Q: A weather balloon with a volume of 44 L is filled with 2.0 moles of helium. What is the final volume, in Litres, if 3.0 moles of helium are added, to give a total of 5.0 moles of helium? (Assume constant T and P.)

$$V_2$$ = $$V_1$$ \frac{$$n_2$$}{$$n_1$$} = 44 \times \frac{5.0}{2.0} = 110 \ L$$

Q: What is the volume at STP of 4.0 moles of methane ($$CH_4$$)?

$$V = n \times 22.4 \ L = 4.0 \times 22.4 = 89.6 \ L$$

Q: If 2.0 moles of $$O_2$$ gas occupy 44.8 L at STP, how many liters will 0.5 moles of $$O_2$$ occupy at STP?

$$V = 0.5 \times 22.4 = 11.2 \ L$$

Question 1

A sample of helium gas has a volume of 0.180 L, a pressure of 0.800 atm, and a temperature of 29°C. At what temperature (in °C) will the helium have a volume of 90.0 mL and a pressure of 3.20 atm, assuming the amount of gas remains constant? Use the Combined Gas Law.

Accepted Answer

$$T_2$$ = \frac{$$P_2$$ $$V_2$$ $$T_1$$}{$$P_1$$ $$V_1$$}$$; \ T_2$ = \frac{3.20 	imes 0.0900 	imes 302}{0.800 	imes 0.180} = 604 \ K ightarrow 331^\circ C$

Question 2

A weather balloon with a volume of 44 L is filled with 2.0 moles of helium. What is the final volume, in Litres, if 3.0 moles of helium are added, to give a total of 5.0 moles of helium? (Assume constant T and P.)

Accepted Answer

$$V_2$$ = $$V_1$$ \frac{$$n_2$$}{$$n_1$$} = 44 	imes \frac{5.0}{2.0} = 110 \ L$$

Question 3

What is the volume at STP of 4.0 moles of methane ($$CH_4$$)?

Accepted Answer

$$V = n 	imes 22.4 \ L = 4.0 	imes 22.4 = 89.6 \ L$$

Question 4

A scuba diver uses a mixture of helium and oxygen with a total pressure of 8.00 atm. If the oxygen has a partial pressure of 1280 mmHg, what is the partial pressure of the helium? (1 atm = 760 mmHg)

Accepted Answer

$$P_{He} = P_{total} - P_{O_2$} = 8.00 - \frac{1280}{760} = 6.32 \ atm$$

Question 5

Which of the following statements best describes Avogadro’s Law?

Accepted Answer

The volume of a gas is directly proportional to the number of moles of gas, at constant temperature and pressure.

Question 6

If 2.0 moles of $$O_2$$ gas occupy 44.8 L at STP, how many liters will 0.5 moles of $$O_2$$ occupy at STP?

Accepted Answer

$$V = 0.5 	imes 22.4 = 11.2 \ L$$

Question 7

A gas sample at 1.00 atm and 273 K occupies 22.4 L. If the pressure is doubled and the temperature is increased to 546 K, what is the new volume?

Accepted Answer

$$V_2$$ = $$V_1$$ \frac{$$P_1$$}{$$P_2$$} \frac{$$T_2$$}{$$T_1$$} = 22.4 	imes \frac{1.00}{2.00} 	imes \frac{546}{273} = 22.4 \ L$$

Question 8

Which of the following is NOT a condition of STP?

Accepted Answer

Pressure of 2 atm

Question 9

A mixture contains 2.0 atm of $$N_2$$, 1.0 atm of $$O_2$$, and 0.5 atm of $$CO_2. $$What is the total pressure according to Dalton’s Law?

Accepted Answer

$$P_{total} = 2.0 + 1.0 + 0.5 = 3.5 \ atm$$

Question 10

A 5.0 L sample of gas at 300 K and 2.0 atm is compressed to 2.5 L and heated to 600 K. What is the final pressure?

Accepted Answer

$$P_2$$ = $$P_1$$ \frac{$$V_1$$}{$$V_2$$} \frac{$$T_2$$}{$$T_1$$} = 2.0 	imes \frac{5.0}{2.5} 	imes \frac{600}{300} = 8.0 \ atm$$

Question 11

Which of the following best explains why 1 mole of any ideal gas occupies 22.4 L at STP?

Accepted Answer

Because the molar volume of an ideal gas at STP is defined as 22.4 L

Question 12

A hospital stores oxygen in a 50.0 L tank at 25°C and 10.0 atm. If the oxygen is used until the pressure drops to 2.0 atm at the same temperature, what volume would the released oxygen occupy at 1.0 atm and 0°C (STP)?

Accepted Answer

$$n = \frac{(10.0-2.0) 	imes 50.0}{0.0821 	imes 298} = 13.5 \ mol; \ V = n 	imes 22.4 = 302.4 \ L$$

Question 13

If a gas mixture contains 3.0 moles of $$N_2$$ and 2.0 moles of $$O_2 at $$STP, what is the total volume of the mixture?

Accepted Answer

$$V_{total} = (3.0 + 2.0) 	imes 22.4 = 112.0 \ L$$

Question 14

A 10.0 L sample of gas at 2.0 atm and 300 K is allowed to expand to 20.0 L at constant temperature. What is the final pressure?

Accepted Answer

$$P_2$$ = $$P_1$$ \frac{$$V_1$$}{$$V_2$$} = 2.0 	imes \frac{10.0}{20.0} = 1.0 \ atm$$

Question 15

Which of the following is a correct application of Dalton’s Law of Partial Pressures?

Accepted Answer

The total pressure in a scuba tank is the sum of the partial pressures of all gases present.

Gas Laws: Combined Gas Law, Avogadro’s Law, STP, and Dalton’s Law of Partial Pressures

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