Chapter 13

The volume of a gas at 99.0 kPa is 300.0 mL. If the pressure is increased to 188 kPa, what will be the new volume?

The pressure of a sample of helium in a 1.00-L container is 0.988 atm. What is the new pressure if the sample is placed in a 2.00-L container?

Challenge Air trapped in a cylinder fitted with a piston occupies 145.7 mL at 1.08 atm pressure. What is the new volume when the piston is depressed, increasing the pressure by 25%?

The pressure in an automobile tire is 1.88 atm at 25.0°C. What will be the pressure if the temperature increases to 37.0°C?

Helium gas in a 2.00-L cylinder is under 1.12 atm pressure. At 36.5°C, that same gas sample has a pressure of 2.56 atm. What was the initial temperature of the gas in the cylinder?

Challenge If a gas sample has a pressure of 30.7 kPa at 0.00°C, by how many degrees Celsius does the temperature have to increase to cause the pressure to double?

A balloon contains 146.0 mL of gas confined at a pressure of 1.30 atm and a temperature of 5.0ºC. If the pressure doubles and the temperature decreases to 2.0ºC, what will be the volume of gas in the balloon?

State the relationship among pressure, temperature, and volume of a fixed amount of gas.

Explain Which of the three variables that apply to equal amounts of gases are directly proportional? Which are inversely proportional?

Analyze A weather balloon is released into the atmosphere. You know the initial volume, temperature, and air pressure. What information will you need to predict its volume when it reaches its final altitude? Which law would you use to calculate this volume?

Infer why gases such as the oxygen used at hospitals are compressed. Why must compressed gases be shielded from high temperatures? What must happen to compressed oxygen before it can be inhaled?

Calculate A rigid plastic container holds 1.00 L of methane gas at 660 torr pressure when the temperature is 22.0ºC. How much pressure will the gas exert if the temperature is raised to 44.6ºC?

Design a concept map that shows the relationships among pressure, volume, and temperature in Boyle’s, Charles’s, and Gay-Lussac’s laws.

What size container do you need to hold 0.0459 mol of \(N_{2}\) gas at STP?

How much carbon dioxide gas, in grams, is in a 1.0-L balloon at STP?

What volume in milliliters will 0.00922 \(g\) of \(H_{2}\) gas occupy at STP?

What volume will 0.416 g of krypton gas occupy at STP?

Calculate the volume that 4.5 \(kg\) of ethylene gas \(\left(C_{2} H_{4}\right)\) will occupy at STP.

Challenge A flexible plastic container contains 0.860 g of helium gas in a volume of 19.2 L. If 0.205 g of helium is removed at constant pressure and temperature, what will be the new volume?

Calculate the volume of a 0.323-mol sample of a gas at 265 K and 0.900 atm.

What is the pressure, in atmospheres, of a 0.108-mol sample of helium gas at a temperature of 20.0°C if its volume is 0.505 L?

If the pressure exerted by a gas at 25°C in a volume of 0.044 L is 3.81 atm, how many moles of gas are present?

Challenge An ideal gas has a volume of 3.0 L. If the number of moles of gas and the temperature are doubled, while the pressure remains constant, what is the new volume?

Explain why Avogadro’s principle holds true for gases that have small particles and for gases that have large particles.

State the equation for the ideal gas law.

Predict the conditions under which a real gas might deviate from ideal behavior.

List common units for each variable in the ideal gas law.

Make and Use Graphs For every 6°C drop in temperature, the air pressure in a car’s tires goes down by about 1 psi (14.7 psi = 1.00 atm). Make a graph illustrating the change in tire pressure from 20°C to -20°C (assume 30.0 psi at 20°C).

What volume of oxygen is needed to completely combust 2.36 \(L\) of methane gas \(\left(CH_{4}\right)?\)

Challenge Nitrogen and oxygen gases react to form dinitrogen oxide gas \( N_{2} O.\) What volume of \(O_{2}\) is needed to produce 34 \(L\) of \(N_{2} O\) ?

When solid calcium carbonate \(\left(CaCO_{3}\right)\) is heated, it decomposes to form solid calcium oxide (CaO) and carbon dioxide gas \(\left(CO_{2}\right) .\) How many liters of carbon dioxide will be produced at STP if 2.38 \(kg\) of calcium carbonate reacts completely?

When iron rusts, it undergoes a reaction with oxygen to form iron(III) oxide. $$4 Fe(s)+3 O_{2}(g) \rightarrow 2 Fe_{2} O_{3}(s)$$ Calculate the volume of oxygen gas at STP that is required to completely react with 52.0 g of iron.

Challenge An excess of acetic acid is added to 28 g of sodium bicarbonate at 25°C and 1 atm pressure. During the reaction, the gas cools to 20°C. What volume of carbon dioxide will be produced? The balanced equation for the reaction is shown below. $$NaHCO_{3}(\mathrm{aq})+CH_{3} \mathrm{COOH}(\mathrm{aq}) \rightarrow NaCH_{3} \mathrm{COO}(\mathrm{aq})+\mathrm{CO}_{2}(\mathrm{g})+H_{2} O(\mathrm{l})$$

Explain When fluorine gas combines with water vapor, the following reaction occurs. $$2 \mathrm{F}_{2}(\mathrm{g})+2 H_{2} O(\mathrm{g}) \rightarrow O_{2}(\mathrm{g})+4 \mathrm{HF}(\mathrm{g})$$ If the reaction starts with 2 L of fluorine gas, how many liters of water vapor react with the fluorine, and how many liters of oxygen and hydrogen fluoride are produced?

Analyze Is the volume of a gas directly or inversely proportional to the number of moles of a gas at constant temperature and pressure? Explain.

Calculate One mole of a gas occupies a volume of 22.4 L at STP. Calculate the temperature and pressure conditions needed to fit 2 mol of a gas into a volume of 22.4 L.

Interpret Data Ethene gas \(\left(C_{2} H_{4}\right)\) reacts with oxygen to form carbon dioxide and water. Write a balanced equation for this reaction, then find the mole ratios of substances on each side of the equation.

State Boyle’s law, Charles’s law, Gay-Lussac’s law, and the combined gas law in words and equations.

If two variables are inversely proportional, what happens to the value of one as the value of the other increases?

If two variables are directly proportional, what happens to the value of one as the value of the other increases?

List the standard conditions for gas measurements.

Identify the units most commonly used for \(P,\) \(V,\) and \(T.\)

Weather Balloons A weather balloon is filled with helium that occupies a volume of \(5.00 \times 10^{4} L\) at 0.995 atm and \(32.0^{\circ} C\) . After it is released, it rises to a location where the pressure is 0.720 atm and the temperature is \(-12.0^{\circ} C .\) What is the volume of the balloon at the new location?

Use Boyle’s, Charles’s, or Gay-Lussac’s law to calculate the missing value in each of the following. a. \(V_{1}=2.0 L, P_{1}=0.82 \mathrm{atm}, V_{2}=1.0 \mathrm{L}, P_{2}=?\) b. \(V_{1}=250 \mathrm{mL}, T_{1}=?, V_{2}=400 \mathrm{mL}, T_{2}=298 \mathrm{K}\) c. \(V_{1}=0.55 L, P_{1}=740 mm \mathrm{Hg}, V_{2}=0.80 \mathrm{L}, P_{2}=?\)

Hot-Air Balloons A sample of air occupies 2.50 L at a temperature of 22.0°C. What volume will this sample occupy inside a hot-air balloon at a temperature of 43.0°C? Assume that the pressure inside the balloon remains constant.

What is the pressure of a fixed volume of hydrogen gas at 30.0°C if it has a pressure of 1.11 atm at 15.0°C?

State Avogadro’s principle.

State the ideal gas law.

What volume is occupied by 1 mol of a gas at STP? What volume does 2 mol occupy at STP?

Define the term ideal gas, and explain why there are no true ideal gases in nature.