Q: 5.59 g of an ideal gas in a 5.00-L flask exerts a pressure of 1.15 atm at 350 K. What is the molar mass of the gas? (Use the ideal gas law.)

$$M = \frac{mRT}{PV} = \frac{5.59 \times 0.0821 \times 350}{1.15 \times 5.00} \approx 28.0\ \text{g/mol}$$

Q: In a simulation, both the red and blue gases occupy the same volume at the same temperature. There are 30 particles of the red and 10 of the blue. If the total pressure is 48 mm Hg, what is the pressure exerted by the blue particles?

$$P_{\text{blue}} = \frac{10}{40} \times 48 = 12\ \text{mm Hg}$$

Q: 1.0 mol $$\mathrm{H_2$(g)}$$ and 0.20 mol $$\mathrm{O_2$(g)}$$ are added to a cylinder. Before reaction, the total pressure is 1.00 atm at 25 °C. Calculate the final pressure in the cylinder if the final temperature is 225 °C and the cylinder volume is constant. ($$\mathrm{O_2$(g) + 2H_2(g) \rightarrow 2H_2O(g)})$$

$$P_2 = 1.00$$ \times \frac{0.60}{1.20} \times \frac{498}{298} \approx 0.84$$ atm

Q: A sample of gas has a density of 1.25 g/L at STP. What is its molar mass? (Use $$M = dRT/P)$$

$$M = 1.25 \times 0.0821 \times 273 / 1.00 \approx 28.0\ \text{g/mol}$$

Q: A mixture of gases contains 0.50 mol $$\mathrm{CO_2$}$$, 0.30 mol $$\mathrm{O_2$}$$, and 0.20 mol $$\mathrm{N_2$} at a $$total pressure of 2.0 atm. What is the partial pressure of $$\mathrm{O_2$}$$?

$$P_{O_2$} = X_{O_2$} \times P_{\text{total}} = \frac{0.30}{1.00} \times 2.0 = 0.60\ \text{atm}$$

Question 1

A 3.0-L helium balloon is purchased in Salt Lake City at a pressure of 645 mm Hg and a temperature of 86 °F (30 °C). The balloon is taken to the summit of the Pfeifferhorn, where the pressure is 509 mm Hg and the temperature is 50 °F (10 °C). Assuming the amount of helium remains constant, what will be the new volume of the balloon? (Use the combined gas law.)

Accepted Answer

$$V_2$$ = \frac{$$P_1$$ $$V_1$$ $$T_2$$}{$$P_2$$ $$T_1$$} = \frac{645 	imes 3.0 	imes 283}{509 	imes 303} \approx 3.6\ 	ext{L}$$

Question 2

5.59 g of an ideal gas in a 5.00-L flask exerts a pressure of 1.15 atm at 350 K. What is the molar mass of the gas? (Use the ideal gas law.)

Accepted Answer

$$M = \frac{mRT}{PV} = \frac{5.59 	imes 0.0821 	imes 350}{1.15 	imes 5.00} \approx 28.0\ 	ext{g/mol}$$

Question 3

Which of the following gases is more dense than air at STP?

Accepted Answer

Radon ($$\mathrm{Rn})$$

Question 4

If the radioactive element radon is present in a multilevel house, where would the radon most likely be found in greater concentrations?

Accepted Answer

In the basement

Question 5

In a simulation, both the red and blue gases occupy the same volume at the same temperature. There are 30 particles of each. Which exerts the greater pressure?

Accepted Answer

Both exert the same pressure

Question 6

In a simulation, both the red and blue gases occupy the same volume at the same temperature. There are 30 particles of the red and 10 of the blue. If the total pressure is 48 mm Hg, what is the pressure exerted by the blue particles?

Accepted Answer

$$P_{	ext{blue}} = \frac{10}{40} 	imes 48 = 12\ 	ext{mm Hg}$$

Question 7

A balloon filled with $$\mathrm{NO_2$(g)}$$ has an initial volume of 8 L. If half the $$\mathrm{NO_2$}$$ reacts to form $$\mathrm{N_2O_4(g)} at $$constant temperature and pressure, what is the final volume of the balloon?

Accepted Answer

6 L

Question 8

TNT ($$\mathrm{C_7H_5N_3O_6}) $$reacts with $$\mathrm{O_2$(g)} to $$form $$\mathrm{CO_2$(g)}$$, $$\mathrm{H_2O(g)}$$, and $$\mathrm{N_2$(g)}. If 5 kg of $$TNT completely reacts, what is the pressure of each product if they are produced at 300 K in a 10.0-L box? (Assume ideal gas behavior and complete reaction.)

Accepted Answer

Calculate moles of TNT, use stoichiometry for each product, then $$P = \frac{nRT}{V}$$ for each. Each product will have a different pressure based on its mole ratio.

Question 9

1.0 mol $$\mathrm{H_2$(g)}$$ and 0.20 mol $$\mathrm{O_2$(g)}$$ are added to a cylinder. Before reaction, the total pressure is 1.00 atm at 25 °C. Calculate the total number of moles of gas in the cylinder at the end of the reaction if the yield of $$\mathrm{H_2O} is 80$$%. ($$\mathrm{O_2$(g) + 2H_2(g) \rightarrow 2H_2O(g)})$$

Accepted Answer

0.60 mol

Question 10

1.0 mol $$\mathrm{H_2$(g)}$$ and 0.20 mol $$\mathrm{O_2$(g)}$$ are added to a cylinder. Before reaction, the total pressure is 1.00 atm at 25 °C. Calculate the final pressure in the cylinder if the final temperature is 225 °C and the cylinder volume is constant. ($$\mathrm{O_2$(g) + 2H_2(g) \rightarrow 2H_2O(g)})$$

Accepted Answer

$$P_2 = 1.00$$ 	imes \frac{0.60}{1.20} 	imes \frac{498}{298} \approx 0.84$$ atm

Question 11

Which equation best represents the relationship between pressure, volume, and temperature for a fixed amount of gas?

Accepted Answer

$$\frac{P_1$ V_1$}{T_1$} = \frac{P_2$ V_2$}{T_2$}$$

Question 12

Which of the following statements about Dalton’s Law of Partial Pressures is correct?

Accepted Answer

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

Question 13

A mixture contains 2.0 mol $$\mathrm{N_2$}$$ and 3.0 mol $$\mathrm{O_2$} in a 10.0-L $$container at 300 K. What is the mole fraction of $$\mathrm{O_2$}$$?

Accepted Answer

$$X_{O_2$} = \frac{3.0}{2.0 + 3.0} = 0.60$$

Question 14

Which of the following will increase the density of a gas at constant temperature?

Accepted Answer

Increasing the pressure

Question 15

A sample of gas has a density of 1.25 g/L at STP. What is its molar mass? (Use $$M = dRT/P)$$

Accepted Answer

$$M = 1.25 	imes 0.0821 	imes 273 / 1.00 \approx 28.0\ 	ext{g/mol}$$

Question 16

A mixture of gases contains 0.50 mol $$\mathrm{CO_2$}$$, 0.30 mol $$\mathrm{O_2$}$$, and 0.20 mol $$\mathrm{N_2$} at a $$total pressure of 2.0 atm. What is the partial pressure of $$\mathrm{O_2$}$$?

Accepted Answer

$$P_{O_2$} = X_{O_2$} 	imes P_{	ext{total}} = \frac{0.30}{1.00} 	imes 2.0 = 0.60\ 	ext{atm}$$

Question 17

Which of the following best explains why radon gas accumulates in basements?

Accepted Answer

Radon is denser than air and tends to settle in lower areas.

Question 18

If the pressure of a gas is doubled at constant temperature, what happens to its volume?

Accepted Answer

The volume is halved.

Gas Laws II and Stoichiometry in Gas-Phase Reactions: Study Notes

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