Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law

Practice Questions

Sometimes leaving a bicycle in the sun on a hot day will cause a blowout. Why?

Explain how the volume of the bubbles exhausted by a scuba diver ([link]) change as they rise to the surface, assuming that they remain intact.

Solution

As the bubbles rise, the pressure decreases, so their volume increases as suggested by Boyle’s law.

One way to state Boyle’s law is “All other things being equal, the pressure of a gas is inversely proportional to its volume.” (a) What is the meaning of the term “inversely proportional?” (b) What are the “other things” that must be equal?

An alternate way to state Avogadro’s law is “All other things being equal, the number of molecules in a gas is directly proportional to the volume of the gas.” (a) What is the meaning of the term “directly proportional?” (b) What are the “other things” that must be equal?

Solution

(a) The number of particles in the gas increases as the volume increases. (b) temperature, pressure

How would the graph in [link] change if the number of moles of gas in the sample used to determine the curve were doubled?

Solution

The curve would be farther to the right and higher up, but the same basic shape.

In addition to the data found in [link], what other information do we need to find the mass of the sample of air used to determine the graph?

Determine the volume of 1 mol of CH₄ gas at 150 K and 1 atm, using [link].

Solution

About 12.5 L

Determine the pressure of the gas in the syringe shown in [link] when its volume is 12.5 mL, using:

(a) the appropriate graph

(b) Boyle’s law

A spray can is used until it is empty except for the propellant gas, which has a pressure of 1344 torr at 23 °C. If the can is thrown into a fire (T = 475 °C), what will be the pressure in the hot can?

Solution

3.40 $\times$ 10³ torr

What is the temperature of an 11.2-L sample of carbon monoxide, CO, at 744 torr if it occupies 13.3 L at 55 °C and 744 torr?

A 2.50-L volume of hydrogen measured at –196 °C is warmed to 100 °C. Calculate the volume of the gas at the higher temperature, assuming no change in pressure.

Solution

12.1 L

A balloon inflated with three breaths of air has a volume of 1.7 L. At the same temperature and pressure, what is the volume of the balloon if five more same-sized breaths are added to the balloon?

A weather balloon contains 8.80 moles of helium at a pressure of 0.992 atm and a temperature of 25 °C at ground level. What is the volume of the balloon under these conditions?

Solution

217 L

The volume of an automobile air bag was 66.8 L when inflated at 25 °C with 77.8 g of nitrogen gas. What was the pressure in the bag in kPa?

How many moles of gaseous boron trifluoride, BF₃, are contained in a 4.3410-L bulb at 788.0 K if the pressure is 1.220 atm? How many grams of BF₃?

Solution

8.190 $\times$ 10^–2 mol; 5.553 g

Iodine, I₂, is a solid at room temperature but sublimes (converts from a solid into a gas) when warmed. What is the temperature in a 73.3-mL bulb that contains 0.292 g of I₂ vapor at a pressure of 0.462 atm?

How many grams of gas are present in each of the following cases?

(a) 0.100 L of CO₂ at 307 torr and 26 °C

(b) 8.75 L of C₂H₄, at 378.3 kPa and 483 K

Solution

(a) 7.24 $\times$ 10^–2 g; (b) 23.1 g; (c) 1.5 $\times$ 10^–4 g

A high altitude balloon is filled with 1.41 $\times$ 10⁴ L of hydrogen at a temperature of 21 °C and a pressure of 745 torr. What is the volume of the balloon at a height of 20 km, where the temperature is –48 °C and the pressure is 63.1 torr?

A cylinder of medical oxygen has a volume of 35.4 L, and contains O₂ at a pressure of 151 atm and a temperature of 25 °C. What volume of O₂ does this correspond to at normal body conditions, that is, 1 atm and 37 °C?

Solution

5561 L

A large scuba tank ([link]) with a volume of 18 L is rated for a pressure of 220 bar. The tank is filled at 20 °C and contains enough air to supply 1860 L of air to a diver at a pressure of 2.37 atm (a depth of 45 feet). Was the tank filled to capacity at 20 °C?

A 20.0-L cylinder containing 11.34 kg of butane, C₄H₁₀, was opened to the atmosphere. Calculate the mass of the gas remaining in the cylinder if it were opened and the gas escaped until the pressure in the cylinder was equal to the atmospheric pressure, 0.983 atm, and a temperature of 27 °C.

Solution

46.4 g

While resting, the average 70-kg human male consumes 14 L of pure O₂ per hour at 25 °C and 100 kPa. How many moles of O₂ are consumed by a 70 kg man while resting for 1.0 h?

For a given amount of gas showing ideal behavior, draw labeled graphs of:

(a) the variation of P with V

(b) the variation of V with T

(d) the variation of $\frac{1}{P}$ with V

Solution

For a gas exhibiting ideal behavior:

A liter of methane gas, CH₄, at STP contains more atoms of hydrogen than does a liter of pure hydrogen gas, H₂, at STP. Using Avogadro’s law as a starting point, explain why.

The effect of chlorofluorocarbons (such as CCl₂F₂) on the depletion of the ozone layer is well known. The use of substitutes, such as CH₃CH₂F(g), for the chlorofluorocarbons, has largely corrected the problem. Calculate the volume occupied by 10.0 g of each of these compounds at STP:

(a) CCl₂F₂(g)

(b) CH₃CH₂F(g)

Solution

(a) 1.85 L CCl₂F₂; (b) 4.66 L CH₃CH₂F

As 1 g of the radioactive element radium decays over 1 year, it produces 1.16 $\times$ 10¹⁸ alpha particles (helium nuclei). Each alpha particle becomes an atom of helium gas. What is the pressure in pascal of the helium gas produced if it occupies a volume of 125 mL at a temperature of 25 °C?

A balloon with a volume of 100.21 L at 21 °C and 0.981 atm is released and just barely clears the top of Mount Crumpit in British Columbia. If the final volume of the balloon is 144.53 L at a temperature of 5.24 °C, what is the pressure experienced by the balloon as it clears Mount Crumpet?

Solution

0.644 atm

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

If the volume of a fixed amount of a gas is tripled at constant temperature, what happens to the pressure?

Solution

The pressure decreases by a factor of 3.

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