Q: A weather balloon is filled with 5.00 mol of helium gas at 1.00 atm and 273 K. What is the volume of the balloon under these conditions? Use the ideal gas constant $$R = 0.0821\ \mathrm{L\cdot atm\cdot $$mol^{-1}$$\cdot K$$^{-1}$$}.$$

$$V = \frac{nRT}{P} = \frac{5.00 \times 0.0821 \times 273}{1.00} = 112\ \mathrm{L}$$

Q: A gas sample has a density of $$1.96\ \mathrm{g/L} at$$ $$2.00\ \mathrm{atm}$$ and $$273\ \mathrm{K}. $$What is its molar mass? Use $$R = 0.0821\ \mathrm{L\cdot atm\cdot $$mol^{-1}$$\cdot K$$^{-1}$$}.$$

$$M = \frac{dRT}{P} = \frac{1.96 \times 0.0821 \times 273}{2.00} = 21.9\ \mathrm{g/mol}$$

Q: A 2.00 L container holds a mixture of 1.00 mol He and 2.00 mol Ne at 300 K. What is the total pressure in the container? ($$R = 0.0821\ \mathrm{L\cdot atm\cdot $$mol^{-1}$$\cdot K$$^{-1}$$})$$

$$P = \frac{nRT}{V} = \frac{(1.00 + 2.00) \times 0.0821 \times 300}{2.00} = 36.9\ \mathrm{atm}$$

Question 1

A weather balloon is filled with 5.00 mol of helium gas at 1.00 atm and 273 K. What is the volume of the balloon under these conditions? Use the ideal gas constant $$R = 0.0821\ \mathrm{L\cdot atm\cdot $$mol^{-1}$$\cdot K$$^{-1}$$}.$$

Accepted Answer

$$V = \frac{nRT}{P} = \frac{5.00 	imes 0.0821 	imes 273}{1.00} = 112\ \mathrm{L}$$

Question 2

A scuba tank contains 12.0 L of air at a pressure of 200 atm. If the air is released into a balloon at 1.00 atm and 298 K, what volume will the air occupy? Assume temperature is constant and use Boyle’s Law.

Accepted Answer

$$P_1V_1 = P_2V_2 \Rightarrow V_2$ = \frac{P_1V_1}{P_2$} = \frac{200 	imes 12.0}{1.00} = 2400\ \mathrm{L}$$

Question 3

Which of the following best explains why gases are highly compressible compared to liquids and solids?

Accepted Answer

Gas molecules occupy a negligible fraction of the total volume, allowing them to be compressed easily.

Question 4

A sample of nitrogen gas occupies 10.0 L at 300 K. If the temperature is increased to 600 K at constant pressure, what will be the new volume?

Accepted Answer

$$\frac{V_1$}{T_1$} = \frac{V_2$}{T_2$} \Rightarrow V_2$ = V_1$ \frac{T_2$}{T_1$} = 10.0 	imes \frac{600}{300} = 20.0\ \mathrm{L}$$

Question 5

Which of the following statements about the kinetic-molecular theory is FALSE?

Accepted Answer

Gas molecules experience significant attractive and repulsive forces.

Question 6

A mixture contains 2.0 mol of O$$_2$$ and 3.0 mol of N$$_2 in a 10.0 L $$container at 298 K. What is the mole fraction of O$$_2$$?

Accepted Answer

$$\chi_{O_2$} = \frac{n_{O_2$}}{n_{total}} = \frac{2.0}{2.0 + 3.0} = 0.40$$

Question 7

Which gas will effuse fastest through a pinhole at the same temperature: H$$_2$$, O$$_2$$, N$$_2$$, or CO$$_2$$?

Accepted Answer

H$$_2$$, because it has the lowest molar mass.

Question 8

A gas sample has a density of $$1.96\ \mathrm{g/L} at$$ $$2.00\ \mathrm{atm}$$ and $$273\ \mathrm{K}. $$What is its molar mass? Use $$R = 0.0821\ \mathrm{L\cdot atm\cdot $$mol^{-1}$$\cdot K$$^{-1}$$}.$$

Accepted Answer

$$M = \frac{dRT}{P} = \frac{1.96 	imes 0.0821 	imes 273}{2.00} = 21.9\ \mathrm{g/mol}$$

Question 9

Which of the following best describes the main reason real gases deviate from ideal behavior at high pressures?

Accepted Answer

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

Question 10

A 2.00 L container holds a mixture of 1.00 mol He and 2.00 mol Ne at 300 K. What is the total pressure in the container? ($$R = 0.0821\ \mathrm{L\cdot atm\cdot $$mol^{-1}$$\cdot K$$^{-1}$$})$$

Accepted Answer

$$P = \frac{nRT}{V} = \frac{(1.00 + 2.00) 	imes 0.0821 	imes 300}{2.00} = 36.9\ \mathrm{atm}$$

Question 11

Which of the following is the correct van der Waals equation for real gases?

Accepted Answer

$$\left( P + \frac{n^2$a}{V^2$} \right) (V - nb) = nRT$$

Question 12

A gas mixture contains 4.0 mol of O$$_2$$ and 1.0 mol of CO$$_2. If $$the total pressure is 5.0 atm, what is the partial pressure of CO$$_2$$?

Accepted Answer

$$P_{CO_2$} = X_{CO_2$} P_{total} = \frac{1.0}{4.0 + 1.0} 	imes 5.0 = 1.0\ \mathrm{atm}$$

Question 13

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

Accepted Answer

Gas molecules lose energy during collisions.

Question 14

If the rate of effusion of H$$_2 is 4 $$times that of an unknown gas, what is the molar mass of the unknown gas? (Use Graham’s Law.)

Accepted Answer

$$\frac{r_{H_2$}}{r_{unknown}} = 4 = \sqrt{\frac{M_{unknown}}{M_{H_2$}}} \Rightarrow M_{unknown} = 16 	imes 2.0 = 32\ \mathrm{g/mol}$$

Question 15

A 10.0 g sample of an unknown gas occupies 5.00 L at 2.00 atm and 300 K. What is the molar mass of the gas?

Accepted Answer

$$M = \frac{mRT}{PV} = \frac{10.0 	imes 0.0821 	imes 300}{2.00 	imes 5.00} = 24.6\ \mathrm{g/mol}$$

Question 16

Which of the following best explains why the volume of a gas increases with temperature at constant pressure?

Accepted Answer

The average kinetic energy of the molecules increases, causing them to move faster and occupy more space.

Question 17

A reaction produces 2.00 mol of CO$$_2$$ gas at 1.00 atm and 273 K. What volume will the CO$$_2$$ occupy?

Accepted Answer

$$V = \frac{nRT}{P} = \frac{2.00 	imes 0.0821 	imes 273}{1.00} = 44.8\ \mathrm{L}$$

Chapter 10: Gases – Properties, Laws, and Theories

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