Solved: Identify the Maxwell speed distribution curves

Calculate the volume (in liters) occupied by 2.12 moles of nitric oxide (NO) at 6.54 atm and 76°C.

Compare the changes in volume when the temperature of a gas is doubled at constant pressure from (a) 200K to 400 K and (b) 200°C to 400°C.

When you are in a plane flying at high altitudes, your ears often experience pain. This discomfort can be temporarily relieved by yawning or swallowing some water. Explain.

What is the volume (in liters) occupied by 49.8 g of HCl at STP?

Assuming ideal behavior, which of the following gases will have the greatest volume at STP? (a) 0.82 mole of He, (b) 24 g of \(N_{2}\). (c) \(5.0 \times 10^{23}\) molecules of \(\mathrm{Cl}_{2}\), Which gas will have the greatest density?

Why is mercury a more suitable substance to use in a barometer than water?

A sample of chlorine gas occupies a volume of 946 mL, at a pressure of 726 mmHg. Calculate the pressure of the gas (in mmHg) if the volume is reduced at constant temperature to 154 mL.

Each of the color spheres represents a different gas molecule. Calculate the partial pressures of the gases if the total pressure is 2.6 atm.

Explain why the height of mercury in a barometer is independent of the cross-sectional area of the tube. Would the barometer still work if the tubing were tilted at an angle, say 15° (see Figure 5.3)?

A sample of oxygen gas initially at 0.97 atm is cooled from 21°C to ?68°C at constant volume. What is its final pressure (in atm)?

Problem 6RC If one mole each of He and Cl2 gases are compared at STP, which of the following quantities will be equal to each other? (a) Root-mean-square speed, (b) effusion rate, (c) average kinetic energy, (d) volume.

Explain how a unit of length (mmHg) can be used as a unit for pressure.

A gas initially at \(4.0 \mathrm{~L}, 1.2\) atm, and \(66^{\circ} \mathrm{C}\) undergoes a change so that its final volume and temperature are \(1.7 \mathrm{~L}\) and \(42^{\circ} \mathrm{C}\). What is its final pressure? Assume the number of moles remains unchanged.

What pressure and temperature conditions cause the most deviation from ideal gas behavior?

Describe what would happen to the column of mercury in the following manometers when the stopcock is opened.

What is the density (in \(\mathrm{g} / \mathrm{L}\) ) of uranium hexafluoride \(\left(\mathrm{UF}_{6}\right)\) at 779 \(\mathrm{mmHg}\) and \(62^{\circ} \mathrm{C}\) ?

What is the difference between a gas and a vapor? At 25°C, which of the following substances in the gas phase should be properly called a gas and which should be callled a vapor: molecular nitrogen (\(N_{2}\)) mercury?

The density of a gaseous organic compound is 3.38 g/L at 40°C and 1.97 atm. What is its molar mass?

If the maximum distance that water may be brought up a well by a suction pump is 34 ft (10.3 m), how is it possible to obtain water and oil from hundreds of feet below the surface of Earth?

A gaseous compound is 78.14 percent boron and 21.86 percent hydrogen. At 27°C, 74.3 mL of the gas exerted a pressure of 1.12 atm. If the mass of the gas was 0.0934 g, what is its molecular formula?

Why is it that if the barometer reading falls in one part of the world, it must rise somewhere else?

Assuming no change in temperature and pressure, calculate the volume of \(O_2\) (in liters) required for the complete combustion of 14.9 L of butane (\(C_4H_{10}\)): \(2C_4{H}_{10}(g)+13{O}_2(g)\longrightarrow 8{CO}_2(g)+10{H}_2{O}(l)\)

Why do astronauts have to wear protective suits when they are on the surface of the moon?

Convert 562 mmHg to atm.

The equation for the metabolic breakdown of glucose (\(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\)) is the same as the equation for the combustion of glucose in air: \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(\mathrm{s})+6 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 6 \mathrm{CO}_{2}(\mathrm{g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})\) Calculate the volume of \(\mathrm{CO}_{2}\) produced at 37? and 1.00 atm when 5.60 g of glucose is used up in the reaction.

A 2.14-L sample of hydrogen chloride (HCl) gas at 2.61 atm and 28°C is completely dissolved in 668 mL of water to form hydrochloric acid solution. Calculate the molarity of the acid solution. Assume no change in volume.

The atmospheric pressure at the summit of Mt. McKinley is \(606 \ \mathrm{mmHg}\) on a certain day. What is the pressure in atm and in kPa?

A sample of natural gas contains 8.24 moles of methane (\(C_{4}\)), 0.421 mole of ethane (\(C_{2} H_{6}\)), and 0.116 mole of propane (\(C_{3} H_{8}\)). If the total pressure of the gases is 1.37 atm, what are the partial pressures of the gases?

State the following gas laws in words and also in the form of an equation: Boyle’s law, Charles’s law, Avogadro’s law. In each case, indicate the conditions under which the law is applicable, and give the units for each quantity in the equation.

Hydrogen gas generated when calcium metal reacts with water is collected as shown in Figure 5.15. The volume of gas collected at 30°C and pressure of 988 mmHg is 641 mL. What is the mass (in grams) of the hydrogen gas obtained? The pressure of water vapor at 30°C is 31.82 mmHg.

Calculate the root-mean-square speed of molecular chlorine in m/s at 20°C.

A certain amount of gas is contained in a closed a mercury manometer as shown here. Assuming no other parameters change, would h increase, decrease or remain the same if (a) the amount of the gas were increased; (b) the molar mass of the gas were doubled; (c) the temperature of the gas was increased; (e) the mercury in the tube were replaced with a less dense fluid; (f) some gas was added to the vacuum at the top of the right-side tube; (g) a hole was drilled in the top of the right side tube?

A gaseous sample of a substance is cooled at constant pressure. Which of the following diagrams best represents the situation if the final temperature is (a) above the boiling point of the substance and (b) below the boiling point but above the freezing point of the substance?

It takes 192 s for an unknown gas to effuse through a porous wall and 84 s for the same volume of \(N_{2}\) gas to effuse at the same temperature and pressure. What is the molar mass of the unknown gas?

Consider the following gaseous sample in a cylinder fitted with a movable piston. Initially there are n moles of the gas at temperature T, pressure P. and volume V. Choose the cylinder that correctly represents the gas after each of the following changes. (1) The pressure on the piston is tripled at constant n and T. (2) The temperature is doubled at constant n and P. (3) n moles of another gas are added at constant T and P. (4) T is halved and pressure on the piston is reduced to a quarter of its original value

Using the data shown in Table 5.4, calculate the pressure exerted by 4.37 moles of molecular chlorine confined in a volume of 2.45 L at 38°C. Compare the pressure with that calculated using the ideal gas equation.

A gas occupying a volume of \(725 \mathrm{~mL}\) at a pressure of \(0.970 \mathrm{~atm}\) is allowed to expand at constant temperature until its pressure reaches \(0.541 \mathrm{~atm}\). What is its final volume?

At 46°C a sample of ammonia gas exerts a pressure of 5.3 atm. What is the pressure when the volume of the gas is reduced to one-tenth (0.10) of the original value at the same temperature?

The volume of gas is 5.80L, measured at 1.00 atm. what is the pressure of the gas in mmHg if the volume is changed to 9.65L? (The temperature remains constant.)

A sample of air occupies 3.8 L when the pressure is 1.2 atm. (a) What volume does it occupy at 6.6 atm? (b) What pressure is required in order to compress it to 0.075 L? (The temperature is kept constant.)

A 36.4-L volume of methane gas is heated from \(25^{\circ} \mathrm{C}\) to \(88^{\circ} \mathrm{C}\) at constant pressure. What is the final volume of the gas?

Under constant-pressure conditions a sample of hydrogen gas initially at 88°C and 9.6 L is cooled until its final volume is 3.4 L. What is its final temperature ?

Ammonia burns in oxygen gas to form nitric oxide \((\mathrm{NO})\) and water vapor. How many volumes of \(\mathrm{NO}\) are obtained from one volume of ammonia at the same temperature and pressure?

Molecular chlorine and molecular fluorine combine to form a gaseous product. Under the same conditions of temperature and pressure it is found that one volume of \(\mathrm{Cl}_{2}\) reacts with three volumes of \(F_{2}\) to yield two volumes of the product. What is the formula of the product?

List the characteristics of an ideal gas. Write the ideal gas equation and also state it in words. Give the units for each term in the equation.

Use Equation (5.9) to derive all the gas laws.

What is the significance of STP in relation to the volume of 1 mole of an ideal gas?

Why is the density of a gas much lower than that of a liquid or solid under atmospheric conditions? What units are normally used to express the density of gases?

A sample of nitrogen gas kept in a container of volume \(2.3 \mathrm{~L}\) and at a temperature of \(32^{\circ} \mathrm{C}\) exerts a pressure of \(4.7 \mathrm{~atm}\). Calculate the number of moles of gas present.

Given that 6.9 moles of carbon monoxide gas are present in a container of volume \(30.4 \mathrm{~L}\), what is the pressure of the gas (in atm) if the temperature is \(62^{\circ} \mathrm{C}\)?

What volume will \(5.6\) moles of sulfur hexafluoride \(\left(\mathrm{SF}_{6}\right)\) gas occupy if the temperature and pressure of the gas are \(128^{\circ} \mathrm{C}\) and \(9.4 \mathrm{~atm}\)?

Under the same conditions of temperature and pressure, why does one liter of moist air weigh less than one liter of dry air? In weather forecasts, an oncoming low-pressure front usually means imminent rainfall. Explain.

Air entering the lungs ends up in tiny sacs called alveoli. It is from the alveoli that oxygen diffuses into the blood. The average radius of the alveoli is 0.0050 cm and the air inside contains 14 percent oxygen. Assuming that the pressure in the alveoli is 1.0 atm and the temperature is \(37^{\circ} \mathrm{C}\), calculate the number of oxygen molecules in one of the alveoli. (Hint: The volume of a sphere of radius r is \(\frac{4}{3} \pi r^{3}\).)

A student breaks a thermometer and spills most of the mercury (Hg) onto the floor of a laboratory that measures 15.2 m long, 6.6 m wide, and 2.4 m high. (a) Calculate the mass of mercury vapor (in grams) in the room at \(20^{\circ} \mathrm{C}\). The vapor pressure of mercury at \(20^{\circ} \mathrm{C}\) is \(1.7 \times 10^{-6}\ \mathrm{atm}\). (b) Does the concentration of mercury vapor exceed the air quality regulation of \(0.050\ \mathrm{mg\ Hg} / \mathrm{m}^{3}\) of air? (c) One way to treat small quantities of spilled mercury is to spray sulfur powder over the metal. Suggest a physical and a chemical reason for this action.

Consider two bulbs containing argon (left) and oxygen (right) gases. After the stopcock is opened, the pressure of the combined gases is 1.08 atm. Calculate the volume of the right bulb. The temperature is kept at \(20^{\circ} \mathrm{C}\). Assume ideal behavior.

Nitrogen dioxide \(\left(\mathrm{NO}_{2}\right)\) cannot be obtained in a pure form in the gas phase because it exists as a mixture of \(\mathrm{NO}_{2}\) and \(\mathrm{N}_{2} \mathrm{O}_{4}\). At \(25^{\circ} \mathrm{C}\) and 0.98 atm, the density of this gas mixture is 2.7 g/L. What is the partial pressure of each gas?

The Chemistry in Action essay on p. 208 describes the cooling of rubidium vapor to \(1.7 \times 10^{-7}\ \mathrm{K}\). Calculate the root-mean-square speed and average kinetic energy of a Rb atom at this temperature.

Lithium hydride reacts with water as follows: \(\mathrm{LiH}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{LiOH}(a q)+\mathrm{H}_{2}(g)\) During World War II, U.S. pilots carried LiH tablets. In the event of a crash landing at sea, the LiH would react with the seawater and fill their life belts and lifeboats with hydrogen gas. How many grams of LiH are needed to fill a 4.1-L life belt at 0.97 atm and \(12^{\circ} \mathrm{C}\)?

The atmosphere on Mars is composed mainly of carbon dioxide. The surface temperature is 220 K and the atmospheric pressure is about 6.0 mmHg. Taking these values as Martian "STP," calculate the molar volume in liters of an ideal gas on Mars.

Venus's atmosphere is composed of 96.5 percent \(\mathrm{CO}_{2}\), 3.5 percent \(N_{2}\), and 0.015 percent \(\mathrm{SO}_{2}\) by volume. Its standard atmospheric pressure is \(9.0 \times 10^{6}\ \mathrm{Pa}\). Calculate the partial pressures of the gases in pascals.

A student tries to determine the volume of a bulb like the one shown on p. 191. These are her results: Mass of the bulb filled with dry air at \(23^{\circ} \mathrm{C}\) and 744 mmHg = 91.6843 g; mass of evacuated bulb = 91.4715 g. Assume the composition of air is 78 percent \(N_{2}\), 21 percent \(\mathrm{O}_{2}\), and 1 percent argon. What is the volume (in milliliters) of the bulb? (Hint: First calculate the average molar mass of air, as shown in Problem 3.152.)

Apply your knowledge of the kinetic theory of gases to the following situations. (a) Two flasks of volumes \(V_{1}\) and \(V_{2}\left(V_{2}>V_{1}\right)\) contain the same number of helium atoms at the same temperature. (i) Compare the root-mean-square (rms) speeds and average kinetic energies of the helium (He) atoms in the flasks. (ii) Compare the frequency and the force with which the He atoms collide with the walls of their containers. (b) Equal numbers of He atoms are placed in two flasks of the same volume at temperatures \(T_{1}\) and \(T_{2}\left(T_{2}>T_{1}\right)\). (i) Compare the rms speeds of the atoms in the two flasks. (ii) Compare the frequency and the force with which the He atoms collide with the walls of their containers. (c) Equal numbers of He and neon (Ne) atoms are placed in two flasks of the same volume, and the temperature of both gases is \(74^{\circ} \mathrm{C}\). Comment on the validity of the following statements: (i) The rms speed of He is equal to that of Ne. (ii) The average kinetic energies of the two gases are equal. (iii) The rms speed of each He atom is \(1.47 \times 10^{3}\ \mathrm{m} / \mathrm{s}\).

It has been said that every breath we take, on average, contains molecules that were once exhaled by Wolfgang Amadeus Mozart (1756-1791). The following calculations demonstrate the validity of this statement. (a) Calculate the total number of molecules in the atmosphere. (Hint: Use the result in Problem 5.106 and 29.0 g/mol as the molar mass of air.) (b) Assuming the volume of every breath (inhale or exhale) is 500 mL, calculate the number of molecules exhaled in each breath at \(37^{\circ} \mathrm{C}\), which is the body temperature. (c) If Mozart's life span was exactly 35 years, what is the number of molecules he exhaled in that period? (Given that an average person breathes 12 times per minute.) (d) Calculate the fraction of molecules in the atmosphere that was exhaled by Mozart. How many of Mozart's molecules do we breathe in with every inhalation of air? Round off your answer to one significant figure. (e) List three important assumptions in these calculations.

At what temperature will He atoms have the same \(u_{r m s}\) value as \(N_{2}\) molecules at \(25^{\circ} \mathrm{C}\)?

Which of the noble gases would not behave ideally under any circumstances? Why?

Estimate the distance (in nanometers) between molecules of water vapor at \(100^{\circ} \mathrm{C}\) and 1.0 atm. Assume ideal behavior. Repeat the calculation for liquid water at \(100^{\circ} \mathrm{C}\), given that the density of water is \(0.96\ \mathrm{g} / \mathrm{cm}^{3}\) at that temperature. Comment on your results. (Assume water molecule to be a sphere with a diameter of 0.3 nm.) (Hint: First calculate the number density of water molecules. Next, convert the number density to linear density, that is, number of molecules in one direction.)

A relation known as the barometric formula is useful for estimating the change in atmospheric pressure with altitude. The formula is given by \(P=P_{0} e^{-g \mu h / R T}\), where P and \(P_{0}\) are the pressures at height h and sea level, respectively, g is the acceleration due to gravity \(\left(9.8\ \mathrm{m} / \mathrm{s}^{2}\right)\), \(\mu\) is the average molar mass of air (29.0 g/mol), and R is the gas constant. Calculate the atmospheric pressure in atm at a height of 5.0 km, assuming the temperature is constant at \(5^{\circ} \mathrm{C}\) and \(P_{0}\) = 1.0 atm.

A 5.72-g sample of graphite was heated with 68.4 g of \(\mathrm{O}_{2}\) in a 8.00-L flask. The reaction that took place was \(\mathrm{C}(\text { graphite })+\mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)\) After the reaction was complete, the temperature in the flask was \(182^{\circ} \mathrm{C}\). What was the total pressure inside the flask?

A mixture of calcium carbonate \(\left(\mathrm{CaCO}_{3}\right)\) and magnesium carbonate \(\left(\mathrm{MgCO}_{3}\right)\) of mass 6.26 g reacts completely with hydrochloric acid (HCI) to generate 1.73 L of CO2 at \(48^{\circ} \mathrm{C}\) and 1.12 atm. Calculate the mass percentages of \(\mathrm{CaCO}_{3}\) and \(\mathrm{MgCO}_{3}\) in the mixture.

A 6.11-g sample of a Cu-Zn alloy reacts with HCI acid to produce hydrogen gas. If the hydrogen gas has a volume of 1.26 L at \(22^{\circ} \mathrm{C}\) and 728 mmHg, what is the percent of Zn in the alloy? (Hint: Cu does not react with HCl.)

A stockroom supervisor measured the contents of a partially filled 25.0-gallon acetone drum on a day when the temperature was \(18.0^{\circ} \mathrm{C}\) and atmospheric pressure was 750 mmHg, and found that 15.4 gallons of the solvent remained. After tightly sealing the drum, an assistant dropped the drum while carrying it upstairs to the organic laboratory. The drum was dented and its internal volume was decreased to 20.4 gallons. What is the total pressure inside the drum after the accident? The vapor pressure of acetone at \(18.0^{\circ} \mathrm{C}\) is 400 mmHg. (Hint: At the time the drum was sealed, the pressure inside the drum, which is equal to the sum of the pressures of air and acetone, was equal to the atmospheric pressure.)

In 2.00 min, 29.7 mL of He effuse through a small hole. Under the same conditions of pressure and temperature, 10.0 mL of a mixture of CO and \(\mathrm{CO}_{2}\) effuse through the hole in the same amount of time. Calculate the percent composition by volume of the mixture.

Referring to Figure 5.22, explain the following: (a) Why do the curves dip below the horizontal line labeled ideal gas at low pressures and then why do they arise above the horizontal line at high pressures? (b) Why do the curves all converge to 1 at very low pressures? (c) Each curve intercepts the horizontal line labeled ideal gas. Does it mean that at that point the gas behaves ideally?

A mixture of methane \(\left(\mathrm{CH}_{4}\right)\) and ethane \(\left(C_{2} H_{6}\right)\) is stored in a container at 294 mmHg. The gases are burned in air to form \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\). If the pressure of \(\mathrm{CO}_{2}\) is 356 mmHg measured at the same temperature and volume as the original mixture, calculate the mole fractions of the gases.

Use the kinetic theory of gases to explain why hot air rises.

One way to gain a physical understanding of b in the van der Waals equation is to calculate the "excluded volume." Assume that the distance of closest approach between two similar atoms is the sum of their radii (2r). (a) Calculate the volume around each atom into which the center of another atom cannot penetrate. (b) From your result in (a), calculate the excluded volume for 1 mole of the atoms, which is the constant b. How does this volume compare with the sum of the volumes of 1 mole of the atoms?

Use the van der Waals constants in Table 5.4 to estimate the radius of argon in picometers. (Hint: See Problem 5.160.)

Identify the gas whose root-mean-square speed is 2.82 times that of hydrogen iodide (HI) at the same temperature.

A 5.00-mole sample of \(\mathrm{NH}_{3}\) gas is kept in a 1.92-L container at 300 K. If the van der Waals equation is assumed to give the correct answer for the pressure of the gas, calculate the percent error made in using the ideal gas equation to calculate the pressure.

The root-mean-square speed of a certain gaseous oxide is 493 m/s at \(20^{\circ} \mathrm{C}\). What is the molecular formula of the compound?

Referring to Figure 5.17, we see that the maximum of each speed distribution plot is called the most probable speed \(\left(u_{m p}\right)\) because it is the speed possessed by the largest number of molecules. It is given by \(u_{m p}=\sqrt{2 R T / \mu}\). (a) Compare \(\left(u_{m p}\right)\) with \(u_{r m s}\) for nitrogen at \(25^{\circ} C\). (b) The following diagram shows the Maxwell speed distribution curves for an ideal gas at two different temperatures \(T_{1}\) and \(T_{2}\). Calculate the value of \(T_{2}\).

A gaseous reaction takes place at constant volume and constant pressure in a cylinder shown here Which of the following equations best describes the reaction? The initial temperature (\(T_{1}\)) is twice that of the final temperature (\(T_{2}\)). (a) \(A+B \rightarrow C\) (b) \(A B \rightarrow C+D\) (c) \(A+B \rightarrow C+D\) (d) \(A+B \rightarrow 2 C+D\)

A gaseous hydrocarbon (containing C and H atoms) in a container of volume 20.2 L at 350 K and 6.63 atm reacts with an excess of oxygen to form 205.1 g of \(\mathrm{CO}_{2}\) and 168.0 g of \(\mathrm{H}_{2} \mathrm{O}\). What is the molecular formula of the hydrocarbon?

(a) Show that the pressure exerted by a fluid P (in pascals) is given by P = hdg, where h is the column of the fluid in meters, d is the density in \(\mathrm{kg} / \mathrm{m}^{3}\), and g is the acceleration due to gravity \(\left(9.81\ \mathrm{m} / \mathrm{s}^{2}\right)\). (Hint: See Appendix 2.) (b) The volume of an air bubble that starts at the bottom of a lake at \(5.24^{\circ} \mathrm{C}\) increases by a factor of 6 as it rises to the surface of water where the temperature is \(18.73^{\circ} \mathrm{C}\) and the air pressure is 0.973 atm. The density of the lake water is \(1.02\ \mathrm{g} / \mathrm{cm}^{3}\). Use the equation in (a) to determine the depth of the lake in meters.

Three flasks containing gases A (red) and B (green) are shown here. (i) If the pressure in (a) is 4.0 atm, what are the pressures in (b) and (c)? (ii) Calculate the total pressure and partial pressure of each gas after the valves are opened. The volumes of (a) and (c) are 4.0 L each and that of (b) is 2.0 L. The temperature is the same throughout.

A student first measured the total pressure of a mixture of gases methane \(\left(\mathrm{CH}_{4}\right)\), ethane \(\left(C_{2} H_{6}\right)\), and propane \(\left(C_{3} H_{8}\right)\) at a certain temperature, which turned out to be 4.50 atm. She then recorded the mass spectra of the gases shown here. Calculate the partial pressure of the gases.

Which of the following has a greater mass: a sample of air of volume V at a certain temperature T and pressure P or a sample of air plus water vapor having the same volume and at the same temperature and pressure?

A flask with a volume of 14.5 L contains 1.25 moles of helium gas. Estimate the average distance between He atoms in nanometers.

Hyperbaric oxygen therapy (HBOT) is very effective in treating burns, crush injuries that impede blood flow, and tissue-damaging infections, as well as carbon monoxide poisoning. However, it has generated some controversy in its application to other maladies (for example, autism, multiple sclerosis). A typical oxygen hyperbaric chamber is shown here. HBOT can be administered using pressure up to six atmospheres, but lower pressures are more common. (a) If this chamber was pressurized to 3.0 atm with pure oxygen, how many moles of O2 would be contained in an empty chamber? (b) Given that a full tank of oxygen contains about 2500 moles of the gas, how many times could the chamber be filled with a single tank of oxygen?

(a) Fluorescent light bulbs contain a small amount of mercury, giving a mercury vapor pressure of around \(1 \times 10^{-5}\ \mathrm{atm}\). When excited electrically, the Hg atoms emit UV light, which excites the phosphor coating of the inner tube, which then emits visible (white) light. Estimate the mass of Hg vapor present in the type of long, thin fluorescent tubes used in offices. (b) Ordinary tungsten incandescent lightbulbs used in households are filled with argon gas at about 0.5 atm to retard the sublimation of the tungsten filament. Estimate the number of moles of Ar in a typical lightbulb.

(a) Estimate the volume of air at 1.0 atm and \(22^{\circ} \mathrm{C}\) needed to fill a bicycle tire to a pressure of 5.0 atm at the same temperature. (Note that the 5.0 atm is the gauge pressure, which is the difference between the pressure in the tire and atmospheric pressure.) (b) The tire is pumped by filling the cylinder of a hand pump with air at 1.0 atm and then, by compressing the gas in the cylinder, adding all the air in the pump to the air in the tire. If the volume of the pump is 33 percent of the tire's volume, what is the gauge pressure in the tire after three full strokes of the pump?

On October 15, 2009, a homemade helium balloon was released, and for a while authorities were led to believe that a 6-year-old boy had been carried away in the balloon. (The incident was later revealed to be a hoax.) The balloon traveled more than 50 mi and reached a height of 7000 ft. The shape and span of the balloon are shown in the figure. How much weight could this balloon lift? (A helium balloon can lift a mass equal to the difference in the mass of air and the mass of helium that would be contained in the balloon.) Could it actually lift a 6-year-old boy?

Using the data shown in Table 5.4. calculate the pressure exerted by 2.50 moles of \(\mathrm{CO}_{2}\) confined in a volume of 5.00 L at 450 K. Compare the pressure with that predicted by the ideal gas equation.

At 27°C, 10.0 moles of a gas in a 1.50-L container exert a pressure of 130 atm. Is this an ideal gas?

Discuss the following phenomena in terms of the gas laws: (a) the pressure increase in an automobile tire on a hot day, (b) the “popping” of a paper bag, (c) the expansion of a weather balloon as it rises in the air, (d) the loud noise heard when a lightbulb shatters.

Under the same conditions of temperature and pressure, which of the following gases would behave most ideally: Ne, \(N_{2}\), or \(\mathrm{CH}_{4}\)? Explain.

Nitroglycerin, an explosive compound, decomposes according to the equation \(4 \mathrm{C}_{3} \mathrm{H}_{5}\left(\mathrm{NO}_{3}\right)_{3}(\mathrm{s}) \rightarrow 12 \mathrm{CO}_{2}(\mathrm{g})+10 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})+6 \mathrm{N}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g})\) Calculate the total volume of gases when collected at 1.2 atm and 25°C from \(2.6 \times 10^{2}\) g of nitroglycerin. What are the partial pressures of the gases under these conditions?

The empirical formula of a compound is CH. At 200°C, 0.145 g of this compound occupies 97.2 mL at a pressure of 0.74 atm. What is the molecular formula of the compound?

When ammonium nitrite (\(\mathrm{NH}_{4} \mathrm{NO}_{2}\)) is heated, it decomposes to give nitrogen gas. This property is used to inflate some tennis balls. (a) Write a balanced equation for the reaction. (b) Calculate the quantity (in grams) of \(\mathrm{NH}_{4} \mathrm{NO}_{2}\) needed to inflate a tennis ball to a volume of 86.2 mL at 1.20 atm and 22°C.

The percent by mass of bicarbonate (\(\mathrm{HCO}_{3}^{-}\)) in a certain Alka-Seltzer product is 32.5 percent. Calculate the volume of \(\mathrm{CO}_{2}\) generated (in mL) at 37°C and 1.00 atm when a person ingests a 3.29-g tablet. (Hint: The reaction is between \(\mathrm{HCO}_{3}^{-}\) and HCl acid in the stomach.)

The boiling point of liquid nitrogen is – 196°C. On the basis of this information alone, do you think nitrogen is an ideal gas?

In the metallurgical process of refining nickel, the metal is first combined with carbon monoxide to form tetraearbonylnickel, which is a gas at 43°C: \(\mathrm{Ni}(\mathrm{s})+4 \mathrm{CO}(\mathrm{g}) \rightarrow \mathrm{Ni}(\mathrm{CO})_{4}(\mathrm{g})\) This reaction separates nickel from other solid impurities. (a) Starting with 86.4 g of Ni. calculate the pressure of \(\mathrm{Ni}(\mathrm{CO})_{4}\) in a container of volume 4.00 L. (Assume the above reaction goes to completion.) (b) At temperatures above 43°C. the pressure of the gas is observed to increase much more rapidly than predicted by the ideal gas equation. Explain.

The partial pressure of carbon dioxide varies with seasons. Would you expect the partial pressure in the Northern Hemisphere to be higher in the summer or winter? Explain.

A healthy adult exhales about \(5.0 \times 10^{2}\) mL of a gaseous mixture with each breath. Calculate the number of molecules present in this volume at 37°C and 1.1 atm. List the major components of this gaseous mixture.

Sodium bicarbonate (\(\mathrm{NaHCO}_{3}\)) is called baking soda because when heated, it releases carbon dioxide gas, which is responsible for the rising of cookies, doughnuts, and bread. (a) Calculate the volume (in liters) of \(\mathrm{CO}_{2}\) produced by heating 5.0 g of \(\mathrm{NaHCO}_{3}\) at 180°C and 1.3 atm. (b) Ammonium bicarbonate (\(\mathrm{NH}_{4} \mathrm{HCO}_{3}\)) has also been used for the same purpose. Suggest one advantage and one disadvantage of using \(\mathrm{NH}_{4} \mathrm{HCO}_{3}\) instead of \(\mathrm{NaHCO}_{3}\) for baking.

A barometer having a cross-sectional area of 1.00 \(\mathrm{cm}^{2}\) at sea level measures a pressure of 76.0 cm of mercury. The pressure exerted by this column of mercury is equal to the pressure exerted by all the air on 1 \(\mathrm{cm}^{2}\) of Earth’s surface. Given that the density of mercury is 13.6 g/mL and the average radius of Earth is 6371 km, calculate the total mass of Earth’s atmosphere in kilograms. (Hint: The surface area of a sphere is 4????\(r^{2}\) where r is the radius of the sphere.)

Some commercial drain cleaners contain a mixture of sodium hydroxide and aluminum powder. When the mixture is poured down a clogged drain, the following reaction occurs: \(2 \mathrm{NaOH}(\mathrm{aq})+2 \mathrm{Al}(\mathrm{s})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow 2 \mathrm{NaAl}(\mathrm{OH})_{4}(\mathrm{aq})+3 \mathrm{H}_{2}(\mathrm{g})\) The heat generated in this reaction helps melt away obstructions such as grease, and the hydrogen gas released stirs up the solids clogging the drain, Calculate the volume of \(\mathrm{H}_{2}\) formed at 23°C and 1.00 atm if 3.12 g of Al are treated with an excess of NaOH.

The volume of a sample of pure HCl gas was 189 mL at 25°C and 108 mmHg. It was completely dissolved in about 60 mL of water and titrated with an NaOH solution; 15.7 mL of the NaOH solution were required to neutralize the HCL Calculate the molarity of the NaOH solution.

Propane (\(C_{3} H_{8}\)) burns in oxygen to produce carbon dioxide gas and water vapor. (a) Write a balanced equation for this reaction. (b) Calculate the number of liters of carbon dioxide measured at STP that could be produced from 7.45 g of propane.

Consider the following apparatus. Calculate the partial pressures of helium and neon after the stopcock is open. The temperature remains constant at 16°C.

Nitric oxide (NO) reacts with molecular oxygen as follows: \(2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{NO}_{2}(\mathrm{g})\) Initially NO and \(\mathrm{O}_{2}\) are separated as shown here. When the valve is opened, the reaction quickly goes to completion. Determine what gases remain at the end and calculate their partial pressures. Assume that the temperature remains constant at 25°C.

Consider the apparatus shown here. When a small amount of water is introduced into the flask by squeezing the bulb of the medicine dropper, water is squirted upward out of the long glass tubing. Explain this observation. (Hint: Hydrogen chloride gas is soluble in water.)

Describe how you would measure, by either chemical or physical means, the partial pressures of a mixture of gases of the following composition: (a) \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2}\), (b) He and \(N_{2}\).

A certain hydrate has the formula \(\mathrm{MgSO}_{4} \cdot x \mathrm{H}_{2} \mathrm{O}\). A quantity of 54.2 g of the compound is heated in an oven to drive off the water. If the steam generated exerts a pressure of 24.8 atm in a 2.00-L container at \(120^{\circ} \mathrm{C}\), calculate x.

A mixture of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) and \(\mathrm{MgCO}_{3}\) of mass 7.63 g is reacted with an excess of hydrochloric acid. The \(\mathrm{CO}_{2}\) gas generated occupies a volume of 1.67 L at 1.24 atm and \(26^{\circ} \mathrm{C}\). From these data, calculate the percent composition by mass of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) in the mixture.

The following apparatus can be used to measure atomic and molecular speed. Suppose that a beam of metal atoms is directed at a rotating cylinder in a vacuum. A small opening in the cylinder allows the atoms to strike a target area. Because the cylinder is rotating, atoms traveling at different speeds will strike the target at different positions. In time, a layer of the metal will deposit on the target area, and the variation in its thickness is found to correspond to Maxwell's speed distribution. In one experiment it is found that at \(850^{\circ} \mathrm{C}\) some bismuth (Bi) atoms struck the target at a point 2.80 cm from the spot directly opposite the slit. The diameter of the cylinder is 15.0 cm and it is rotating at 130 revolutions per second. (a) Calculate the speed (m/s) at which the target is moving. (Hint: The circumference of a circle is given by \(2 \pi r\), where r is the radius.) (b) Calculate the time in seconds) it takes for the target to travel 2.80 cm. (c) Determine the speed of the Bi atoms. Compare your result in (c) with the \(u_\mathrm{r m s}\) of Bi at \(850^{\circ} \mathrm{C}\). Comment on the difference.

If 10.00 g of water are introduced into an evacuated flask of volume 2.500 L at \(65^{\circ} \mathrm{C}\), calculate the mass of water vaporized. (Hint: Assume that the volume of the remaining liquid water is negligible; the vapor pressure of water at \(65^{\circ} \mathrm{C}\) is 187.5 mmHg.)

Commercially, compressed oxygen is sold in metal cylinders. If a 120-L cylinder is filled with oxygen to a pressure of 132 atm at \(22^{\circ} \mathrm{C}\), what is the mass (in grams) of \(\mathrm{O}_{2}\) present? How many liters of \(\mathrm{O}_{2}\) gas at 1.00 atm and \(22^{\circ} \mathrm{C}\) could the cylinder produce? (Assume ideal behavior.)

The shells of hard-boiled eggs sometimes crack due to the rapid thermal expansion of the shells at high temperatures. Suggest another reason why the shells may crack.

Ethylene gas (\(C_{2} H_{4}\)) is emitted by fruits and is known to be responsible for their ripening. Based on this information, explain why a bunch of bananas ripens faster in a closed paper bag than in a bowl.

About \(8.0 \times 10^{6}\) tons of urea \(\left[\left(\mathrm{NH}_{2}\right)_{2} \mathrm{CO}\right]\) are used annually as a fertilizer. The urea is prepared at \(200^{\circ} \mathrm{C}\) and under high-pressure conditions from carbon dioxide and ammonia (the products are urea and steam). Calculate the volume of ammonia (in liters) measured at 150 atm needed to prepare 1.0 ton of urea.

Some ballpoint pens have a small hole in the main body of the pen. What is the purpose of this hole?

The gas laws are vitally important to scuba divers. The pressure exerted by 33 ft of seawater is equivalent to 1 atm pressure. (a) A diver ascends quickly to the surface of the water from a depth of 36 ft without exhaling gas from his lungs. By what factor will the volume of his lungs increase by the time he reaches the surface? Assume that the temperature is constant. (b) The partial pressure of oxygen in air is about 0.20 atm. (Air is 20 percent oxygen by volume.) In deep-sea diving, the composition of air the diver breathes must be changed to maintain this partial pressure. What must the oxygen content in percent by volume) be when the total pressure exerted on the diver is 4.0 atm? (At constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of gases.) (Hint: See Chemistry in Action essay on p. 200.)

Nitrous oxide \(\left(N_{2} O\right)\) can be obtained by the thermal decomposition of ammonium nitrate \(\left(\mathrm{NH}_{4} \mathrm{NO}_{3}\right)\). (a) Write a balanced equation for the reaction. (b) In a certain experiment, a student obtains 0.340 L of the gas at 718 mmHg and \(24^{\circ} \mathrm{C}\). If the gas weighs 0.580 g, calculate the value of the gas constant.

Two vessels are labeled A and B. Vessel A contains \(\mathrm{NH}_{3}\) gas at \(70^{\circ} \mathrm{C}\), and vessel B contains Ne gas at the same temperature. If the average kinetic energy of \(\mathrm{NH}_{3}\) is \(7.1 \times 10^{-21}\) J/molecule, calculate the mean square speed of Ne atoms in \(\mathrm{m}^{2} / \mathrm{s}^{2}\).

Which of the following molecules has the largest a value: \(\mathrm{CH}_{4},\ \mathrm{F}_{2},\ \mathrm{C}_{6} \mathrm{H}_{6},\ \mathrm{Ne}\)?

The following procedure is a simple though somewhat crude way to measure the molar mass of a gas. A liquid of mass 0.0184 g is introduced into a syringe like the one shown here by injection through the rubber tip using a hypodermic needle. The syringe is then transferred to a temperature bath heated to \(45^{\circ} \mathrm{C}\), and the liquid vaporizes. The final volume of the vapor (measured by the outward movement of the plunger) is 5.58 mL and the atmospheric pressure is 760 mmHg. Given that the compound's empirical formula is \(\mathrm{CH}_{2}\), determine the molar mass of the compound.

In 1995 a man suffocated as he walked by an abandoned mine in England. At that moment there was a sharp drop in atmospheric pressure due to a change in the weather. Suggest what might have caused the man's death.

Acidic oxides such as carbon dioxide react with basic oxides like calcium oxide (CaO) and barium oxide (Bal) to form salts (metal carbonates). (a) Write equations representing these two reactions. (b) A student placed a mixture of BaO and CaO of combined mass 4.88 g in a 1.46-L flask containing carbon dioxide gas at \(35^{\circ} \mathrm{C}\) and 746 mmHg. After the reactions were complete, she found that the \(\mathrm{CO}_{2}\) pressure had dropped to 252 mmHg. Calculate the percent composition by mass of the mixture. Assume volumes of the solids are negligible.

Identify the Maxwell speed distribution curves shown here with the following gases: \(\mathrm{Br}_{2},\ \mathrm{CH}_{4},\ \mathrm{N}_{2},\ \mathrm{SO}_{3}\).

The running engine of an automobile produces carbon monoxide (CO), a toxic gas, at the rate of about 188 g CO per hour. A car is left idling in a poorly ventilated garage that is 6.0 m long, 4.0 m wide, and 2.2 m high at \(20^{\circ} \mathrm{C}\). (a) Calculate the rate of CO production in moles per minute. (b) How long would it take to build up a lethal concentration of CO of 1000 ppmv (parts per million by volume)?

Interstellar space contains mostly hydrogen atoms at a concentration of about 1 \(\mathrm{atom} / \mathrm{cm}^{3}\). (a) Calculate the pressure of the H atoms. (b) Calculate the volume (in liters) that contains 1.0 g of H atoms. The temperature is 3 K.

Atop Mt. Everest, the atmospheric pressure is \(210 \mathrm{mmHg}\) and the air density is \(0.426 \mathrm{~kg} / \mathrm{m}^{3}\). (a) Calculate the air temperature, given that the molar mass of air is \(29.0 \mathrm{~g} / \mathrm{mol}\). (b) Assuming no change in air composition, calculate the percent decrease in oxygen gas from sea level to the top of Mt. Everest.

Relative humidity is defined as the ratio (expressed as a percentage) of the partial pressure of water vapor in the air to the equilibrium vapor pressure (see Table 5.3) at a given temperature. On a certain summer day in North Carolina the partial pressure of water vapor in the air is \(3.9 \times 10^{3} \mathrm{~Pa}\) at \(30^{\circ} \mathrm{C}\). Calculate the relative humidity.

A certain amount of gas at 25°C and at a pressure of 0.800 atm is contained in a glass vessel. Suppose that the vessel can withstand a pressure of 2.00 atm. How high can you raise the temperature of the gas without bursting the vessel?

A gas-filled balloon having a volume of 2.50 L at 1.2 atm and 25°C is allowed to rise to the stratosphere (about 30 km above the surface of Earth), where the temperature and pressure are -23°C and \(3.00 \times 10^{-3}\) atm, respectively. Calculate the final volume of the balloon.

The temperature of \(2.5 \mathrm{~L}\) of a gas initially at STP is raised to \(250^{\circ} \mathrm{C}\) at constant volume. Calculate the final pressure of the gas in atm.

The pressure of 6.0 L of an ideal gas in a flexible container is decreased to one-third of its original pressure, and its absolute temperature is decreased by one-half. What is the final volume of the gas?

A gas evolved during the fermentation of glucose (wine making) has a volume of 0.78 L at 20.1°C and 1.00 atm. What was the volume of this gas at the fermentation temperature of 36.5°C and 1.00 atm pressure?

An ideal gas originally at 0.85 atm and 66°C was allowed to expand until its final volume, pressure, and temperature were 94 mL, 0.60 atm, and 45°C, respectively. What was its initial volume?

Calculate its volume (in liters) of 88.4 g of \(\mathrm{CO}_{2}\) at STP.

A gas at 772 mmHg and 35.0°C occupies a volume of 6.85 L. Calculate its volume at STP.

Dry ice is solid carbon dioxide. A 0.050-g sample of dry ice is placed in an evacuated 4.6-L vessel at 30°C. Calculate the pressure inside the vessel after all the dry ice has been converted to \(\mathrm{CO}_{2}\) gas.

At STP, 0.280 L of a gas weighs 0.400 g. Calculate the molar mass of the gas.

At 741 torr and 44°C, 7.10 g of a gas occupy a volume of 5.40 L. What is the molar mass of the gas?

Ozone molecules in the stratosphere absorb much of the harmful radiation from the sun. Typically, the temperature and pressure of ozone in the stratosphere are 250 K and \(1.0 \times 10^{-3}\) atm, respectively. How many ozone molecules are present in 1.0 L of air under these conditions?

Assuming that air contains 78 percent \(\mathrm{N}_{2}, 21\) percent \(\mathrm{O}_{2}\), and 1 percent Ar, all by volume, how many molecules of each type of gas are present in 1.0 L of air at STP?

A 2.10-L vessel contains \(4.65 \mathrm{~g}\) of a gas at \(1.00 \mathrm{~atm}\) and \(27.0^{\circ} \mathrm{C}\). (a) Calculate the density of the gas in grams per liter. (b) What is the molar mass of the gas?

Calculate the density of hydrogen bromide (HBr) gas in grams per liter at 733 mmHg and 46°C.

A certain anesthetic contains 64.9 percent \(\mathrm{C}, 13.5\) percent \(\mathrm{H}\), and 21.6 percent \(\mathrm{O}\) by mass. At \(120^{\circ} \mathrm{C}\) and \(750 \mathrm{mmHg}, 1.00 \mathrm{~L}\) of the gaseous compound weighs \(2.30 \mathrm{~g}\). What is the molecular formula of the compound?

A compound has the empirical formula SF4. At \(20^{\circ} \mathrm{C} .0 .100 \mathrm{~g}\) of the gaseous compound occupies a volume of \(22.1 \mathrm{~mL}\) and exerts a pressure of \(1.02 \mathrm{~atm}\). What is the molecular formula of the gas?

What pressure will be required for neon at 30°C to have the same density as nitrogen at 20°C and 1.0 atm?

The density of a mixture of fluorine and chlorine gases is 1.77 g/L at 14°C and 0.893 atm. Calculate the mass percent of the gases.

Consider the formation of nitrogen dioxide from nitric oxide and oxygen: \(2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{NO}_{2}(\mathrm{~g})\) If 9.0 L of NO are reacted with excess \(\mathrm{O}_{2}\) at STP, what is the volume in liters of the \(\mathrm{NO}_{2}\) produced?

Methane, the principal component of natural gas, is used for heating and cooking. The combustion process is \(CH_4\left(g\right)+2O_2\left(g\right)\rightarrow CO_2\left(g\right)+2H_2O\left(l\right)\) If 15.0 moles of \(CH_4\) are reacted, what is the volume of \(CO_2\) (in liters) produced at 23.0°C and 0.985 atm?

When coal is burned, the sulfur present in coal is converted to sulfur dioxide (\(\mathrm{SO}_{2}\)), which is responsible for the acid rain phenomenon. \(\mathrm{S}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{SO}_{2}(\mathrm{~g})\) If 2.54 kg of S are reacted with oxygen, calculate the volume of \(\mathrm{SO}_{2}\) gas (in mL) formed at 30.5°C and 1.12 atm.

In alcohol fermentation, yeast converts glucose to ethanol and carbon dioxide: \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(\mathrm{s}) \rightarrow 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\mathrm{l})+2 \mathrm{CO}_{2}(\mathrm{g})\) If 5.97 g of glucose are reacted and 1.44 L of \(\mathrm{CO}_{2}\) gas are collected at 293 K and 0.984 atm, what is the percent yield of the reaction?

A compound of P and F was analyzed as follows: Heating 0.2324 g of the compound in a 378-\(\mathrm{cm}^{3}\) container turned all of it to gas, which had a pressure of 97.3 mmHg at 77°C. Then the gas was mixed with calcium chloride solution, which turned all of the F to 0.2631 g of \(\mathrm{CaF}_{2}\). Determine the molecular formula of the compound.

A quantity of 0.225 g of a metal M (molar mass = 27.0 g/mol) liberated 0.303 L of molecular hydrogen (measured at 17°C and 741 mmHg) from an excess of hydrochloric acid. Deduce from these data the corresponding equation and write formulas for the oxide and sulfate of M.

What is the mass of the solid \(\mathrm{NH}_{4} \mathrm{Cl}\) formed when 73.0 g of \(\mathrm{NH}_{3}\) are mixed with an equal mass of HCl? What is the volume of the gas remaining, measured at 14.0°C and 752 mmHg? What gas is it?

Dissolving 3.00 g of an impure sample of calcium carbonate in hydrochloric acid produced 0.656 L of carbon dioxide (measured at 20.0°C and 792 mmHg). Calculate the percent by mass of calcium carbonate in the sample. State any assumptions.

Calculate the mass in grams of hydrogen chloride produced when 5.6 L of molecular hydrogen measured at STP react with an excess of molecular chlorine gas.

Ethanol (\(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\)) burns in air: \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\mathrm{l})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l})\) Balance the equation and determine the volume of air in liters at 35.0°C and 790 mmHg required to burn 227 g of ethanol. Assume that air is 21.0 percent \(O_{2}\) by volume.

(a) What volumes (in liters) of ammonia and oxygen must react to form 12.8 L of nitric oxide according to the equation at the same temperature and pressure? \(4 \mathrm{NH}_{3}(\mathrm{g})+5 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 4 \mathrm{NO}(\mathrm{g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) (b) What volumes (in liters) of propane and water vapor must react to form 8.96 L of hydrogen according to the equation at the same temperature and pressure? \(\mathrm{C}_{3} \mathrm{H}_{8}(\mathrm{g})+3 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightarrow 3 \mathrm{CO}(\mathrm{g})+7 \mathrm{H}_{2}(\mathrm{g})\)

A 4.00-g sample of FeS containing nonsulfide impurities reacted with HCl to give 896 mL of \(\mathrm{H}_{2} \mathrm{S}\) at 14°C and 782 mmHg. Calculate mass percent purity of the sample.

State Dalton’s law of partial pressures and explain what mole fraction is. Does mole fraction have units?

A sample of air contains only nitrogen and oxygen gases whose partial pressures are 0.80 atm and 0.20 atm, respectively. Calculate the total pressure and the mole fractions of the gases.

A mixture of gases contains \(0.31\) mol \(\mathrm{CH}_{4}, 0.25\) mol \(\mathrm{C}_{2} \mathrm{H}_{6}\), and \(0.29\) mol \(\mathrm{C}_{3} \mathrm{H}_{8}\). The total pressure is \(1.50 \mathrm{~atm}\). Calculate the partial pressures of the gases.

A \(2.5\)-L flask at \(15^{\circ} \mathrm{C}\) contains a mixture of \(\mathrm{N}_{2}\), He, and Ne at partial pressures of \(0.32\) atm for \(\mathrm{N}_{2}, 0.15 \mathrm{~atm}\) for \(\mathrm{He}\), and \(0.42 \mathrm{~atm}\) for \(\mathrm{Ne}\). (a) Calculate the total pressure of the mixture. (b) Calculate the volume in liters at STP occupied by He and Ne if the \(\mathrm{N}_{2}\) is removed selectively.

Dry air near sea level has the following composition by volume: \(\mathrm{N}_{2}, 78.08\) percent; \(\mathrm{O}_{2}, 20.94\) percent; Ar, 0.93 percent; \(\mathrm{CO}_{2}, 0.05\) percent. The atmospheric pressure is \(1.00 \mathrm{~atm}\). Calculate (a) the partial pressure of each gas in atm and (b) the concentration of each gas in moles per liter at \(0^{\circ} \mathrm{C}\). (Hint: Because volume is proportional to the number of moles present, mole fractions of gases can be expressed as ratios of volumes at the same temperature and pressure.)

A mixture of helium and neon gases is collected over water at 28.0°C and 745 mmHg. If the partial pressure of helium is 368 mmHg. what is the partial pressure of neon? (Vapor pressure of water at 28°C = 28.3 mmHg.)

A piece of sodium metal reacts completely with water as follows: \(2 \mathrm{Na}(\mathrm{s})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow 2 \mathrm{NaOH}(\mathrm{aq})+\mathrm{H}_{2}(\mathrm{g})\) The hydrogen gas generated is collected over water at 25.0°C. The volume of the gas is 246 mL measured at 1.00 atm. Calculate the number of grams of sodium used in the reaction. (Vapor pressure of water at 25°C = 0.0313 atm.)

A sample of zinc metal reacts completely with an excess of hydrochloric acid: \(\mathrm{Zn}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{aq}) \rightarrow \mathrm{ZnCl}_{2}(\mathrm{aq})+\mathrm{H}_{2}(\mathrm{g})\) The hydrogen gas produced is collected over water at 25.0°C using an arrangement similar to that shown in Figure 5.15. The volume of the gas is 7.80 L, and the pressure is 0.980 atm. Calculate the amount of zinc metal in grams consumed in the reaction. (Vapor pressure of water at 25°C = 23.8 mmHg.)

Helium is mixed with oxygen gas for deep-sea divers. Calculate the percent by volume of oxygen gas in the mixture if the diver has to submerge to a depth where the total pressure is 4.2 atm. The partial pressure of oxygen is maintained at 0.20 atm at this depth.

A sample of ammonia \(\left(\mathrm{NH}_{3}\right)\) gas is completely decomposed to nitrogen and hydrogen gases over heated iron wool. If the total pressure is \(866 \mathrm{mmHg}\), calculate the partial pressures of \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\).

Consider the three gas containers shown on p. 219. All of them have the same volume and are at the same temperature. (a) Which container has the smallest mole fraction of gas A (blue sphere)? (b) Which container has the highest partial pressure of gas B (green sphere)?

The volume of the box on the right is twice that of the box on the left. The boxes contain helium atoms (red) and hydrogen molecules (green) at the same temperature. (a) Which box has a higher total pressure? (b) Which box has a lower partial pressure of helium?

What are the basic assumptions of the kinetic molecular theory of gases? How does the kinetic molecular theory explain Boyle’s law, Charles’s law, Avogadro’s law, and Dalton’s law of partial pressures?

What does the Maxwell speed distribution curve tell us? Does Maxwell’s theory work for a sample of 200 molecules? Explain.

Which of the following statements is correct? (a) Heat is produced by the collision of gas molecules against one another. (b) When a gas is heated, the molecules collide with one another more often.

What is the difference between gas diffusion and effusion? State Graham’s law and define the terms in Equation (5.17).

Compare the root-mean-square speeds of \(O_{2}\) and \(U F_{6}\) at 65°C.

The temperature in the stratosphere is –23°C. Calculate the root-mean-square speeds of \(N_{2}\), \(O_{2}\), and \(O_{3}\) molecules in this region.

The average distance traveled by a molecule between successive collisions is called mean free path. For a given amount of a gas, how does the mean free path of a gas depend on (a) density, (b) temperature at constant volume, (c) pressure at constant temperature, (d) volume at constant temperature, and (e) size of the atoms?

Convert 749 mmHg to atmospheres.

Name five elements and five compounds that exist as gases at room temperature.

Rank the following pressures from lowest to highest: (a) 736mmHg, (b) 0.928 atm, (c) 728 torr, (d) \(1.12 \times 10^{5}\) Pa.

List the physical characteristics of gases.

Convert 295 mmHg to kilopascals.

Would it be easier to drink water with a straw on top or at the foot of Mt. Everest?

Define pressure and give the common units for pressure.

At a certain temperature the speeds of six gaseous molecules in a container are 2.0 m/s, 2.2 m/s, 2.6 m/s, 2.7 m/s, 3.3 m/s, and 3.5 m/s. Calculate the root-mean-square speed and the average speed of the molecules. These two average values are close to each other, but the root-mean-square value is always the larger of the two. Why?

Based on your knowledge of the kinetic theory of gases, derive Graham’s law [Equation (5.17)].

The \({ }^{235} \mathrm{U}\) isotope undergoes fission when bombarded with neutrons. However, its natural abundance is only 0.72 percent. To separate it from the more abundant \({ }^{238} \mathrm{U}\) isotope, uranium is first converted to \(U F_{6}\), which is easily vaporized above room temperature. The mixture of the \({ }^{235} U F_{6}\) and \({ }^{238} U F_{6}\) gases is then subjected to many stages of effusion. Calculate the separation factor, that is, the enrichment of \({ }^{235} \mathrm{U}\) relative to \({ }^{238} \mathrm{U}\) after one stage of effusion.

A gas evolved from the fermentation of glucose is found to effuse through a porous barrier in 15.0 min. Under the same conditions of temperature and pressure. it takes an equal volume of \(N_{2}\) 12.0 min to effuse through the same barrier. Calculate the molar mass of the gas and suggest what the gas might be.

Nickel forms a gaseous compound of the formula \(N i(\mathrm{CO})_{x}\). What is the value of x given the fact that under the same conditions of temperature and pressure, methane (\(\mathrm{CH}_{4}\)) effuses 3.3 times faster than the compound?

Problem 89P Nickel forms a gaseous compound of the formula Ni(CO)v. What is the value of x given the fact that under the same conditions of temperature and pressure, methane (CH4) effuses 3.3 times faster than the compound?

Under what set of conditions would a gas be expected to behave most ideally? (a) High temperature and low pressure, (b) high temperature and high pressure, (c) low temperature and high pressure, (d) low temperature and low pressure.

Shown here are plots of PV/RT against P for one mole of a nonideal gas at two different temperatures. Which curve is at the higher temperature?

(a) A real gas is introduced into a flask of volume V. Is the corrected volume of the gas greater or less than V? (b) Ammonia has a larger a value than neon does (see Table 5.4). What can you conclude about the relative strength of the attractive forces between molecules of ammonia and between atoms of neon?

An equimolar mixture of \(\mathrm{H}_{2}\) and \(D_{2}\) effuses through an orifice (small hole) at a certain temperature. Calculate the composition (in mole fractions) of the gases that pass through the orifice. The molar mass of \(D_{2}\) is 2.014 g/mol.