Q: Which of the following correctly expresses the ideal gas law and identifies the value and units of the gas constant R?

$$PV = nRT$$; \quad R = 0.08206\ \text{L} \cdot \text{atm} / (\text{mol} \cdot \text{K})$

Q: A 1.55 g sample of CO$$_2 is $$collected in a 750 mL flask at 27$$^\circC. $$What is the pressure of the gas in the flask? (Molar mass of CO$$_2 = 44.01 g/$$mol)

$$n = \frac{1.55}{44.01} = 0.0352\ \text{mol}$$; \newline P = \frac{nRT}{V} = \frac{0.0352 \times 0.08206 \times 300}{0.750} = 1.15\ \text{atm}$

Q: A mixture of O$$_2$$ and He is allowed to effuse through a pinhole. If the rate of effusion of He is 2.8 times faster than O$$_2$$, what is the molar mass of O$$_2$$ used in the calculation?

$$\frac{\text{Rate}_{\text{He}}}{\text{Rate}_{\text{O}_2}} = \sqrt{\frac{M$$_{\text{O}$$_2}}{M_{\text{He}}}}$$; \newline $$M_{\text{O}_2$$} = 32.0\ \text{g/mol}$

Q: A 0.10 mol sample of a gas occupies 2.50 L at 300 K. What is the pressure of the gas in atm?

$$P = \frac{nRT}{V} = \frac{0.10 \times 0.08206 \times 300}{2.50} = 0.984\ \text{atm}$$

Q: A gas sample has a density of 1.40 g/L at 329 K and 1.17 atm. What is the molar mass of the gas?

$$M = \frac{dRT}{P} = \frac{1.40 \times 0.08206 \times 329}{1.17} = 32.2\ \text{g/mol}$$

Q: If 3.00 mol of CO$$_2 is $$produced at 1.00 atm and 25$$^\circC$$, what volume will it occupy?

$$V = \frac{nRT}{P} = \frac{3.00 \times 0.08206 \times 298}{1.00} = 73.3\ \text{L}$$

Question 1

A sample of CO$$_2$$ gas occupies 2.50 L at 25$$^\circC $$and 1.00 atm. What will be the volume of the gas at 50$$^\circC $$and 2.00 atm, assuming the amount of gas remains constant?

Accepted Answer

$$V_2$$ = \frac{$$P_1$$ $$V_1$$ $$T_2$$}{$$T_1$$ $$P_2$$}$$; 
ewline V_2$ = \frac{(1.00)(2.50)(323)}{(298)(2.00)} = 1.36\ 	ext{L}$

Question 2

Which of the following correctly expresses the ideal gas law and identifies the value and units of the gas constant R?

Accepted Answer

$$PV = nRT$$; \quad R = 0.08206\ 	ext{L} \cdot 	ext{atm} / (	ext{mol} \cdot 	ext{K})$

Question 3

A 1.55 g sample of CO$$_2 is $$collected in a 750 mL flask at 27$$^\circC. $$What is the pressure of the gas in the flask? (Molar mass of CO$$_2 = 44.01 g/$$mol)

Accepted Answer

$$n = \frac{1.55}{44.01} = 0.0352\ 	ext{mol}$$; 
ewline P = \frac{nRT}{V} = \frac{0.0352 	imes 0.08206 	imes 300}{0.750} = 1.15\ 	ext{atm}$

Question 4

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

Accepted Answer

The rate of effusion of a gas is inversely proportional to the square root of its molar mass: $$\frac{	ext{Rate}_1}{	ext{Rate}_2} = \sqrt{\frac{M_2$}{M_1$}}$$

Question 5

A mixture of O$$_2$$ and He is allowed to effuse through a pinhole. If the rate of effusion of He is 2.8 times faster than O$$_2$$, what is the molar mass of O$$_2$$ used in the calculation?

Accepted Answer

$$\frac{	ext{Rate}_{	ext{He}}}{	ext{Rate}_{	ext{O}_2}} = \sqrt{\frac{M$$_{	ext{O}$$_2}}{M_{	ext{He}}}}$$; 
ewline $$M_{	ext{O}_2$$} = 32.0\ 	ext{g/mol}$

Question 6

A 0.10 mol sample of a gas occupies 2.50 L at 300 K. What is the pressure of the gas in atm?

Accepted Answer

$$P = \frac{nRT}{V} = \frac{0.10 	imes 0.08206 	imes 300}{2.50} = 0.984\ 	ext{atm}$$

Question 7

Which of the following scenarios best illustrates the real-world application of Dalton's Law of Partial Pressures?

Accepted Answer

Calculating the total pressure in a scuba tank containing a mixture of O$$_2$$ and N$$_2$$ gases: $$P_{	ext{total}} = P$$_{	ext{O}$$_2} + P$$_{	ext{N}$$_2}$$

Question 8

A gas sample has a density of 1.40 g/L at 329 K and 1.17 atm. What is the molar mass of the gas?

Accepted Answer

$$M = \frac{dRT}{P} = \frac{1.40 	imes 0.08206 	imes 329}{1.17} = 32.2\ 	ext{g/mol}$$

Question 9

If 3.00 mol of CO$$_2 is $$produced at 1.00 atm and 25$$^\circC$$, what volume will it occupy?

Accepted Answer

$$V = \frac{nRT}{P} = \frac{3.00 	imes 0.08206 	imes 298}{1.00} = 73.3\ 	ext{L}$$

Question 10

Which of the following statements about diffusion and effusion is correct?

Accepted Answer

Effusion is the process by which gas molecules escape through a tiny hole into a vacuum, while diffusion is the mixing of gases due to random motion.

Question 11

A 5.00 L container holds 0.250 mol of an ideal gas at 27$$^\circC. $$What is the pressure inside the container?

Accepted Answer

$$P = \frac{nRT}{V} = \frac{0.250 	imes 0.08206 	imes 300}{5.00} = 1.23\ 	ext{atm}$$

Question 12

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

Accepted Answer

Helium is less dense than air, so the buoyant force pushes the balloon upward.

Question 13

A gas sample is collected over water at 25$$^\circC $$and 1.00 atm. The vapor pressure of water at 25$$^\circC is 0.0313 $$atm. What is the partial pressure of the dry gas?

Accepted Answer

$$P_{	ext{gas}} = P_{	ext{total}} - P$$_{	ext{H}$$_2	ext{O}} = 1.00 - 0.0313 = 0.969\ 	ext{atm}$$

Question 14

Which of the following is a correct application of the combined gas law?

Accepted Answer

$$\frac{P_1$ V_1$}{T_1$} = \frac{P_2$ V_2$}{T_2$}$$

Question 15

A 1.00 L flask contains 0.10 mol of a gas at 27$$^\circC. $$What is the pressure in the flask?

Accepted Answer

$$P = \frac{nRT}{V} = \frac{0.10 	imes 0.08206 	imes 300}{1.00} = 2.46\ 	ext{atm}$$

Question 16

Which of the following best describes Avogadro's Law?

Accepted Answer

At constant temperature and pressure, the volume of a gas is directly proportional to the number of moles: $$V \propto n$$

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