Q: A hospital uses a cylinder containing 10.0 mol of O$$_2 at 5.00 $$atm. If 2.0 mol of O$$_2 is $$used, what is the new pressure in the cylinder (volume and temperature constant)?

$$P_2$$ = $$P_1$$ \frac{$$n_2$$}{$$n_1$$} = 5.00 \times \frac{8.0}{10.0} = 4.00\ \mathrm{atm}$$

Question 1

A scuba diver's tank contains 8.0 L of air at 200 atm and 300 K. If the diver releases air into the ocean where the pressure is 1.0 atm and the temperature is 300 K, what volume would the released air occupy (assume ideal behavior)?

Accepted Answer

$$V_2$$ = \frac{$$P_1$$ $$V_1$$}{$$P_2$$} = \frac{(200)(8.0)}{1.0} = 1600\ \mathrm{L}$$

Question 2

A weather balloon is filled with 5.0 mol of helium at 1.00 atm and 273 K. If the balloon rises to a region where the pressure is 0.50 atm and the temperature is 223 K, what is the new volume of the balloon?

Accepted Answer

$$V_2$$ = \frac{$$P_1$$ $$V_1$$ $$T_2$$}{$$T_1$$ $$P_2$$}$$;\ V_1$ = \frac{$$nRT_1$$}{P_1$} = \frac{(5.0)(0.08206)(273)}{1.00} = 112\ \mathrm{L}$$;\ $$V_2$$ = \frac{(1.00)(112)(223)}{(273)(0.50)} = 183\ \mathrm{L}$$

Question 3

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

Accepted Answer

At high pressures, the volume of gas particles and intermolecular attractions become significant, violating the assumptions of the kinetic molecular theory.

Question 4

A mixture contains 4.0 mol of N$$_2$$ and 6.0 mol of O$$_2 in a 10.0 L $$container at 300 K. What is the partial pressure of O$$_2 if $$the total pressure is 5.0 atm?

Accepted Answer

$$X_{O_2$} = \frac{6.0}{10.0} = 0.60;\ P_{O_2$} = (0.60)(5.0) = 3.0\ \mathrm{atm}$$

Question 5

Which gas will have the highest root-mean-square speed ($$u_{rms}) at 298 K$$: Ne, Ar, Kr, or He?

Accepted Answer

He, because it has the lowest molar mass.

Question 6

A sample of gas at 2.00 atm and 300 K occupies 5.00 L. If the pressure is doubled and the temperature is increased to 600 K, what is the new volume?

Accepted Answer

$$V_2$$ = $$V_1$$ \frac{$$P_1$$}{$$P_2$$} \frac{$$T_2$$}{$$T_1$$} = 5.00 	imes \frac{2.00}{4.00} 	imes \frac{600}{300} = 5.00\ \mathrm{L}$$

Question 7

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

Accepted Answer

The average kinetic energy increases because it depends only on temperature.

Question 8

A 2.0 L flask contains 0.10 mol of CO$$_2 at 300 K. $$What is the pressure inside the flask? (Use $$R = 0.08206\ \mathrm{L\cdot atm/(mol\cdot K)})$$

Accepted Answer

$$P = \frac{nRT}{V} = \frac{(0.10)(0.08206)(300)}{2.0} = 1.23\ \mathrm{atm}$$

Question 9

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

Accepted Answer

Gas particles lose energy during collisions.

Question 10

A hospital uses a cylinder containing 10.0 mol of O$$_2 at 5.00 $$atm. If 2.0 mol of O$$_2 is $$used, what is the new pressure in the cylinder (volume and temperature constant)?

Accepted Answer

$$P_2$$ = $$P_1$$ \frac{$$n_2$$}{$$n_1$$} = 5.00 	imes \frac{8.0}{10.0} = 4.00\ \mathrm{atm}$$

Question 11

Which of the following gases will diffuse fastest through a room at 298 K: NH$$_3$$, CO$$_2$$, O$$_2$$, or SO$$_2$$?

Accepted Answer

NH$$_3$$, because it has the lowest molar mass.

Question 12

A gas sample is collected over water at 25$$^\circC. $$The total pressure is 760 torr, and the vapor pressure of water at this temperature is 24 torr. What is the partial pressure of the dry gas?

Accepted Answer

$$P_{	ext{gas}} = P_{	ext{total}} - P_{	ext{water}} = 760 - 24 = 736\ \mathrm{torr}$$

Question 13

Which of the following best explains why the van der Waals equation is needed for real gases at low temperatures?

Accepted Answer

At low temperatures, intermolecular attractions become significant, causing deviations from ideal behavior.

Question 14

A 1.00 L container holds 0.500 mol of a gas at 400 K. What is the pressure in atm? (Use $$R = 0.08206\ \mathrm{L\cdot atm/(mol\cdot K)})$$

Accepted Answer

$$P = \frac{nRT}{V} = \frac{(0.500)(0.08206)(400)}{1.00} = 16.4\ \mathrm{atm}$$

Question 15

If 1.0 L of H$$_2$$ effuses through a porous membrane in 1.0 minute, how long will it take for the same volume of O$$_2 to $$effuse under identical conditions? (Molar masses: H$$_2 = 2 g/$$mol, O$$_2 = 32 g/$$mol)

Accepted Answer

$$	ext{Time}_{O_2$} = 	ext{Time}_{H_2$} 	imes \sqrt{\frac{M_{O_2$}}{M_{H_2$}}} = 1.0 	imes \sqrt{\frac{32}{2}} = 1.0 	imes 4 = 4.0\ 	ext{min}$$

Question 16

Which of the following is the correct expression for the root-mean-square speed ($$u_{rms}) of a $$gas molecule?

Accepted Answer

$$u_{rms} = \sqrt{\frac{3RT}{M}}$$

Question 17

A 5.0 L container holds a mixture of 2.0 mol He and 3.0 mol Ne at 400 K. What is the mole fraction of Ne?

Accepted Answer

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

Question 18

Which of the following is a direct consequence of the assumption that gas particles have negligible volume?

Accepted Answer

The volume of the gas is equal to the volume of the container.

Question 19

A sample of gas is compressed from 4.0 L to 2.0 L at constant temperature. If the initial pressure was 1.5 atm, what is the final pressure?

Accepted Answer

$$P_2$$ = \frac{$$P_1$$ $$V_1$$}{$$V_2$$} = \frac{(1.5)(4.0)}{2.0} = 3.0\ \mathrm{atm}$$

Chapter 10: Gases – Laws, Properties, and Real Gas Behavior

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