Chapter 11

An "empty" \(0.500\) -gallon milk carton sits in a room where the temperature is \(25.20^{\circ} \mathrm{C}\). The barometric pressure is exactly 1 atm. (a) What is the Kelvin temperature of the air inside the carton? (b) What is the pressure in millimeters of mercury of the air inside the carton? (c) What is the volume in liters of the air inside the carton? (1 gallon \(=3.78 \mathrm{~L}\) )

A container is evacuated with a vacuum pump and its mass is measured. Then it is filled with \(\mathrm{H}_{2}\) gas and its mass is measured again. If the mass increase is \(10.50 \mathrm{~g}\), how many moles of \(\mathrm{H}_{2}\) gas are in the container? (Hint: You will need the molar mass of \(\mathrm{H}_{2}\).)

A mercury barometer develops a leak, allowing some air to enter the glass tube. Will such a barometer read too high or too low a pressure? Explain your answer.

According to the ideal gas law, what happens to the pressure of a gas in a container when: (a) You double the absolute temperature of the gas? (b) You double the number of liters the container can hold? (c) You double the number of moles of the gas? (d) You double both the absolute temperature of the gas and the number of liters the container can hold?

Suppose that \(3.00 \mathrm{~g}\) of gaseous nitrogen, \(\mathrm{N}_{2}\), is placed in a \(2.00 \mathrm{~L}\) container. The pressure is measured to be \(450.5 \mathrm{~mm} \mathrm{Hg}\). What is the Celsius temperature of the gas? (Hint: Your first step should be solving the ideal gas equation for \(T\).)

An automobile tire is filled with \(\mathrm{O}_{2}\) gas to a total pressure of \(40.0 \mathrm{lb} / \mathrm{in} .^{2}\). The temperature is \(22.5^{\circ} \mathrm{C}\). The inside volume of the inflated tire is \(10.5\) gallons. How many grams of \(\mathrm{O}_{2}\) are in the tire? \(\left(760 \mathrm{~mm} \mathrm{Hg}=14.696 \mathrm{lb} / \mathrm{in} .^{2} ; 1\right.\) gallon \(=3.785 \mathrm{~L}\). (Hint: Your first step should be solving the ideal gas equation for \(n\).)

A steel cylinder contains \(0.01378 \mathrm{~kg}\) of an unknown gas. Combustion analysis indicates that the gas has the empirical formula \(\mathrm{H}_{2}\) S. The volume of the cylinder is. \(2.20 \times 10^{3} \mathrm{~mL}\), and the pressure inside the cylinder is \(3.42 \times 10^{3} \mathrm{~mm} \mathrm{Hg}\). The cylinder is stored in a closet at \(25.0^{\circ} \mathrm{C} .\) What is the molecular formula of the gas?

Suppose you have a sample of \(\mathrm{CO}_{2}\) gas and want to know its mass without bothering to use a balance. How could you do this?

A sample of hydrogen gas, \(\mathrm{H}_{2}\), is in an outdoor 1000.0-gallon tank. It is winter, and the temperature is \(-4.50^{\circ} \mathrm{C}\). A pressure gauge indicates that the pressure inside the tank is \(32.6\) atm. How many pounds of hydrogen are left in the tank? (Hint: Examine the solution to Problem 11.9.)

What do you get when you divide the mass in grams of a sample of a pure substance by the molar mass of the substance? Prove your answer is correct.

A steel cylinder is filled with a gas. The initial pressure of this gas is \(5.00 \mathrm{~atm}\), and the initial temperature is \(200.00^{\circ} \mathrm{C}\). The cylinder is heated to a final temperature of \(400.00{ }^{\circ} \mathrm{C}\). It appears that the temperature has doubled, but the final pressure is not \(10.0 \mathrm{~atm}\). Why doesn't the pressure double as it did in the previous example? What is the final pressure? What valuable lesson does this question teach you?

Why is it proper to think of the gas phase of matter as being more chaotic than either of the condensed phases?

What assumption is made for an ideal gas, and what gives us the right to make that assumption?

Consider a container of gas with the pressure inside the container the same as the room pressure outside the container. If a tiny hole is punched in the side of the container, will the gas leak out? Explain your answer.

How does a gas create pressure?

Why does liquid rise up a straw when you suck on the liquid through the straw?

Describe how a mercury barometer works.

What is the value of normal atmospheric pressure in millimeters of mercury? In atmospheres?

True or false? \(1 \mathrm{~atm}=76 \mathrm{~mm} \mathrm{Hg}=760 \mathrm{~cm} \mathrm{Hg}\). If false, fix it.

A weather forecaster reports the barometric pressure as \(29.7\) inches of mercury. \([1 \mathrm{in.}=2.54 \mathrm{~cm}]\) (a) How many millimeters of mercury is this? (b) How many atmospheres is this?

The pressure in a tank of oxygen is \(2000.5 \mathrm{lb} / \mathrm{in} .{ }^{2}\) \(\left[760.00 \mathrm{~mm} \mathrm{Hg}=14.696 \mathrm{lb} / \mathrm{in}^{2}\right]\) (a) How many millimeters of mercury is this? (b) How many atmospheres is this?

How do you convert from \({ }^{\circ} \mathrm{C}\) to \(\mathrm{K}\) ? Convert room temperature \(\left(22.0^{\circ} \mathrm{C}\right)\) to Kelvin.

Regarding temperatures in kelvins: (a) Convert \(-100.5^{\circ} \mathrm{C}\) to kelvins. (b) What is wrong with someone telling you the temperature of something is \(-100.5 \mathrm{~K} ?\) (c) What is the coldest possible temperature in \({ }^{\circ} \mathrm{C} ?\)

A balloon of methane gas, \(\mathrm{CH}_{4}\), has a temperature of \(-2.0^{\circ} \mathrm{C}\) and contains \(2.35 \mathrm{~g}\) of the gas. What is the temperature of the gas in Kelvin? How many moles of the gas does the balloon contain?

A tank of acetylene gas \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\) contains \(48.5 \mathrm{lb}\) of the gas and is at a pressure of \(600.2 \mathrm{lb} / \mathrm{in} .^{2}\) Express the pressure of the gas in atmospheres and the amount of gas in moles. \([760.0 \mathrm{~mm} \mathrm{Hg}=\) \(\left.14.696 \mathrm{lb} / \mathrm{in} .^{2}, 453.6 \mathrm{~g}=1 \mathrm{lb}\right]\)

State how the pressure of a gas depends on its volume at constant moles and temperature both with a mathematical relationship and an English statement. Also, make a graph that demonstrates the mathematical relationship.

State how the pressure of a gas at constant moles and volume depends on its temperature both with a mathematical relationship and an English statement. Also, make a graph that demonstrates the mathematical relationship.

State how the pressure of a gas at constant volume and temperature depends on the amount of gas present both with a mathematical relationship and an English statement. Also, make a graph that demonstrates the mathematical relationship.

What do we mean by inverse proportionality? By direct proportionality? Give an example of each using the way the pressure of a gas depends on something else.

Suppose the variable \(x\) is proportional to \(1 / y\). What does this tell you about how the numeric value of \(x\) changes as the numeric value of \(y\) changes?

"The older I get, the fewer hairs I have on my head." What kind of relationship (proportion or inverse proportion) exists between this gentleman's age and his hair? Explain your answer.

Rewrite the ideal gas law solving for \(V\). Also show how all units cancel to leave you with just units of volume.

Rewrite the ideal gas law solving for \(T\). Also show how all units cancel to leave you with just units of temperature.

Rewrite the ideal gas law solving for \(n\). Also show how all units cancel to leave you with just units of moles.

According to the ideal gas law: (a) If you measured \(P, V, n\), and \(T\) for any gas sample and then calculated the quantity \(P V / n T\), what would be the units and numerical value of the result? (b) If you measured \(P, V, n\), and \(T\) for any gas sample and then calculated \(P V / n R T\), what would be the units and numerical value of the result?

According to the ideal gas law, what would happen to the pressure of a gas if you doubled the amount of gas in a container while also decreasing the volume of the container to one-half its initial volume? Explain.

According to the ideal gas law, what would happen to the pressure of a gas if you doubled the amount of gas in a container while also tripling the Kelvin temperature of the gas? Explain.

A student thinks he remembers reading that if you double the temperature of an ideal gas, its. pressure doubles. He is given a problem where he has an ideal gas at \(25.0{ }^{\circ} \mathrm{C}\) and \(2.5 \mathrm{~atm}\). He is asked what the temperature must be raised to in order to double the pressure to \(5.0 \mathrm{~atm}\). He answers, \(^{\prime \prime} 50.0{ }^{\circ} \mathrm{C}\), of course." Why is he wrong? What lesson should he learn about using the ideal gas law? What is the temperature increase in Celsius degrees that will double the pressure?

The gas inside a balloon is characterized by the following measurements: pressure \(=745.5 \mathrm{~mm} \mathrm{Hg}\); volume \(=250.0 \mathrm{~mL} ;\) temperature \(=25.5^{\circ} \mathrm{C}\). What is the number of moles of gas in the balloon?

A gas is in a container whose volume is variable. The container is in an ice bath at \(0.00^{\circ} \mathrm{C}\), and there are \(2.0\) moles of gas in it. What must the volume in liters be if the gas has a pressure of \(2.5 \mathrm{~atm}\) ?

What must the Celsius temperature be if \(2.0\) moles of a gas in a 4.0-L steel container has a measured pressure of \(100 \mathrm{~atm} ?\)

An automobile tire at \(22^{\circ} \mathrm{C}\) with an internal volume of \(20.0 \mathrm{~L}\) is filled with air to a total pressure of 30 psi (pounds per square inch). \(\left[1 \mathrm{~atm}=14.696 \mathrm{lb} / \mathrm{in} .^{2}\right]\) (a) What is the amount in moles of air in the tire? (b) If the air were entirely nitrogen \(\left(\mathrm{N}_{2}\right)\), how many grams of it would be in the tire? How many pounds of it would be in the tire? \([453.6 \mathrm{~g}=1 \mathrm{lb}]\)

Why are the results that are calculated using the ideal gas law not exactly equal to the "true" results obtained by an experimental measurement?

Suppose you want to carry out the chemical reaction: \(\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \rightarrow 2 \mathrm{HCl}(g)\) and you have 1 mole of \(\mathrm{Cl}_{2}\) gas. (a) What volume in liters of \(\mathrm{H}_{2}\) gas would you need in order to have 1 mole of \(\mathrm{H}_{2}\), given that the \(\mathrm{H}_{2}\) pressure and temperature are \(1.00 \mathrm{~atm}\) and \(22.5^{\circ} \mathrm{C}\) ? (b) What would the volume of the product be if it were collected at \(1.00 \mathrm{~atm}\) and \(22.5^{\circ} \mathrm{C}\) ?

Given some mass \(m\) of a known pure substance, what is the quickest way to determine the number of moles \(n\) you have of the substance?

A 7.24-g sample of gas is contained in a 4.00-L flask. Its pressure is \(765.0 \mathrm{~mm} \mathrm{Hg}\), and its temperature is \(25.0^{\circ} \mathrm{C}\). What is the molar mass of this gas?

A 1.56-g sample of gas is contained in a \(250.0-\mathrm{mL}\) cylinder. Its pressure is \(1255.6 \mathrm{~mm} \mathrm{Hg}\), and its temperature is \(22.7{ }^{\circ} \mathrm{C}\). (a) What is the molar mass of the gas? (b) Combustion analysis reveals the empirical formula of this gas to be \(\mathrm{NO}_{2}\). What is the molecular formula?

A balloon is filled with \(\mathrm{H}_{2}\) gas to a volume of \(1610.2 \mathrm{~mL}\). The pressure of the gas in the balloon is \(745.4 \mathrm{~mm} \mathrm{Hg}\), and the temperature is \(22.7^{\circ} \mathrm{C}\). What is the mass in grams of the \(\mathrm{H}_{2}\) in the balloon?

A balloon filled with He gas and another balloon filled with \(\mathrm{H}_{2}\) gas have the same values for \(P\) and \(\bar{T}\). (a) The density of the He gas is greater than the density of the \(\mathrm{H}_{2}\) gas. How can you prove this using the ideal gas law? (b) How much more dense than the \(\mathrm{H}_{2}\) gas is the He gas?

Carbon dioxide and carbon monoxide are very different gases. For example, you exhale CO_2. but \(C O\) is extremely toxic. Suppose you have two balloons, one filled with \(1.00\) mole of CO and the other filled with 1 mole of \(\mathrm{CO}_{2}\). Both gases are at \(1.00 \mathrm{~atm}\) and \(25.0^{\circ} \mathrm{C}\). (a) What is the volume in liters of each balloon? (b) What did you learn about gases from doing this problem?