Q: Which of the following correctly describes the relationship between the rate of effusion of two gases, according to Graham's law?

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

Question 1

A sample of gas occupies 8.50 L at 1.00 atm and 25.0°C. If the pressure is increased to 2.50 atm and the temperature is raised to 75.0°C, what will be the new volume of the gas? (Assume ideal gas behavior.)

Accepted Answer

$$V_2$$ = \frac{$$P_1$$ $$V_1$$ $$T_2$$}{$$P_2$$ $$T_1$$} = \frac{(1.00\ \mathrm{atm})(8.50\ \mathrm{L})(348.15\ \mathrm{K})}{(2.50\ \mathrm{atm})(298.15\ \mathrm{K})} = 3.98\ \mathrm{L}$$

Question 2

Which of the following best explains why gases are compressible, according to the kinetic molecular theory?

Accepted Answer

Gas molecules are far apart relative to their size, so they can be pushed closer together.

Question 3

A 2.00 L flask contains a mixture of nitrogen and oxygen gases at 27°C and a total pressure of 1.50 atm. If the partial pressure of nitrogen is 1.20 atm, what is the mole fraction of oxygen in the mixture?

Accepted Answer

$$X_{O_2$} = \frac{0.30}{1.50} = 0.20$$

Question 4

A 5.00 g sample of CO$$_2 is $$collected in a 2.00 L container at 27°C. What is the pressure of the gas in the container? (R = 0.08206 L·atm/K·mol, molar mass CO$$_2 = 44.01 g/$$mol)

Accepted Answer

$$n = \frac{5.00\ \mathrm{g}}{44.01\ \mathrm{g/mol}} = 0.1136\ \mathrm{mol}$$
$$P = \frac{nRT}{V} = \frac{(0.1136)(0.08206)(300.15)}{2.00} = 1.40\ \mathrm{atm}$$

Question 5

A diver takes a breath at the surface, filling his lungs with 5.82 L of air at 1.00 atm. What volume will the air in his lungs occupy when he dives to a depth where the pressure is 1.92 atm? (Assume constant temperature.)

Accepted Answer

$$V_2$$ = \frac{$$P_1$$ $$V_1$$}{$$P_2$$} = \frac{(1.00\ \mathrm{atm})(5.82\ \mathrm{L})}{1.92\ \mathrm{atm}} = 3.03\ \mathrm{L}$$

Question 6

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

Accepted Answer

Gas molecules exert attractive and repulsive forces on each other.

Question 7

A 0.525 L sample of hydrogen gas is collected over water at 25°C and a total pressure of 0.967 atm. The vapor pressure of water at 25°C is 23.8 torr. What is the mass of hydrogen gas collected? (Molar mass H$$_2 = 2.016 g/$$mol)

Accepted Answer

First, $$P_{H_2$} = 0.967\ \mathrm{atm} - 0.0313\ \mathrm{atm} = 0.936\ \mathrm{atm}$$
$$n = \frac{(0.936)(0.525)}{(0.08206)(298.15)} = 0.0208\ \mathrm{mol}$$
$$	ext{mass} = 0.0208\ \mathrm{mol} 	imes 2.016\ \mathrm{g/mol} = 0.0405\ \mathrm{g}$$

Question 8

Which of the following correctly describes the relationship between the rate of effusion of two gases, according to Graham's law?

Accepted Answer

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

Question 9

A 10.0 L gas cylinder at 25°C contains 6.022 mol of N$$_2$$ and 0.007 mol of NO. If the total pressure is 14.8 atm, what is the partial pressure of NO?

Accepted Answer

$$X_{NO} = \frac{0.007}{6.022 + 0.007} = 0.00116$$
$$P_{NO} = X_{NO} 	imes P_{	ext{total}} = 0.00116 	imes 14.8 = 0.0172\ \mathrm{atm}$$

Question 10

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

Accepted Answer

It corrects for the volume occupied by gas molecules and the intermolecular attractions between them.

Question 11

A 50.0 g sample of sodium azide (NaN$$_3$$, molar mass = 65.02 g/mol) is used to inflate an airbag. If the decomposition occurs at 85.0°C and 1.00 atm, what volume of N$$_2$$ gas is produced? (R = 0.08206 L·atm/K·mol)

Accepted Answer

Moles NaN$$_3$$ = $$\frac{50.0}{65.02} = 0.769\ \mathrm{mol}$$
$$2\ \mathrm{NaN}_3 ightarrow 3\ \mathrm{N}_2$$
Moles N$$_2$$ = $$0.769 	imes \frac{3}{2} = 1.15\ \mathrm{mol}$$
$$V = \frac{nRT}{P} = \frac{(1.15)(0.08206)(358.15)}{1.00} = 33.8\ \mathrm{L}$$

Question 12

Which of the following best describes the effect of increasing temperature on the average kinetic energy of gas molecules?

Accepted Answer

The average kinetic energy increases proportionally with the absolute temperature.

Question 13

A 6.25-L helium balloon is released at 28.5°C and 757.2 mmHg. What will be the volume of the balloon when it rises to an altitude where the temperature is 28.5°C and the pressure is 366.4 mmHg? (Assume the amount of gas and temperature remain constant.)

Accepted Answer

$$V_2$$ = \frac{$$P_1$$ $$V_1$$}{$$P_2$$} = \frac{(757.2\ \mathrm{mmHg})(6.25\ \mathrm{L})}{366.4\ \mathrm{mmHg}} = 12.9\ \mathrm{L}$$

Question 14

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

Accepted Answer

Gas molecules are attracted to each other by strong forces.

Question 15

Which of the following gases will have the highest root-mean-square (rms) speed at 298 K?

Accepted Answer

Helium ($$M = 4.00\ \mathrm{g/mol})$$

Question 16

Which of the following conditions would cause a real gas to deviate most from ideal behavior?

Accepted Answer

High pressure and low temperature

Question 17

A 1.00 L sample of O$$_2$$ gas at 25°C and 1.00 atm is compressed to 0.500 L and cooled to 0°C. What is the final pressure?

Accepted Answer

$$P_2$$ = \frac{$$P_1$$ $$V_1$$ $$T_2$$}{$$T_1$$ $$V_2$$} = \frac{(1.00)(1.00)(273.15)}{(298.15)(0.500)} = 1.83\ \mathrm{atm}$$

General Chemistry: Chapter 10 – Gases (Study Notes)

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