occupy the same volume.

Question 12

If the temperature of a gas is doubled at constant pressure, what happens to its volume?

Accepted Answer

The volume doubles.

Question 13

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

Accepted Answer

Hydrogen, H$$_2$$

Question 14

A 1.00 L flask contains 0.040 mol of CO$$_2 at 300 K. $$What is the pressure in the flask?

Accepted Answer

$$P = \frac{nRT}{V} = \frac{0.040 	imes 0.08206 	imes 300}{1.00} = 0.984 	ext{ atm}$$

Question 15

Which of the following changes will increase the mean free path of gas molecules in a container?

Accepted Answer

Decreasing the pressure.

Question 16

A mixture contains 2.0 mol N$$_2$$ and 3.0 mol O$$_2. $$What is the mole fraction of O$$_2$$?

Accepted Answer

$$X_{O_2$} = \frac{3.0}{2.0 + 3.0} = 0.60$$

Question 17

Which of the following best describes the effect of intermolecular attractions on the pressure of a real gas compared to an ideal gas at low temperature?

Accepted Answer

The pressure of the real gas is lower than that predicted by the ideal gas law.

Question 18

A 1.00 L sample of gas at 1.00 atm and 273 K is compressed to 0.500 L at constant temperature. What is the final pressure?

Accepted Answer

$$P_2$$ = $$P_1$$ \frac{$$V_1$$}{$$V_2$$} = 1.00 	ext{ atm} 	imes \frac{1.00}{0.500} = 2.00 	ext{ atm}$$

Question 19

Which of the following is a correct rearrangement of the ideal gas law to solve for density ($$d$$)?

Accepted Answer

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

Chapter 6: Gases – Properties, Laws, and Kinetic Molecular Theory

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