Chapter 10

If you get jabbed by a pencil, why does it hurt so much more if it's with the sharp point rather than the eraser? Explain in terms of the concepts of force and pressure.

Write expressions that could be used to form conversion factors to convert between: (a) kilopascal and atm, (b) torr and \(\mathrm{mm} \mathrm{Hg}\), (c) bar and pascal, (d) torr and atm, (e) torr and pascal, (f) bar and atm.

At \(20^{\circ} \mathrm{C}\) the density of mercury is \(13.6 \mathrm{~g} \mathrm{~mL}^{-1}\) and that of water is \(1.00 \mathrm{~g} \mathrm{~mL}^{-1}\). At \(20^{\circ} \mathrm{C}\), the vapor pressure of mercury is 0.0012 torr and that of water is 18 torr. Give and explain two reasons why water would be an inconvenient fluid to use in a Torricelli barometer.

What is the advantage of using a closed-end manometer, rather than an open-end one, when measuring the pressure of a trapped gas? What is the disadvantage?

Express the following gas laws in equation form: (a) temperature-volume law (Charles' law), (b) temperaturepressure law (Gay-Lussac's law), (c) pressure- volume law (Boyle's law), (d) combined gas law.

Which of the four important variables in the study of the physical properties of gases are assumed to be held constant in each of the following laws? (a) Boyle's law, (b) Charles' law, (c) Gay-Lussac's law, (d) combined gas law.

Determine how to plot the two properties of gases listed with each of the following gas laws so that the graph will be a straight line: (a) temperature- volume law (Charles" law), (b) temperature-pressure law (Gay-Lussac's law), (c) pressure-volume law (Boyle's law).

What is meant by an ideal gas? Under what conditions does a real gas behave most like an ideal gas?

Explain Avogadro's principle in your own words. Explain why the volumes need to be measured at a constant temperature and pressure.

State the ideal gas law in the form of an equation. What is the value of the gas constant in units of \(\mathrm{L}\) atm \(\mathrm{mol}^{-1} \mathrm{~K}^{-1} ?\)

Using the ideal gas law, show that at STP, the molar volume of an ideal gas is \(22.4 \mathrm{~L}\).

The molar mass of a gas can be determined from its mass, volume, pressure, and temperature. Derive the equation from the ideal gas law and the definition of molar mass.

The density of a gas can vary with pressure, volume, and temperature. Develop an equation for density from the ideal gas law.

State Dalton's law of partial pressures in the form of an equation.

Define mole fraction. How is the partial pressure of a gas related to its mole fraction and the total pressure?

Explain how a gas is collected over water. Why does the temperature of the gas need to be known to determine the pressure of the gas collected over water?

What is the difference between diffusion and effusion? State Graham's law in the form of an equation.

Describe the model of a gas proposed by the kinetic theory of gases.

Use the kinetic molecular theory of gases to explain (a) Charles' law and (b) Boyle's law.

If the molecules of a gas at constant volume are somehow given a lower average kinetic energy, what two measurable properties of the gas will change and in what direction?

Explain how raising the temperature of a gas causes it to expand at constant pressure. (Hint: Describe how the model of an ideal gas connects the increase in temperature to the gas expansion.)

Explain in terms of the kinetic theory how raising the temperature of a confined gas makes its pressure increase.

How does the kinetic theory explain the existence of an absolute zero, \(0 \mathrm{~K}\) ?

What does a small value for the van der Waals constant \(a\) suggest about the molecules of the gas?

Under the same conditions of \(T\) and \(V\), why is the pressure of a real gas less than the pressure the gas would exert if it were ideal? At a given \(T\) and \(P\), why is the volume of a real gas larger than it would be if the gas were ideal?

Suppose we have a mixture of helium and argon. On average, which atoms are moving faster at \(25^{\circ} \mathrm{C},\) and why?

Carry out the following unit conversions: (a) 1.26 atm to torr, (b) 740 torr to atm, (c) 738 torr to \(\mathrm{mm} \mathrm{Hg}\), (d) \(1.45 \times 10^{3} \mathrm{~Pa}\) to torr.

Carry out the following unit conversions: (a) 0.625 atm to torr, (b) 825 torr to atm, (c) \(62 \mathrm{~mm} \mathrm{Hg}\) to torr, (d) \(1.22 \mathrm{kPa}\) to bar.

What is the pressure in torr of the following? (a) 0.329 atm (summit of \(M \mathrm{t}\). Everest, the world's highest mountain) (b) 0.460 atm (summit of Mt. Denali, the highest mountain in the United States)

What is the pressure in atm of each of the following? (These are the values of the pressures exerted individually by \(\mathrm{N}_{2}, \mathrm{O}_{2},\) and \(\mathrm{CO}_{2},\) respectively, in typical inhaled air.) (a) 595 torr, (b) 160 torr (c) 0.300 torr

An open-end manometer containing mercury was connected to a vessel holding a gas at a pressure of 720 torr. The atmospheric pressure was 765 torr. Sketch a diagram of the apparatus showing the relative heights of the mercury in the two arms of the manometer. What is the difference in the heights of the mercury expressed in centimeters?

An open-end manometer containing mercury was connected to a vessel holding a gas at a pressure of 820 torr. The atmospheric pressure was 750 torr. Sketch a diagram of the apparatus showing the relative heights of the mercury in the two arms of the manometer. What is the difference in the heights of the mercury expressed in centimeters?

An open-end mercury manometer was connected to a flask containing a gas at an unknown pressure. The mercury in the arm open to the atmosphere was \(65 \mathrm{~mm}\) higher than the mercury in the arm connected to the flask. The atmospheric pressure was 748 torr. What was the pressure of the gas in the flask (in torr)?

An open-end mercury manometer was connected to a flask containing a gas at an unknown pressure. The mercury in the arm open to the atmosphere was \(65 \mathrm{~mm}\) higher than the mercury in the arm connected to the flask. The atmospheric pressure was 748 torr. What was the pressure of the gas in the flask (in torr)?

A sample of nitrogen has a volume of \(880 \mathrm{~mL}\) and a pressure of 740 torr. What pressure will change the volume to \(550 \mathrm{~mL}\) at the same temperature?

A gas has a volume of \(255 \mathrm{~mL}\) at 725 torr. What volume will the gas occupy at 365 torr if the temperature of the gas doesn't change?

A gas has a volume of \(3.86 \mathrm{~L}\) at \(45^{\circ} \mathrm{C}\). What will the volume of the gas be if its temperature is raised to \(87^{\circ} \mathrm{C}\) while its pressure is kept constant?

A sample of a gas has a pressure of 854 torr at \(285^{\circ} \mathrm{C}\). To what Celsius temperature must the gas be heated to double its pressure if there is no change in the volume of the gas?

A sample of helium at a pressure of 745 torr and in a volume of \(2.58 \mathrm{~L}\) was heated from 24.0 to \(75.0^{\circ} \mathrm{C}\). The volume of the container expanded to \(2.81 \mathrm{~L}\). What was the final pressure (in torr) of the helium?

When a sample of neon with a volume of \(648 \mathrm{~mL}\) and a pressure of 0.985 atm was heated from 16.0 to \(63.0^{\circ} \mathrm{C}\), its volume became \(689 \mathrm{~mL}\). What was its final pressure (in atm)?

When \(286 \mathrm{~mL}\) of oxygen at 741 torr and \(18.0{ }^{\circ} \mathrm{C}\) was warmed to \(33.0^{\circ} \mathrm{C}\), the pressure became 765 torr. What was the final volume (in \(\mathrm{mL}\) )?

A sample of argon with a volume of \(6.18 \mathrm{~L}\), a pressure of 761 torr, and a temperature of \(20.0^{\circ} \mathrm{C}\) expanded to a volume of \(9.45 \mathrm{~L}\) and a pressure of 373 torr. What was its final temperature in \({ }^{\circ} \mathrm{C}\) ?

A sample of a refrigeration gas in a volume of \(455 \mathrm{~mL},\) at a pressure of 1.51 atm and at a temperature of \(25.0^{\circ} \mathrm{C}\), was compressed into a volume of \(222 \mathrm{~mL}\) with a pressure of \(2.00 \mathrm{~atm}\). To what temperature (in \({ }^{\circ} \mathrm{C}\) ) did it have to change?

How many milliliters of oxygen are required to react completely with \(175 \mathrm{~mL}\) of \(\mathrm{C}_{4} \mathrm{H}_{10}\) if the volumes of both gases are measured at the same temperature and pressure? The reaction is $$ 2 \mathrm{C}_{4} \mathrm{H}_{10}(g)+13 \mathrm{O}_{2}(g) \longrightarrow 8 \mathrm{CO}_{2}(g)+10 \mathrm{H}_{2} \mathrm{O}(g) $$

A chemist isolated a gas in a glass bulb with a volume of \(255 \mathrm{~mL}\) at a temperature of \(25.0{ }^{\circ} \mathrm{C}\) and a pressure (in the bulb) of 10.0 torr. The gas weighed \(12.1 \mathrm{mg}\). What is the molar mass of this gas?

At \(22.0^{\circ} \mathrm{C}\) and a pressure of 755 torr, a gas was found to have a density of \(1.13 \mathrm{~g} \mathrm{~L}^{-1}\). Calculate its molar mass.

To three significant figures, calculate the density in \(\mathrm{g} \mathrm{L}^{-1}\) of the following gases at STP: (a) \(\mathrm{C}_{2} \mathrm{H}_{6}\) (ethane), (b) \(\mathrm{N}_{2}\), (c) \(\mathrm{Cl}_{2}\) (d) Ar.

To three significant figures, calculate the density in \(\mathrm{g} \mathrm{L}^{-1}\) of the following gases at \(S T P\) : (a) \(\mathrm{Ne}\), (b) \(\mathrm{O}_{2},\) (c) \(\mathrm{CH}_{4}\) (methane), (d) CF \(_{4}\).

A mixture of gases contains 315 torr \(\mathrm{N}_{2}, 275\) torr \(\mathrm{O}_{2}\), and 285 torr Ar. What is the total pressure of the mixture? What is the mole fraction of \(\mathrm{O}_{2}\) in this mixture?

A certain biological incubator gas mixture contains 29 torr \(\mathrm{CO}_{2}, 313\) torr \(\mathrm{H}_{2}, 383\) torr \(\mathrm{N}_{2}\). What is the total pressure of the mixture? What is the mole fraction of \(\mathrm{H}_{2}\) in this mixture?