Chapter 10

Suppose the temperature of the gas in Figure \(\mathrm{P} 10.2(\mathrm{b})\) increases from \(200 \mathrm{K}\) to \(400 \mathrm{K}\) but that the pressure on the piston remains constant. Does the position of the piston change? If so, by how much does the volume of the gas change?

What is meant by the root-mean-square speed of gas particles?

Why is the root-mean-square speed of gas particles greater than the simple average of their speeds?

Does pressure affect the root-mean-square speed of the particles in a gas? Why or why not?

How is the rate of effusion of a gas related to each of the following? a. Molar mass b. Root-mean-square speed c. Temperature d. Density

Rank the gases \(\mathrm{NO}, \mathrm{NO}_{2}, \mathrm{N}_{2} \mathrm{O}_{4},\) and \(\mathrm{N}_{2} \mathrm{O}_{5}\) in order of increasing root-mean-square speed at \(0^{\circ} \mathrm{C}\).

Chlorofluorocarbons Chlorofluorocarbons with the general formula \(\mathrm{CF}_{n} \mathrm{Cl}_{4-n}\) were used for decades in refrigerators and air conditioners until they were found to degrade Earth's ozone layer. For which value of \(n\) is the rate of effusion the slowest? Which compound will effuse at the fastest rate?

Molecular hydrogen effuses 4.0 times as fast as gas \(\mathrm{X}\) at the same temperature. What is the molar mass of gas X?

Which noble gas effuses 3.2 times faster than argon at \(0^{\circ} \mathrm{C}\)?

Methane, \(\mathrm{CH}_{4},\) and propane, \(\mathrm{C}_{3} \mathrm{H}_{8},\) are both used as fuel for cooking. a. What are the root-mean-square speeds of \(\mathrm{CH}_{4}\), ethane \(\left(\mathrm{C}_{2} \mathrm{H}_{6}\right),\) and \(\mathrm{C}_{3} \mathrm{H}_{8}\) at \(298 \mathrm{K} ?\) b. Plot the root-mean-square speeds of these gases as a function of their molar mass and use it to predict the root-mean-square speed of butane \(\left(\mathrm{C}_{4} \mathrm{H}_{10}\right)\) and pentane \(\left(\mathrm{C}_{5} \mathrm{H}_{12}\right)\) c. Of the major components of natural gas, \(\mathrm{CH}_{4}, \mathrm{C}_{2} \mathrm{H}_{6}\) \(\mathrm{C}_{3} \mathrm{H}_{8},\) and \(\mathrm{C}_{4} \mathrm{H}_{10},\) which gas effuses from a sample of natural gas the most rapidly?

The London dispersion forces in the three different isomers of \(\mathrm{C}_{5} \mathrm{H}_{12}\) lead to different boiling points for pentane, 2-methylbutanc, and 2,2 -dimethylbutanc \((309 \mathrm{K}, 301 \mathrm{K}\) and \(282 \mathrm{K}\), respectively, Figure 6.3 ). a. What are the root-mean-square speeds of the three isomers of pentane at \(325 \mathrm{K} ?\) b. Using the KMT model, describe why calculated root-mean-square speeds are not influenced by the inter-molecular forces that the molecules of these isomers apparently experience.

Determine the root-mean-square speed of \(\mathrm{CO}_{2}\) molecules that have an average kinetic energy of \(3.2 \times 10^{-21} \mathrm{J}\) per molecule.

A flask of ammonia is connected to a flask of an unknown acid HX by a \(1.00 \mathrm{m}\) glass tube. As the two gases diffuse down the tube, a white ring of \(\mathrm{NH}_{4} \mathrm{X}\) forms \(68.5 \mathrm{cm}\) from the ammonia flask. Identify element X.

Enriching Uranium The two isotopes of uranium, \(^{238} \mathrm{U}\) and \(^{235} \mathrm{U},\) can be separated by diffusion of the corresponding UF \(_{6}\) gases. What is the ratio of the root-mean-square speed of \(^{238} \mathrm{UF}_{6}\) to that of \(^{235} \mathrm{UF}_{6}\) at constant temperature?

Describe the difference between force and pressure.

Why does atmospheric pressure decrease with increasing elevation?

Three barometers based on Torricelli's design are constructed using water (density \(d=1.00 \mathrm{g} / \mathrm{mL}),\) ethanol \((d=0.789 \mathrm{g} / \mathrm{mL}),\) and mercury \((d=13.546 \mathrm{g} / \mathrm{mL}) .\) Which barometer contains the tallest column of liquid?

In constructing a barometer based on Torricelli's design, what advantage is there in choosing a dense liquid?

Why does an ice skater exert more pressure on ice when wearing newly sharpened skates than when wearing skates with dull blades?

Convert the following pressures into atmospheres: (a) \(2.0 \mathrm{kPa} ;\) (b) \(562 \mathrm{mmHg}\)

Convert the following pressures into millimeters of mercury: (a) 0.541 atm; (b) 2.8 kPa.

Record Low Atmospheric Pressure Despite the destruction from Hurricane Katrina in August \(2005,\) the lowest pressure for a hurricane in the Atlantic Ocean was measured several weeks after Katrina. Hurricane Wilma registered an atmospheric pressure of \(88.2 \mathrm{kPa}\) on October \(19,2005,\) about \(2 \mathrm{kPa}\) lower than Hurricane Katrina. What was the difference in pressure between the two hurricanes in (a) millimeters of mercury, (b) atmospheres, and (c) millibars?

How does kinetic molecular theory explain why pressure is directly proportional to temperature at fixed volume (Amontons's law)?

Explain Boyle's law using kinetic molecular theory.

A hot-air balloonist is rising too fast for her liking. Should she increase or decrease the temperature of the gas in the balloon?

The volume of a quantity of gas at 1.00 atm is compressed from \(3.25 \mathrm{L}\) to \(2.24 \mathrm{L} .\) What is the final pressure of the gas if there is no change in temperature?

The pressure on a sample of an ideal gas is increased from \(715 \mathrm{mmHg}\) to 3.55 atm at constant temperature. If the initial volume of the gas is \(485 \mathrm{mL},\) what is the final volume of the gas?

A \(4.66 \mathrm{L}\) sample of gas is warmed from \(273 \mathrm{K}\) to a final temperature of \(398 \mathrm{K}\). Assuming no change in pressure, what is the final volume of the gas?

A 22.5 L sample of gas is cooled from \(145^{\circ} \mathrm{C}\) to a temperature at which its volume is \(18.3 \mathrm{L}\). What is the new temperature? Assume no change in pressure of the gas.

Balloons for a New Year's Eve party in Potsdam, New York, are filled to a volume of \(5.0 \mathrm{L}\) at a temperature of \(20^{\circ} \mathrm{C}\) and then hung outside where the temperature is \(-25^{\circ} \mathrm{C} .\) What is the volume of the balloons after they have cooled to the outside temperature? Assume that atmospheric pressure inside and outside the house is the same.

The air inside a balloon is heated to \(45^{\circ} \mathrm{C}\) and then cools to \(25^{\circ} \mathrm{C} .\) By what percentage does the volume of the balloon change during cooling?

Scuba Diving A popular scuba tank for sport diving has an internal volume of \(12.0 \mathrm{L}\) and can be filled with air up to a pressure of 232 bar. Suppose a diver consumes air at the rate of \(21 \mathrm{L} / \mathrm{min}\) while diving on a coral reef where the sum of atmospheric pressure and water pressure averages 2.2 bar. How long will it take the diver to use up a full tank of air if the temperatures of the air and water on the reef are both \(28^{\circ} \mathrm{C} ?\)

Which of the following actions would produce the greater increase in the volume of a gas sample? a. Lowering the pressure from \(760 \mathrm{mm} \mathrm{Hg}\) to \(700 \mathrm{mmHg}\) at constant temperature b. Raising the temperature from \(10^{\circ} \mathrm{C}\) to \(35^{\circ} \mathrm{C}\) at constant pressure

Which of the following actions would produce the greater increase in the volume of a gas sample? a. Doubling the amount of gas in the sample at constant temperature and pressure b. Raising the temperature from \(244^{\circ} \mathrm{C}\) to \(1100^{\circ} \mathrm{C}\)

What happens to the volume of gas in a cylinder with a movable piston under the following conditions? a. Both the absolute temperature and the external pressure on the piston double. b. The absolute temperature is halved, and the external pressure on the piston doubles. c. The absolute temperature increases by \(75 \%,\) and the external pressure on the piston increases by \(50 \%\).

What happens to the pressure of a gas under the following conditions? a. The absolute temperature is halved and the volume doubles. b. Both the absolute temperature and the volume double. c. The absolute temperature increases by \(75 \%,\) and the volume decreases by \(50 \%\).

A \(150.0 \mathrm{L}\), weather balloon contains 6.1 moles of helium but loses it at a rate of \(10 \mathrm{mmol} / \mathrm{h}\). What is the volume of the balloon after \(24 \mathrm{h}\) ?

Which has the greater effect on the volume of a gas at constant temperature: doubling the number of moles of gas or reducing the pressure by half?

Temperature Effects on Bicycle Tires A bicycle racer inflates his tires to 7.1 atm on a warm autumn afternoon when temperatures reach \(27^{\circ} \mathrm{C} .\) By morning the temperature has dropped to \(5.0^{\circ} \mathrm{C} .\) What is the pressure in the tires if we assume that the volume of the tire does not change significantly?

The volume of a weather balloon is \(200.0 \mathrm{L}\) and its internal pressure is 1.17 atm when it is launched at \(20^{\circ} \mathrm{C}\). The balloon rises to an altitude in the stratosphere where its internal pressure is \(63 \mathrm{mmHg}\) and the temperature is \(210 \mathrm{K} .\) What is the volume of the balloon at this altitude?

What is meant by standard temperature and pressure (STP)? What is the volume of one mole of an ideal gas at STP?

Which of the following are not characteristics of an ideal gas? a. The molecules of gas have insignificant volume compared with the volume that they occupy. b. Its volume is independent of temperature. c. The density of all ideal gases is the same. d. Gas atoms or molecules do not interact with one another.

How many moles of air must there be in a racing bicycle tire with a volume of \(2.36 \mathrm{L}\) if it has an internal pressure of 6.8 atm at \(17.0^{\circ} \mathrm{C} ?\)

At what temperature will 1.00 mol of an ideal gas in a \(1.00 \mathrm{L}\) container exert a pressure of 1.00 atm?

Hyperbolic Oxygen Therapy Hyperbolic oxygen chambers are used to treat divers suffering from decompression sickness (the "bends") with pure oxygen at greater than atmospheric pressure. Other clinical uses include treatment of patients with thermal burns and CO poisoning. What is the pressure in a chamber with a volume of \(4.85 \times 10^{3} \mathrm{L}\) that contains \(15.00 \mathrm{kg}\) of \(\mathrm{O}_{2}(g)\) at per ef \(298 \mathrm{K} ?\)

In some cities public buses are fueled by compressed natural gas (mostly methane, \(\mathrm{CH}_{4}\) ). How many grams of \(\mathrm{CH}_{4}\) gas are in a \(250 \mathrm{L}\) fuel tank at a pressure of 255 bar at \(20^{\circ} \mathrm{C} ?\)

Liquid Nitrogen-Powered Car Students at the University of North Texas and the University of Washington built a car propelled by compressed nitrogen gas. The gas was obtained by boiling liquid nitrogen stored in a \(182 \mathrm{L}\) tank. What volume of \(\mathrm{N}_{2}\) is released at 0.927 atm of pressure and \(25^{\circ} \mathrm{C}\) from a tank full of liquid \(\mathrm{N}_{2}\) \((d=0.808 \mathrm{g} / \mathrm{mL}) ?\)

A balloon vendor at a street fair is using a tank of helium to fill her balloons. The tank has an internal volume of \(45.0 \mathrm{L}\) and a pressure of 195 atm at \(22^{\circ} \mathrm{C}\). After a while she notices that the valve has not been closed properly and the pressure has dropped to 115 atm. How many moles of He have been lost?

The volume of 0.50 mol of a noble gas was measured at the temperatures listed in the following table. The pressure of the gas was 1.00 atm at all times. Use the data in the table to calculate the value of \(R,\) the ideal gas law constant. $$\begin{array}{cc}V(L) & T(K) \\\3.94 & 96 \\\\\hline 1.97 & 48 \\\\\hline 0.79 & 24 \\\\\hline 0.39 & 9.6 \\\\\hline 0.20 & 4.8 \\\\\hline\end{array}$$

Do all gases at the same pressure and temperature have the same density? Explain your answer.