Q: A sample of nitrogen gas (N$$_2) is $$collected at 25$$^\circC $$and 1.00 atm in a 2.50 L container. How many moles of N$$_2$$ are present in the container? (Use $$R = 0.08206 L$$·atm·mol$$^{-1}$$·K$$^{-1})$$

$$n = \dfrac{PV}{RT} = \dfrac{1.00 \times 2.50}{0.08206 \times 298} = 0.102$$ mol

Q: A mixture of gases contains 0.75 mol O$$_2$$, 0.22 mol CO$$_2$$, and 0.15 mol Cl$$_2. If $$the total pressure of the mixture is 1.0 atm, what is the partial pressure of CO$$_2$$?

$$P_{CO_2$} = X_{CO_2$} \times P_{total} = \dfrac{0.22}{0.75+0.22+0.15} \times 1.0 = 0.18$$ atm

Q: A 0.300 g sample of a liquid was vaporized at 150.0$$^\circC. $$The vapor occupied a volume of 180.0 mL at 0.998 atm. What is the molar mass of the liquid? ($$R = 0.08206 L$$·atm·mol$$^{-1}$$·K$$^{-1})$$

$$n = \dfrac{PV}{RT} = \dfrac{0.998 \times 0.180}{0.08206 \times 423.15} = 0.0051$$ mol; $$M = \dfrac{0.300}{0.0051} = 58.8 g/$$mol

Q: A 2.00 L container is filled with gas at a pressure of 2.00 atm at 25$$^\circC. $$What pressure will develop within the sealed container if it is warmed to 75$$^\circC$$?

$$P_2$$ = $$P_1$$ \dfrac{$$T_2$$}{$$T_1$$} = 2.00 \times \dfrac{348}{298} = 2.34$$ atm

Question 1

A sample of nitrogen gas (N$$_2) is $$collected at 25$$^\circC $$and 1.00 atm in a 2.50 L container. How many moles of N$$_2$$ are present in the container? (Use $$R = 0.08206 L$$·atm·mol$$^{-1}$$·K$$^{-1})$$

Accepted Answer

$$n = \dfrac{PV}{RT} = \dfrac{1.00 	imes 2.50}{0.08206 	imes 298} = 0.102$$ mol

Question 2

A 1.00 L sample of gas is collected at 25$$^\circC $$and 1.25 atm. What is the pressure of the gas (in mm Hg) at 20$$^\circC if $$the volume is 1.40 L?

Accepted Answer

$$P_2$$ = \dfrac{$$P_1$$ $$V_1$$ $$T_2$$}{$$T_1$$ $$V_2$$} = \dfrac{1.25 	imes 1.00 	imes 293}{298 	imes 1.40} = 0.88$$ atm = 669$ mm Hg

Question 3

Which of the following statements best explains why gases are compressible?

Accepted Answer

Gas particles are far apart relative to their size, so the volume can decrease significantly under pressure.

Question 4

A mixture of gases contains 0.75 mol O$$_2$$, 0.22 mol CO$$_2$$, and 0.15 mol Cl$$_2. If $$the total pressure of the mixture is 1.0 atm, what is the partial pressure of CO$$_2$$?

Accepted Answer

$$P_{CO_2$} = X_{CO_2$} 	imes P_{total} = \dfrac{0.22}{0.75+0.22+0.15} 	imes 1.0 = 0.18$$ atm

Question 5

A 3.00 kg sample of CO$$_2$$ occupies a volume of 100.0 L at 266 torr. What is the temperature of the gas in $$^\circC$$? ($$R = 0.08206 L$$·atm·mol$$^{-1}$$·K$$^{-1}$$, $$M_{CO_2$} = 44.0 g/$$mol)

Accepted Answer

$$n = \dfrac{3000}{44.0} = 68.18$$ mol; $$P = \dfrac{266}{760} = 0.350$$ atm; $$T = \dfrac{PV}{nR} = \dfrac{0.350 	imes 100.0}{68.18 	imes 0.08206} = 62.3 K$$ $$= -210.9^\circC$$

Question 6

Which of the following best describes Dalton's Law of Partial Pressures?

Accepted Answer

The total pressure of a mixture of gases is equal to the sum of the partial pressures of each individual gas.

Question 7

A 0.300 g sample of a liquid was vaporized at 150.0$$^\circC. $$The vapor occupied a volume of 180.0 mL at 0.998 atm. What is the molar mass of the liquid? ($$R = 0.08206 L$$·atm·mol$$^{-1}$$·K$$^{-1})$$

Accepted Answer

$$n = \dfrac{PV}{RT} = \dfrac{0.998 	imes 0.180}{0.08206 	imes 423.15} = 0.0051$$ mol; $$M = \dfrac{0.300}{0.0051} = 58.8 g/$$mol

Question 8

According to Graham's law, which gas will effuse faster: hydrogen (H$$_2) or $$oxygen (O$$_2$$)?

Accepted Answer

Hydrogen, because its molar mass is lower than that of oxygen.

Question 9

A 2.00 L container is filled with gas at a pressure of 2.00 atm at 25$$^\circC. $$What pressure will develop within the sealed container if it is warmed to 75$$^\circC$$?

Accepted Answer

$$P_2$$ = $$P_1$$ \dfrac{$$T_2$$}{$$T_1$$} = 2.00 	imes \dfrac{348}{298} = 2.34$$ atm

Question 10

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

Accepted Answer

Gas particles exert attractive and repulsive forces on each other.

Question 11

A sample of air has a density of 0.572 g/L at 90.0$$^\circC $$and 380.0 mm Hg pressure. What is the molar mass of the gas? ($$R = 0.08206 L$$·atm·mol$$^{-1}$$·K$$^{-1})$$

Accepted Answer

$$M = \dfrac{dRT}{P} = \dfrac{0.572 	imes 0.08206 	imes 363.15}{0.500} = 34.0 g/$$mol

Question 12

A mixture of CO and CO$$_2$$ has partial pressures of 0.200 atm and 0.600 atm, respectively. What is the mole fraction of CO in the mixture?

Accepted Answer

$$X_{CO} = \dfrac{P_{CO}}{P_{CO} + P_{CO_2$}} = \dfrac{0.200}{0.200 + 0.600} = 0.25$$

Question 13

A barometer is used to measure atmospheric pressure. If the height of the mercury column is 740 mm, what is the atmospheric pressure in atm?

Accepted Answer

$$P = \dfrac{740}{760} = 0.974$$ atm

Question 14

Which of the following real-life scenarios best illustrates the concept of diffusion?

Accepted Answer

The smell of perfume spreading throughout a room after being sprayed.

Question 15

A sample of gas occupies 5.00 L at 20$$^\circC $$and 1.00 atm. What will be its volume at 45$$^\circC $$and 2.00 atm?

Accepted Answer

$$V_2$$ = $$V_1$$ \dfrac{$$P_1$$}{$$P_2$$} \dfrac{$$T_2$$}{$$T_1$$} = 5.00 	imes \dfrac{1.00}{2.00} 	imes \dfrac{318}{293} = 2.71$$ L

Question 16

Which of the following best explains why lighter gases effuse faster than heavier gases?

Accepted Answer

According to Graham's law, the rate of effusion is inversely proportional to the square root of the molar mass.

Question 17

A 5.00 L tank contains 2.00 mol of O$$_2 at 27$^\circC. $$What is the pressure in the tank? ($$R = 0.08206 L$$·atm·mol$$^{-1}$$·K$$^{-1})$$

Accepted Answer

$$P = \dfrac{nRT}{V} = \dfrac{2.00 	imes 0.08206 	imes 300.15}{5.00} = 9.85$$ atm

Question 18

If the density of a gas is 1.25 g/L at 0.750 atm and 25$$^\circC$$, what is its molar mass? ($$R = 0.08206 L$$·atm·mol$$^{-1}$$·K$$^{-1})$$

Accepted Answer

$$M = \dfrac{dRT}{P} = \dfrac{1.25 	imes 0.08206 	imes 298.15}{0.750} = 40.8 g/$$mol

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