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.)

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

Q: What is the volume at STP of 4.00 g of methane ($$CH_4$$)?

$$\text{Moles of } CH_4$ = \frac{4.00}{16.05} = 0.249\ mol$$; $$V = 0.249 \times 22.4 = 5.58\ L$$

Q: Calculate the molar mass of ethanol ($$C_2H_6O).$$

$$2 \times 12.01 + 6 \times 1.01 + 1 \times 16.00 = 46.08\ g/mol$$

Q: If 3.0 moles of nitrogen gas occupy 67.2 L at STP, what is the molar volume of a gas at STP?

$$\text{Molar volume} = \frac{67.2}{3.0} = 22.4\ L/mol$$

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

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

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

Question 3

What is the volume at STP of 4.00 g of methane ($$CH_4$$)?

Accepted Answer

$$	ext{Moles of } CH_4$ = \frac{4.00}{16.05} = 0.249\ mol$$; $$V = 0.249 	imes 22.4 = 5.58\ L$$

Question 4

Calculate the molar mass of ethanol ($$C_2H_6O).$$

Accepted Answer

$$2 	imes 12.01 + 6 	imes 1.01 + 1 	imes 16.00 = 46.08\ g/mol$$

Question 5

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

$$P_{O_2$} = \frac{1280}{760} = 1.68\ atm$$; $$P_{He} = 8.00 - 1.68 = 6.32\ atm$$

Question 6

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 7

If 3.0 moles of nitrogen gas occupy 67.2 L at STP, what is the molar volume of a gas at STP?

Accepted Answer

$$	ext{Molar volume} = \frac{67.2}{3.0} = 22.4\ L/mol$$

Question 8

A gas sample at 1.50 atm and 300 K occupies 2.00 L. What will be its volume at 3.00 atm and 400 K? (Assume n is constant.)

Accepted Answer

$$V_2$$ = \frac{$$P_1$$ $$V_1$$ $$T_2$$}{$$P_2$$ $$T_1$$} = \frac{1.50 	imes 2.00 	imes 400}{3.00 	imes 300} = 1.33\ L$$

Question 9

Which of the following is NOT a correct statement about STP?

Accepted Answer

STP is defined as 1 atm pressure and 298 K temperature.

Question 10

A mixture contains 2.0 atm of nitrogen, 1.0 atm of oxygen, and 0.5 atm of argon. What is the total pressure according to Dalton’s Law?

Accepted Answer

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

Question 11

Which of the following best describes the steps to calculate the molar mass of a compound?

Accepted Answer

Obtain the molar mass of each element, multiply by the subscript, and sum the results.

Question 12

A 5.00 L sample of gas at 2.00 atm and 350 K is compressed to 3.00 L and heated to 400 K. What is the final pressure?

Accepted Answer

$$P_2$$ = \frac{$$P_1$$ $$V_1$$ $$T_2$$}{$$V_2$$ $$T_1$$} = \frac{2.00 	imes 5.00 	imes 400}{3.00 	imes 350} = 3.81\ atm$$

Question 13

Which of the following is the correct conversion factor for the molar volume of a gas at STP?

Accepted Answer

$$1\ mol\ gas = 22.4\ L$$

Question 14

If the volume of a gas is doubled while the temperature and pressure remain constant, what happens to the number of moles of gas present?

Accepted Answer

The number of moles doubles.

Question 15

A 10.0 L container holds a mixture of gases: 2.0 moles of $$O_2$$, 1.0 mole of $$N_2$$, and 1.0 mole of $$CO_2 at $$STP. What is the total pressure in the container?

Accepted Answer

$$n_{total} = 2.0 + 1.0 + 1.0 = 4.0\ mol$$; $$P = \frac{nRT}{V} = \frac{4.0 	imes 0.0821 	imes 273}{10.0} = 8.97\ atm$$

Gas Laws, Molar Mass, and Dalton’s Law: Study Notes for GOB Chemistry

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