Q: A 2.0 L rigid container holds 0.50 mol of helium gas at 27$$^ ext{o}C. $$What is the pressure inside the container? (Use $$R = 0.0821 \ \frac{L \cdot atm}{mol \cdot K})$$

$$P = \frac{nRT}{V} = \frac{0.50 \times 0.0821 \times 300}{2.0} = 6.15 \ atm$$

Q: A 5.00 L scuba tank contains 2.3 mol of $$O_2 at 15$^ ext{o}C. $$What pressure does the gas exert? (Use $$R = 0.0821 \ \frac{L \cdot atm}{mol \cdot K})$$

$$P = \frac{2.3 \times 0.0821 \times 288}{5.00} = 10.8 \ atm$$

Q: A 2.5 L fire extinguisher contains $$CO_2 at 1345 $$kPa and 25$$^ ext{o}C. $$How many grams of $$CO_2$$ are present? (Molar mass $$CO_2 = 44.0$$ \ g/mol$$, R = 8.31$$ \ \frac{kPa \cdot L}{mol \cdot K}$$)

$$n = \frac{PV}{RT} = \frac{1345 \times 2.5}{8.31 \times 298} = 1.36 \ mol$$, $$1.36 \times 44.0 = 59.8 \ g$$

Q: A sample of air has a volume of 550.0 mL at 106$$^ ext{o}C. At $$what temperature will its volume be 700.0 mL at constant pressure?

$$\frac{V_1$}{T_1$} = \frac{V_2$}{T_2$} \rightarrow T_2$ = \frac{V_2$ T_1$}{V_1$} = \frac{700.0 \times 379}{550.0} = 482 \ K = 209 \ ^\circ C$$

Q: A 2.4 L container holds $$CO_2 at 1.3 $$atm and 0$$^ ext{o}C. $$How many grams of $$CO_2$$ are present? (Molar mass $$CO_2 = 44.0$$ \ g/mol$$, R = 0.0821$$ \ \frac{L \cdot atm}{mol \cdot K}$$)

$$n = \frac{PV}{RT} = \frac{1.3 \times 2.4}{0.0821 \times 273} = 0.139 \ mol$$, $$0.139 \times 44.0 = 6.12 \ g$$

Question 1

According to the Kinetic Molecular Theory (KMT), which of the following statements is NOT true about ideal gases?

Accepted Answer

Gas molecules experience significant attractive and repulsive forces.

Question 2

A 2.0 L rigid container holds 0.50 mol of helium gas at 27$$^	ext{o}C. $$What is the pressure inside the container? (Use $$R = 0.0821 \ \frac{L \cdot atm}{mol \cdot K})$$

Accepted Answer

$$P = \frac{nRT}{V} = \frac{0.50 	imes 0.0821 	imes 300}{2.0} = 6.15 \ atm$$

Question 3

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

Accepted Answer

The gas molecules move faster and collide with the walls more frequently and with greater force.

Question 4

A manometer is used to measure the pressure of a gas sample. If the mercury column on the side open to the atmosphere is 20 mm higher than the side connected to the gas, and atmospheric pressure is 760 mmHg, what is the pressure of the gas?

Accepted Answer

$$P_{gas} = 760 \ mmHg - 20 \ mmHg = 740 \ mmHg$$

Question 5

A 5.00 L scuba tank contains 2.3 mol of $$O_2 at 15$^	ext{o}C. $$What pressure does the gas exert? (Use $$R = 0.0821 \ \frac{L \cdot atm}{mol \cdot K})$$

Accepted Answer

$$P = \frac{2.3 	imes 0.0821 	imes 288}{5.00} = 10.8 \ atm$$

Question 6

Which of the following is the correct conversion for 1 atm to mmHg?

Accepted Answer

$$1 \ atm = 760 \ mmHg$$

Question 7

A 2.5 L fire extinguisher contains $$CO_2 at 1345 $$kPa and 25$$^	ext{o}C. $$How many grams of $$CO_2$$ are present? (Molar mass $$CO_2 = 44.0$$ \ g/mol$$, R = 8.31$$ \ \frac{kPa \cdot L}{mol \cdot K}$$)

Accepted Answer

$$n = \frac{PV}{RT} = \frac{1345 	imes 2.5}{8.31 	imes 298} = 1.36 \ mol$$, $$1.36 	imes 44.0 = 59.8 \ g$$

Question 8

A sample of air has a volume of 550.0 mL at 106$$^	ext{o}C. At $$what temperature will its volume be 700.0 mL at constant pressure?

Accepted Answer

$$\frac{V_1$}{T_1$} = \frac{V_2$}{T_2$} ightarrow T_2$ = \frac{V_2$ T_1$}{V_1$} = \frac{700.0 	imes 379}{550.0} = 482 \ K = 209 \ ^\circ C$$

Question 9

A gas sample at 104$$^	ext{o}C $$and 0.870 atm occupies 3.0 L. What volume would this gas occupy at 60$$^	ext{o}C $$and 1.7 atm?

Accepted Answer

$$V_2$$ = $$V_1$$ \frac{$$P_1$$}{$$P_2$$} \frac{$$T_2$$}{$$T_1$$} = 3.0 	imes \frac{0.870}{1.7} 	imes \frac{333}{377} = 1.37 \ L$$

Question 10

A 2.4 L container holds $$CO_2 at 1.3 $$atm and 0$$^	ext{o}C. $$How many grams of $$CO_2$$ are present? (Molar mass $$CO_2 = 44.0$$ \ g/mol$$, R = 0.0821$$ \ \frac{L \cdot atm}{mol \cdot K}$$)

Accepted Answer

$$n = \frac{PV}{RT} = \frac{1.3 	imes 2.4}{0.0821 	imes 273} = 0.139 \ mol$$, $$0.139 	imes 44.0 = 6.12 \ g$$

Question 11

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

Accepted Answer

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

Question 12

A mixture contains 9 mol $$N_2$$ and 11 mol $$O_2. $$What is the mole fraction of $$N_2$$?

Accepted Answer

$$X_{N_2$} = \frac{9}{9+11} = 0.45$$

Question 13

If the total pressure in a tank is 2.0 atm and the mole fraction of $$O_2 is 0.30$$, what is the partial pressure of $$O_2$$?

Accepted Answer

$$P_{O_2$} = 2.0 	imes 0.30 = 0.60 \ atm$$

Question 14

A 12.0 L tank contains a mixture of $$O_2$$ and $$N_2 at 30$^	ext{o}C $$and a total pressure of 1.75 atm. If the partial pressure of $$O_2 is 0.350 $$atm, how many moles of $$O_2$$ are present? (Use $$R = 0.0821 \ \frac{L \cdot atm}{mol \cdot K})$$

Accepted Answer

$$n = \frac{PV}{RT} = \frac{0.350 	imes 12.0}{0.0821 	imes 303} = 0.169 \ mol$$

Question 15

Which of the following best describes the effect of decreasing the volume of a gas at constant temperature?

Accepted Answer

The pressure increases because the gas molecules collide with the walls more frequently.

Question 16

A rigid container holds a fixed amount of gas. If the temperature is doubled (in Kelvin), what happens to the pressure?

Accepted Answer

The pressure doubles.

Question 17

Which of the following is a correct statement about the behavior of gases in a container with elastic walls when temperature increases?

Accepted Answer

The volume increases while the pressure remains constant.

Question 18

A hospital uses a 10.0 L cylinder of oxygen at 200 atm and 25$$^	ext{o}C. $$How many liters of oxygen gas at 1.0 atm and 0$$^	ext{o}C $$can be supplied to patients? (Assume ideal gas behavior.)

Accepted Answer

$$V_2$$ = $$V_1$$ \frac{$$P_1$$}{$$P_2$$} \frac{$$T_2$$}{$$T_1$$} = 10.0 	imes \frac{200}{1.0} 	imes \frac{273}{298} = 1830 \ L$$

Pressure and Gas Laws: Kinetic Molecular Theory, Gas Laws, and Applications

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