Q: A sample of oxygen gas occupies 2.50 L at 1.00 atm and 25°C. If the pressure is increased to 2.00 atm at constant temperature, what will be the new volume of the gas? (Assume ideal behavior.)

$$V_2$$ = \frac{$$P_1$$ $$V_1$$}{$$P_2$$} = \frac{1.00 \times 2.50}{2.00} = 1.25\ \text{L}$$

Q: A 4.00 g sample of helium gas is placed in a 10.0 L container at 27°C. What is the pressure exerted by the gas? (Use $$R = 0.0821\ \text{L}\cdot\text{atm}/\text{mol}\cdot\text{K})$$

$$P = \frac{nRT}{V} = \frac{1.00 \times 0.0821 \times 300}{10.0} = 2.46\ \text{atm}$$

Q: A gas sample at STP has a density of 1.25 g/L. What is the molar mass of the gas? (STP: $$P = 1.00\ \text{atm}$$, $$T = 273\ \text{K}$$, $$R = 0.0821\ \text{L}\cdot\text{atm}/\text{mol}\cdot\text{K})$$

$$M = \text{density} \times \frac{RT}{P} = 1.25 \times \frac{0.0821 \times 273}{1.00} = 28.0\ \text{g/mol}$$

Q: A 3.0 L container holds a mixture of hydrogen and argon gases at a total pressure of 2.0 atm. If the partial pressure of hydrogen is 1.2 atm, what is the partial pressure of argon?

$$P_{Ar} = P_{total} - P_{H_2$} = 2.0 - 1.2 = 0.8\ \text{atm}$$

Q: A 5.0 g sample of methane ($$CH_4) is $$combusted in excess oxygen. What volume of $$CO_2$$ gas is produced at STP? ($$CH_4 + 2O_2$$ \rightarrow $$CO_2 + 2H_2O$; molar mass CH_4$ = 16.0\ \text{g/mol})$$

$$\text{Volume} = \frac{5.0}{16.0} \times 22.4 = 7.0\ \text{L}$$

Question 1

A sample of oxygen gas occupies 2.50 L at 1.00 atm and 25°C. If the pressure is increased to 2.00 atm at constant temperature, what will be the new volume of the gas? (Assume ideal behavior.)

Accepted Answer

$$V_2$$ = \frac{$$P_1$$ $$V_1$$}{$$P_2$$} = \frac{1.00 	imes 2.50}{2.00} = 1.25\ 	ext{L}$$

Question 2

Which statement best describes the kinetic molecular theory as it applies to ideal gases?

Accepted Answer

Gas particles are in constant, random motion and collisions are perfectly elastic.

Question 3

A 4.00 g sample of helium gas is placed in a 10.0 L container at 27°C. What is the pressure exerted by the gas? (Use $$R = 0.0821\ 	ext{L}\cdot	ext{atm}/	ext{mol}\cdot	ext{K})$$

Accepted Answer

$$P = \frac{nRT}{V} = \frac{1.00 	imes 0.0821 	imes 300}{10.0} = 2.46\ 	ext{atm}$$

Question 4

Which of the following correctly describes Avogadro’s law?

Accepted Answer

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

Question 5

A mixture contains 2.0 mol of nitrogen and 3.0 mol of oxygen in a 5.0 L container at 27°C. What is the mole fraction of oxygen in the mixture?

Accepted Answer

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

Question 6

A gas sample at STP has a density of 1.25 g/L. What is the molar mass of the gas? (STP: $$P = 1.00\ 	ext{atm}$$, $$T = 273\ 	ext{K}$$, $$R = 0.0821\ 	ext{L}\cdot	ext{atm}/	ext{mol}\cdot	ext{K})$$

Accepted Answer

$$M = 	ext{density} 	imes \frac{RT}{P} = 1.25 	imes \frac{0.0821 	imes 273}{1.00} = 28.0\ 	ext{g/mol}$$

Question 7

A 3.0 L container holds a mixture of hydrogen and argon gases at a total pressure of 2.0 atm. If the partial pressure of hydrogen is 1.2 atm, what is the partial pressure of argon?

Accepted Answer

$$P_{Ar} = P_{total} - P_{H_2$} = 2.0 - 1.2 = 0.8\ 	ext{atm}$$

Question 8

Which gas law explains why a balloon shrinks when placed in a freezer?

Accepted Answer

Charles’s law: $$V \propto T at $$constant pressure

Question 9

A 5.0 g sample of methane ($$CH_4) is $$combusted in excess oxygen. What volume of $$CO_2$$ gas is produced at STP? ($$CH_4 + 2O_2$$ ightarrow $$CO_2 + 2H_2O$; molar mass CH_4$ = 16.0\ 	ext{g/mol})$$

Accepted Answer

$$	ext{Volume} = \frac{5.0}{16.0} 	imes 22.4 = 7.0\ 	ext{L}$$

Question 10

According to the Maxwell distribution, which statement is true about molecular speeds in a gas at higher temperature?

Accepted Answer

The distribution broadens and the average molecular speed increases.

Question 11

A 2.0 L container contains 0.5 mol of $$N_2$$ and 0.5 mol of $$O_2 at 27$$°C. What is the total pressure in the container? ($$R = 0.0821\ 	ext{L}\cdot	ext{atm}/	ext{mol}\cdot	ext{K})$$

Accepted Answer

$$P = \frac{nRT}{V} = \frac{1.0 	imes 0.0821 	imes 300}{2.0} = 12.3\ 	ext{atm}$$

Question 12

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

Accepted Answer

Gas particles exert attractive forces on each other.

Question 13

A scuba tank contains 8.0 mol of air at 20°C in a 12.0 L tank. What is the pressure inside the tank? ($$R = 0.0821\ 	ext{L}\cdot	ext{atm}/	ext{mol}\cdot	ext{K})$$

Accepted Answer

$$P = \frac{nRT}{V} = \frac{8.0 	imes 0.0821 	imes 293}{12.0} = 16.0\ 	ext{atm}$$

Question 14

A gas occupies 3.0 L at 300 K and 1.0 atm. What will be its volume at 600 K and 1.0 atm?

Accepted Answer

$$V_2$$ = $$V_1$$ 	imes \frac{$$T_2$$}{$$T_1$$} = 3.0 	imes \frac{600}{300} = 6.0\ 	ext{L}$$

Question 15

A hospital uses a cylinder containing 10.0 L of oxygen at 25°C and 150 atm. How many moles of oxygen are in the cylinder? ($$R = 0.0821\ 	ext{L}\cdot	ext{atm}/	ext{mol}\cdot	ext{K})$$

Accepted Answer

$$n = \frac{PV}{RT} = \frac{150 	imes 10.0}{0.0821 	imes 298} = 61.3\ 	ext{mol}$$

Question 16

Which equation represents the combined gas law?

Accepted Answer

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

Question 17

A mixture of gases contains 0.2 mol $$CO_2$$, 0.3 mol $$O_2$$, and 0.5 mol $$N_2. If $$the total pressure is 1.0 atm, what is the partial pressure of $$O_2$$?

Accepted Answer

$$P_{O_2$} = X_{O_2$} 	imes P_{total} = \frac{0.3}{1.0} 	imes 1.0 = 0.3\ 	ext{atm}$$

Question 18

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

Accepted Answer

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

Chapter 10: Gases – Laws, Properties, and Kinetic Theory

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