Chapter 13

Assume that the temperature and the amount of gas are constant in the following problems. The volume of a gas at 99.0 \(\mathrm{kPa}\) is 300.0 \(\mathrm{mL} .\) If the pressure is increased to 188 \(\mathrm{kPa}\) , what will be the new volume?

Assume that the temperature and the amount of gas are constant in the following problems. The pressure of a sample of helium in a \(1.00-\mathrm{L}\) container is 0.988 atm. What is the new pressure if the sample is placed in a \(2.00-\mathrm{L}\) container?

Assume that the temperature and the amount of gas are constant in the following problems. Challenge Air trapped in a cylinder fitted with a piston occupies 145.7 \(\mathrm{mL}\) at 1.08 atm pressure. What is the new volume when the piston is depressed, increasing the pressure by 25\(\% ?\)

Assume that the pressure and the amount of gas remain constant in the following problems. A gas at \(89^{\circ}\) occupies a volume of 0.67 \(\mathrm{L}\) . At what Celsius temperature will the volume increase to 1.12 \(\mathrm{L} ?\)

Assume that the pressure and the amount of gas remain constant in the following problems. The Celsius temperature of a 3.00-\(\mathrm{L}\) sample of gas is lowered from \(80.0^{\circ} \mathrm{C}\) to \(30.0^{\circ} \mathrm{C}\). What will be the resulting volume of this gas?

Assume that the pressure and the amount of gas remain constant in the following problems. Challenge A gas occupies 0.67 \(\mathrm{L}\) at 350 \(\mathrm{K}\) . What temperature is required to reduce the volume by 45\(\% ?\)

Assume that the volume and the amount of gas are constant in the following problems. The pressure in an automobile tire is 1.88 atm at \(25.0^{\circ} \mathrm{C} .\) What will be the pressure if the temperature increases to \(37.0^{\circ} \mathrm{C} ?\)

Assume that the volume and the amount of gas are constant in the following problems. Helium gas in a 2.00-L cylinder is under 1.12 atm pressure. At \(36.5^{\circ} \mathrm{C}\) , that same gas sample has a pressure of 2.56 atm. What was the initial temperature of the gas in the cylinder?

Assume that the volume and the amount of gas are constant in the following problems. Challenge If a gas sample has a pressure of 30.7 \(\mathrm{kPa}\) at \(0.00^{\circ} \mathrm{C},\) by how many degrees Celsius does the temperature have to increase to cause the pressure to double?

Assume that the amount of gas is constant in the following problems. A sample of air in a syringe exerts a pressure of 1.02 atm at \(22.0^{\circ} \mathrm{C}\) . The syringe is placed in a boiling-water bath at \(100.0^{\circ} \mathrm{C}\) . The pressure is increased to 1.23 atm by pushing the plunger in, which reduces the volume to 0.224 \(\mathrm{mL} .\) What was the initial volume?

Assume that the amount of gas is constant in the following problems. A balloon contains 146.0 \(\mathrm{mL}\) of gas confined at a pressure of 1.30 atm and a temperature of \(5.0^{\circ} \mathrm{C}\) . If the pressure doubles and the temperature decreases to \(2.0^{\circ} \mathrm{C},\) what will be the volume of gas in the balloon?

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

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 \(22.0^{\circ} \mathrm{C}\) . How much pressure will the gas exert if the temperature is raised to \(44.6^{\circ} \mathrm{C}\) ?

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 \(\mathrm{N}_{2}\) gas at STP?

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

What volume in milliliters will 0.0092 g of \(\mathrm{H}_{2}\) gas occupy at STP?

What volume will 0.416 \(\mathrm{g}\) of krypton gas occupy at STP?

Calculate the volume that 4.5 \(\mathrm{kg}\) of ethylene gas \(\left(\mathrm{C}_{2} \mathrm{H}_{4}\right)\) 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?

Determine the Celsius temperature of 2.49 mol of a gas contained in a 1.00-L vessel at a pressure of 143 kPa

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 \(20.0^{\circ} \mathrm{C}\) if its volume is 0.505 L?

If the pressure exerted by a gas at \(25^{\circ} \mathrm{C}\) 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.

Calculate A 2.00-L flask is filled with propane gas \(\left(C_{3} H_{8}\right)\) at a pressure of 1.00 atm and a temperature of \(-15.0^{\circ} C .\) What is the mass of the propane in the flask?

Make and Use Graphs For every \(6^{\circ}\mathrm{C}\) 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 \(20^{\circ} \mathrm{C}\) to \(-20^{\circ} \mathrm{C}\) (assume 30.0 psi at \(20^{\circ} \mathrm{C}\) ).

How many liters of propane gas \(\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)\) will undergo complete combustion with 34.0 \(\mathrm{L}\) of oxygen gas?

Determine the volume of hydrogen gas needed to react completely with 5.00 L of oxygen gas to form water.

Ammonium nitrate is a common ingredient in chemical fertilizers. Use the reaction shown to calculate the mass of solid ammonium nitrate that must be used to obtain 0.100 L of dinitrogen oxide gas at STP. $$\mathrm{NH}_{4} \mathrm{NO}_{3}(\mathrm{s}) \rightarrow \mathrm{N}_{2} \mathrm{O}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})$$

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

When iron rusts, it undergoes a reaction with oxygen to form iron(lli) oxide. $$4 \mathrm{Fe}(\mathrm{s})+3 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})$$ 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 \(25^{\circ} \mathrm{C}\) and 1 atm pressure. During the reaction, the gas cools to \(20^{\circ} \mathrm{C}\) . What volume of carbon dioxide will be produced? The balanced equation for the reaction is shown below. $$\mathrm{NaHCO}_{3}(\mathrm{aq})+\mathrm{CH}_{3} \mathrm{COOH}(\mathrm{aq}) \rightarrow \mathrm{NaCH}_{3} \mathrm{COO}(\mathrm{aq})+\mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{I})$$

Explain When fluorine gas combines with water vapor, the following reaction occurs. $$2 \mathrm{F}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightarrow \mathrm{O}_{2}(\mathrm{g})+4 \mathrm{HF}(\mathrm{g})$$ If the reaction starts with 2 L of fluorine gas, how many many many liter 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 \(\left(\mathrm{C}_{2} \mathrm{H}_{4}\right)\) reacts with oxyen 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?

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

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

Hot-Air Balloons A sample of air occupies 2.50 \(\mathrm{L}\) at a temperature of \(22.0^{\circ} \mathrm{C}\) . What volume will this sample occupy inside a hot-air balloon at a temperature of \(43.0^{\circ} \mathrm{C} ?\) Assume that the pressure inside the balloon remains constant.

State Avogadros principle.

State the ideal gas law.

What volume is occupied by 1 \(\mathrm{mol}\) of a gas at STP? What volume does 2 mol occupy at STP?