Q: A sample of gas has a volume of 3.1 L at 305 K and 0.97 bar. How many moles of gas are present?

$$n = \frac{PV}{RT} = \frac{(0.97)(3.1)}{0.08314 \times 305} = 0.12\ \mathrm{mol}$$

Question 1

Which of the following correctly expresses the relationship described by Boyle's Law for an ideal gas?

Accepted Answer

$$V \propto \frac{1}{P}$$

Question 2

A 1.00 mol sample of an ideal gas occupies 22.7 L at STP. What is the value of STP used in this calculation?

Accepted Answer

$$T = 273.15\ \mathrm{K},\ P = 1.00\ \mathrm{bar}$$

Question 3

Which of the following is the correct form of the ideal gas law?

Accepted Answer

$$PV = nRT$$

Question 4

If the pressure on a 50.0 L cylinder of oxygen at 21 $$^\circC is $$reduced from 18.5 bar to 1.00 bar at constant temperature, what will be the new volume of the gas?

Accepted Answer

$$V_2$$ = \frac{$$P_1$$ $$V_1$$}{$$P_2$$} = \frac{(50.0)(18.5)}{1.00} = 925\ \mathrm{L}$$

Question 5

Which of the following is the correct expression for the density $$d of a $$gas in terms of its molar mass $$M$$, pressure $$P$$, and temperature $$T$$?

Accepted Answer

$$d = \frac{PM}{RT}$$

Question 6

A 0.50 mol sample of oxygen gas is confined at 0 $$^\circC in a $$cylinder with a moving piston. The gas has an initial pressure of 1.0 bar. The gas is then compressed by the piston so that its final volume is half the initial volume. The final pressure of the gas is 2.2 bar. What is the final temperature of the gas in Kelvin?

Accepted Answer

$$T_2$$ = \frac{$$P_2$$ $$V_2$$ $$T_1$$}{$$P_1$$ $$V_1$$} = \frac{2.2 	imes 0.5 	imes 273.15}{1.0 	imes 1.0} = 300.5\ \mathrm{K}$$

Question 7

Which of the following values for the gas constant $$R$$ would you use if pressure is in bar and volume is in liters?

Accepted Answer

$$R = 0.08314\ \mathrm{L\ bar\ $$mol^{-1}$$\ K$$^{-1}$$}$$

Question 8

A 70-kg person expends 480 kcal of energy per hour shoveling snow. The oxidation of organic nutrients such as glucose during metabolism liberates approximately 384 kcal of energy per gram of oxygen consumed. If air is 21% oxygen, what volume of air at STP is needed to produce enough energy for this person to shovel snow for 1 hour?

Accepted Answer

$$V = 281\ \mathrm{L}$$

Question 9

Which of the following statements about the ideal gas law is correct?

Accepted Answer

It describes the relationship between pressure, volume, temperature, and number of moles for ideal gases.

Question 10

A driver with a nearly empty fuel tank may ask the following in an emergency: If a 56.8 L automobile gas tank and only gasoline vapor in it, what is the farthest the vehicle could travel if it gets 85 km/L on liquid gasoline? Assume the density of gasoline is 0.75 g/mL, the pressure is 743 mm Hg, and the temperature is 25 $$^\circC.$$

Accepted Answer

$$2.7\ \mathrm{km}$$

Question 11

Which of the following is the correct rearrangement of the ideal gas law to solve for molarity $$M$$?

Accepted Answer

$$M = \frac{P}{RT}$$

Question 12

Four 3.0 L flasks, each at a pressure of 878 mmHg, are in a room. The flasks contain H$$_2$$, Ar, and Xe, respectively. Which flask contains the most atoms of gas?

Accepted Answer

The flask with H$$_2$$

Question 13

Which of the following is NOT an assumption of the ideal gas law?

Accepted Answer

Gas particles lose energy during collisions.

Question 14

If the temperature of a gas is doubled at constant pressure, what happens to its volume according to Charles's Law?

Accepted Answer

The volume doubles.

Question 15

Which of the following equations can be used to relate the initial and final states of a gas when the number of moles is constant?

Accepted Answer

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

Question 16

In the industrial process for making nitric acid, ammonia reacts with oxygen at 850 $$^\circC $$and 5.00 bar. How many liters of NH$$_3 at $$these conditions are required to react with 1.00 mol of O$$_2 in $$the reaction $$4\ \mathrm{NH}_3 (g) + 5\ \mathrm{O}_2 (g) \rightarrow 4\ \mathrm{NO} (g) + 6\ \mathrm{H}_2\mathrm{O} (g)$$?

Accepted Answer

$$0.8\ \mathrm{mol} NH$_3$$

Question 17

Which of the following would increase the density of a gas, assuming all other variables are held constant?

Accepted Answer

Increasing the molar mass

Question 18

A sample of gas has a volume of 3.1 L at 305 K and 0.97 bar. How many moles of gas are present?

Accepted Answer

$$n = \frac{PV}{RT} = \frac{(0.97)(3.1)}{0.08314 	imes 305} = 0.12\ \mathrm{mol}$$

Ideal Gas Law and Gas Law Relationships – Study Notes

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