Q: A scuba diver’s tank contains a mixture of oxygen and nitrogen. If the partial pressure of oxygen is 2.0 atm and the partial pressure of nitrogen is 4.0 atm, what is the total pressure in the tank?

$$P_{\text{total}} = P$$_{\text{O}$$_2} + P$$_{\text{N}$$_2} = 2.0\ \text{atm} + 4.0\ \text{atm} = 6.0\ \text{atm}$$

Q: A sample of oxygen gas has a volume of 12.0 L at 600 mmHg. What is the new pressure if the volume is changed to 36.0 L at constant temperature and amount?

$$P_2$$ = \frac{$$P_1$$ $$V_1$$}{$$V_2$$} = \frac{600\ \text{mmHg} \times 12.0\ \text{L}}{36.0\ \text{L}} = 200\ \text{mmHg}$$

Q: A balloon has a volume of 785 mL at 21°C. If the temperature drops to 0.0°C at constant pressure and moles, what is the new volume of the balloon?

$$V_2$$ = $$V_1$$ \frac{$$T_2$$}{$$T_1$$} = 785\ \text{mL} \times \frac{273\ \text{K}}{294\ \text{K}} = 729\ \text{mL}$$

Q: At STP, what is the volume occupied by 4.00 g of methane ($$\text{CH}_4$$)? (Molar mass of $$\text{CH}_4 = 16.0\ \text{g/mol})$$

$$n = \frac{4.00\ \text{g}}{16.0\ \text{g/mol}} = 0.25\ \text{mol}$$; $$V = n \times 22.4\ \text{L} = 0.25 \times 22.4 = 5.60\ \text{L}$$

Q: A mixture of gases contains 80% nitrogen and 20% oxygen by mole. If the total pressure is 1.00 atm, what is the partial pressure of oxygen?

$$P_{\text{O}_2$$} = 0.20 \times 1.00\ \text{atm} = 0.20\ \text{atm}$$

Question 1

A weather balloon is filled with 5.00 L of helium gas at 1.00 atm and 25°C. If the balloon rises to an altitude where the pressure is 0.500 atm and the temperature is -25°C, what will be the new volume of the balloon? (Assume the amount of gas remains constant.)

Accepted Answer

$$V_2$$ = \frac{$$P_1$$ $$V_1$$ $$T_2$$}{$$T_1$$ $$P_2$$} = \frac{(1.00\ 	ext{atm})(5.00\ 	ext{L})(248\ 	ext{K})}{(298\ 	ext{K})(0.500\ 	ext{atm})} = 8.33\ 	ext{L}$$

Question 2

Which of the following statements best describes Boyle’s Law?

Accepted Answer

At constant temperature and amount, the pressure of a gas is inversely proportional to its volume.

Question 3

A 2.00 L container holds 1.00 mole of an ideal gas at 273 K. What is the pressure inside the container? (Use $$R = 0.0821\ 	ext{L} \cdot 	ext{atm} / 	ext{mol} \cdot 	ext{K})$$

Accepted Answer

$$P = \frac{nRT}{V} = \frac{(1.00)(0.0821)(273)}{2.00} = 1.12\ 	ext{atm}$$

Question 4

A scuba diver’s tank contains a mixture of oxygen and nitrogen. If the partial pressure of oxygen is 2.0 atm and the partial pressure of nitrogen is 4.0 atm, what is the total pressure in the tank?

Accepted Answer

$$P_{	ext{total}} = P$$_{	ext{O}$$_2} + P$$_{	ext{N}$$_2} = 2.0\ 	ext{atm} + 4.0\ 	ext{atm} = 6.0\ 	ext{atm}$$

Question 5

A sample of oxygen gas has a volume of 12.0 L at 600 mmHg. What is the new pressure if the volume is changed to 36.0 L at constant temperature and amount?

Accepted Answer

$$P_2$$ = \frac{$$P_1$$ $$V_1$$}{$$V_2$$} = \frac{600\ 	ext{mmHg} 	imes 12.0\ 	ext{L}}{36.0\ 	ext{L}} = 200\ 	ext{mmHg}$$

Question 6

A balloon has a volume of 785 mL at 21°C. If the temperature drops to 0.0°C at constant pressure and moles, what is the new volume of the balloon?

Accepted Answer

$$V_2$$ = $$V_1$$ \frac{$$T_2$$}{$$T_1$$} = 785\ 	ext{mL} 	imes \frac{273\ 	ext{K}}{294\ 	ext{K}} = 729\ 	ext{mL}$$

Question 7

At STP, what is the volume occupied by 4.00 g of methane ($$	ext{CH}_4$$)? (Molar mass of $$	ext{CH}_4 = 16.0\ 	ext{g/mol})$$

Accepted Answer

$$n = \frac{4.00\ 	ext{g}}{16.0\ 	ext{g/mol}} = 0.25\ 	ext{mol}$$; $$V = n 	imes 22.4\ 	ext{L} = 0.25 	imes 22.4 = 5.60\ 	ext{L}$$

Question 8

Which of the following best explains why a barometer uses mercury rather than water to measure atmospheric pressure?

Accepted Answer

Mercury is much denser than water, so the height of the mercury column is manageable for measuring atmospheric pressure.

Question 9

A mixture of gases contains 80% nitrogen and 20% oxygen by mole. If the total pressure is 1.00 atm, what is the partial pressure of oxygen?

Accepted Answer

$$P_{	ext{O}_2$$} = 0.20 	imes 1.00\ 	ext{atm} = 0.20\ 	ext{atm}$$

Question 10

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

Accepted Answer

Gas particles are attracted to each other by strong forces.

Question 11

A 1.00 L flask contains 1.00 mole of gas at 25°C. If the temperature is increased to 50°C at constant volume, what happens to the pressure?

Accepted Answer

The pressure increases because $$P \propto T at $$constant $$V$$ and $$n.$$

Question 12

Which of the following correctly expresses Avogadro’s Law?

Accepted Answer

$$\frac{V_1$}{n_1$} = \frac{V_2$}{n_2$}$$

Question 13

A 3.00 L container holds 0.500 mol of gas at 27°C. What is the pressure inside the container? (Use $$R = 0.0821\ 	ext{L} \cdot 	ext{atm} / 	ext{mol} \cdot 	ext{K})$$

Accepted Answer

Question 14

A gas sample is transferred from a 2.0 L container at 1.5 atm to a 6.0 L container at constant temperature. What is the final pressure?

Accepted Answer

$$P_2$$ = \frac{$$P_1$$ $$V_1$$}{$$V_2$$} = \frac{1.5 	imes 2.0}{6.0} = 0.50\ 	ext{atm}$$

Question 15

Which of the following is a correct statement about the relationship between temperature and volume for a gas at constant pressure and amount?

Accepted Answer

Volume and temperature (in Kelvin) are directly proportional.

Question 16

A 10.0 L tank contains 2.00 moles of nitrogen gas at 27°C. What is the pressure in the tank? (Use $$R = 0.0821\ 	ext{L} \cdot 	ext{atm} / 	ext{mol} \cdot 	ext{K})$$

Accepted Answer

$$P = \frac{nRT}{V} = \frac{(2.00)(0.0821)(300)}{10.0} = 4.93\ 	ext{atm}$$

Question 17

If the temperature of a fixed amount of gas is doubled (in Kelvin) at constant pressure, what happens to the volume?

Accepted Answer

The volume doubles.

Question 18

Which of the following is the correct value for the gas constant $$R in $$the ideal gas law when using units of L, atm, mol, and K?

Accepted Answer

$$R = 0.0821\ 	ext{L} \cdot 	ext{atm} / 	ext{mol} \cdot 	ext{K}$$

Chapter 8: Gases – Properties, Laws, and Applications

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