Q: A 5.00 L container holds a mixture of 2.00 mol of nitrogen gas and 3.00 mol of oxygen gas at 300 K. What is the partial pressure of oxygen gas in the mixture?

$$P_{O_2$} = X_{O_2$} P_{\text{total}}$$;\nFirst, $$n_{\text{total}} = 2.00 + 3.00 = 5.00$$ mol.\n$$X_{O_2$} = 3.00/5.00 = 0.60$$\n$$P_{\text{total}} = nRT/V = (5.00)(0.0821)(300)/5.00 = 24.63$$ atm\n$$P_{O_2$} = 0.60 \times 24.63 = 14.78$$ atm$

Q: A sample of hydrogen gas is collected over water at 25$$^\circC. $$The total pressure in the collection flask is 755 mmHg. If the vapor pressure of water at 25$$^\circC is 23.8 $$mmHg, what is the partial pressure of hydrogen gas?

$$P_{H_2$} = 755\ \text{mmHg} - 23.8\ \text{mmHg} = 731.2\ \text{mmHg}$$

Question 1

A 5.00 L container holds a mixture of 2.00 mol of nitrogen gas and 3.00 mol of oxygen gas at 300 K. What is the partial pressure of oxygen gas in the mixture?

Accepted Answer

$$P_{O_2$} = X_{O_2$} P_{	ext{total}}$$;
First, $$n_{	ext{total}} = 2.00 + 3.00 = 5.00$$ mol.
$$X_{O_2$} = 3.00/5.00 = 0.60$$
$$P_{	ext{total}} = nRT/V = (5.00)(0.0821)(300)/5.00 = 24.63$$ atm
$$P_{O_2$} = 0.60 	imes 24.63 = 14.78$$ atm$

Question 2

A sample of hydrogen gas is collected over water at 25$$^\circC. $$The total pressure in the collection flask is 755 mmHg. If the vapor pressure of water at 25$$^\circC is 23.8 $$mmHg, what is the partial pressure of hydrogen gas?

Accepted Answer

$$P_{H_2$} = 755\ 	ext{mmHg} - 23.8\ 	ext{mmHg} = 731.2\ 	ext{mmHg}$$

Question 3

A mixture contains 0.50 mol He, 0.30 mol Ne, and 0.20 mol Ar in a 10.0 L container at 298 K. What is the mole fraction of Ne in the mixture?

Accepted Answer

$$X_{Ne} = \frac{0.30}{0.50 + 0.30 + 0.20} = \frac{0.30}{1.00} = 0.30$$

Question 4

A 12.5-L scuba tank contains 24.2 g of He and 4.32 g of O$$_2 at 298 K. $$What is the total pressure in the tank?

Accepted Answer

$$n_{He} = 24.2/4.003 = 6.05$$ mol; $$n_{O_2$} = 4.32/32.00 = 0.135$$ mol; $$n_{total} = 6.18$$ mol
$$P_{total} = \frac{nRT}{V} = \frac{6.18 	imes 0.0821 	imes 298}{12.5} = 12.1$$ atm

Question 5

A gas mixture contains 2.0 mol of N$$_2$$ and 3.0 mol of O$$_2. If $$the total pressure is 5.0 atm, what is the partial pressure of N$$_2$$?

Accepted Answer

$$X_{N_2$} = \frac{2.0}{2.0 + 3.0} = 0.4$$; $$P_{N_2$} = 0.4 	imes 5.0 = 2.0$$ atm

Question 6

A sample of an unknown gas effuses at a rate that is 0.462 times that of nitrogen gas (N$$_2). $$What is the molar mass of the unknown gas?

Accepted Answer

$$M_{unk} = \frac{M_{N_2$}}{(r_{unk}/r_{N_2$})^2$} = \frac{28.01}{(0.462)^2$} = 131 g/$$mol

Question 7

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

Accepted Answer

Gas molecules exert attractive and repulsive forces on each other.

Question 8

According to Graham’s law, how many times faster does hydrogen gas (H$$_2) $$diffuse compared to krypton gas (Kr)? (M$$_{H_2$} = 2.016 g/$$mol, M$$_{Kr} = 83.80 g/$$mol)

Accepted Answer

$$\frac{r_{H_2$}}{r_{Kr}} = \sqrt{\frac{M_{Kr}}{M_{H_2$}}} = \sqrt{\frac{83.80}{2.016}} = 6.45$$

Question 9

Which of the following best explains why a helium-filled balloon deflates faster than an air-filled balloon?

Accepted Answer

Helium atoms have a lower molar mass and therefore effuse through the balloon faster than the larger molecules in air.

Question 10

Which of the following is a direct consequence of the kinetic-molecular theory?

Accepted Answer

The pressure of a gas is caused by collisions of molecules with the walls of the container.

Question 11

Calculate the root-mean-square speed ($$u_{rms}) of $$oxygen molecules at 25$$^\circC. (M$_{O_2$} = 32.00 g/$$mol, R = 8.314 J/mol·K)

Accepted Answer

$$u_{rms} = \sqrt{\frac{3RT}{M}} = \sqrt{\frac{3 	imes 8.314 	imes 298}{0.032}} = 482 m/s$$

Question 12

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

Accepted Answer

High pressure and low temperature

Question 13

A 1.00 L flask contains a mixture of He, Ne, and Ar at 298 K. If the partial pressures are 341 mmHg (He) and 112 mmHg (Ne), what is the partial pressure of Ar if the total pressure is 663 mmHg?

Accepted Answer

$$P_{Ar} = 663 - 341 - 112 = 210$$ mmHg

Question 14

Which of the following best describes the relationship between temperature and the average kinetic energy of a gas?

Accepted Answer

The average kinetic energy is directly proportional to the absolute temperature (in K).

Question 15

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

Accepted Answer

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

Question 16

A real gas at high pressure is found to exert a lower pressure than predicted by the ideal gas law. Which factor best explains this observation?

Accepted Answer

Attractive intermolecular forces become significant at high pressures.

Question 17

Which of the following best explains why the sum of the mole fractions of all gases in a mixture equals 1?

Accepted Answer

The total number of moles is the sum of the moles of each component, so $$X_A + X_B + X_C + ... = 1$$

Question 18

Which of the following is a correct application of Dalton’s law of partial pressures?

Accepted Answer

The total pressure of a gas mixture is the sum of the partial pressures of each component gas.

chapter 9 lec 2

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