Solution: The Ideal-Gas Equation (Section)Suppose you are

You have a sample of gas in a container with a movable piston, such as the one in the drawing. (a) Redraw the container to show what it might look like if the temperature of the gas is increased from 300 to 500 K while the pressure is kept constant. (b) Redraw the container to show what it might look like if the external pressure on the piston is increased from 1.0 atm to 2.0 atm while the temperature is kept constant. (c) Redraw the container to show what it might look like if the temperature of the gas decreases from 300 to 200 K while the pressure is kept constant (assume the gas does not liquefy). [Section 10.3]

Consider the sample of gas depicted here. What would the drawing look like if the volume and temperature remained constant while you removed enough of the gas to decrease the pressure by a factor of 2? [Section 10.3]

Imagine that the reaction 2 CO1g2 + O21g2 2 CO21g2 occurs in a container that has a piston that moves to maintain a constant pressure when the reaction occurs at constant temperature. Which of the following statements describes how the volume of the container changes due to the reaction: (a) the volume increases by 50%, (b) the volume increases by 33%, (c) the volume remains constant, (d) the volume decreases by 33%, (e) the volume decreases by 50%. [Sections 10.3 and 10.4]

Suppose you have a fixed amount of an ideal gas at a constant volume. If the pressure of the gas is doubled while the volume is held constant, what happens to its temperature? [Section 10.4]

The apparatus shown here has two gas-filled containers and one empty container, all attached to a hollow horizontal tube. When the valves are opened and the gases are allowed to mix at constant temperature, what is the distribution of atoms in each container? Assume that the containers are of equal volume and ignore the volume of the connecting tube. Which gas has the greater partial pressure after the valves are opened? [Section 10.6]

The accompanying drawing represents a mixture of three different gases. (a) Rank the three components in order of increasing partial pressure. (b) If the total pressure of the mixture is 1.40 atm, calculate the partial pressure of each gas. [Section 10.6]

On a single plot, qualitatively sketch the distribution of molecular speeds for (a) Kr(g) at -50 C, (b) Kr(g) at 0 C, (c) Ar(g) at 0 C. [Section 10.7]

Consider the following graph. (a) If curves A and B refer to two different gases, He and O2, at the same temperature, which curve corresponds to He? (b) If A and B refer to the same gas at two different temperatures, which represents the higher temperature? (c) For each curve which speed is highest: the most probable speed, the root-mean-square speed, or the average speed? [Section 10.7] Molecular speed A B Fraction of molecules

Consider the following samples of gases: (i) (ii) (iii) = He = N2 If the three samples are all at the same temperature, rank them with respect to (a) total pressure, (b) partial pressure of helium, (c) density, (d) average kinetic energy of particles. [Section 10.6 and 10.7

A thin glass tube 1 m long is filled with Ar gas at 1 atm, and the ends are stoppered with cotton plugs: HCl NH3 a b c HCl gas is introduced at one end of the tube, and simultaneously NH3 gas is introduced at the other end. When the two gases diffuse through the cotton plugs down the tube and meet, a white ring appears due to the formation of NH4Cl1s2. At which location a, b, or cdo you expect the ring to form? [Section 10.8]

The graph below shows the change in pressure as the temperature increases for a 1-mol sample of a gas confined to a 1-L container. The four plots correspond to an ideal gas and three real gases: CO2, N2, and Cl2. (a) At room temperature, all three real gases have a pressure less than the ideal gas. Which van der Waals constant, a or b, accounts for the influence intermolecular forces have in lowering the pressure of a real gas? (b) Use the van der Waals constants in Table 10.3 to match the labels in the plot (A, B, and C) with the respective gases (CO2, N2, and Cl2). [Section 10.9] 250 300 350 400 450 500 Ideal gas Gas A Gas B Gas C 550 20 25 30 15 40 35 45 Temperature (K) Pressure (atm)

How does a gas compare with a liquid for each of the following properties: (a) density, (b) compressibility, (c) ability to mix with other substances of the same phase to form homogeneous mixtures, (d) ability to conform to the shape of its container?

(a) A liquid and a gas are moved to larger containers. How does their behavior differ once they are in the larger containers? Explain the difference in molecular terms

(b) Although liquid water and carbon tetrachloride, CCl41l2, do not mix, their vapors form a homogeneous mixture. Explain.

(c) Gas densities are generally reported in grams per liter, whereas liquid densities are reported in grams per milliliter. Explain the molecular basis for this difference.

Suppose that a woman weighing 130 lb and wearing highheeled shoes momentarily places all her weight on the heel of one foot. If the area of the heel is 0.50 in. 2 , calculate the pressure exerted on the underlying surface in (a) kilopascals, (b) atmospheres, and (c) pounds per square inch.

A set of bookshelves rests on a hard floor surface on four legs, each having a cross-sectional dimension of 3.0 * 4.1 cm in contact with the floor. The total mass of the shelves plus the books stacked on them is 262 kg. Calculate the pressure in pascals exerted by the shelf footings on the surface.

(a) How high in meters must a column of water be to exert a pressure equal to that of a 760-mm column of mercury? The density of water is 1.0 g>mL, whereas that of mercury is 13.6 g>mL.

(b) What is the pressure, in atmospheres, on the body of a diver if he or she is 39 ft below the surface of the water when atmospheric pressure at the surface is 0.97 atm?

The compound 1-iodododecane is a nonvolatile liquid with a density of 1.20 g>mL. The density of mercury is 13.6 g>mL. What do you predict for the height of a barometer column based on 1- iodododecane, when the atmospheric pressure is 749 torr?

The typical atmospheric pressure on top of Mt. Everest (29,028 ft) is about 265 torr. Convert this pressure to (a) atm, (b) mm Hg, (c) pascals, (d) bars, (e) psi.

Perform the following conversions: (a) 0.912 atm to torr, (b) 0.685 bar to kilopascals, (c) 655 mm Hg to atmospheres, (d) 1.323 * 105 Pa to atmospheres, (e) 2.50 atm to psi.

In the United States, barometric pressures are generally reported in inches of mercury (in. Hg). On a beautiful summer day in Chicago, the barometric pressure is 30.45 in. Hg. (a) Convert this pressure to torr. (b) Convert this pressure to atm

Hurricane Wilma of 2005 is the most intense hurricane on record in the Atlantic basin, with a low- pressure reading of 882 mbar (millibars). Convert this reading into (a) atmospheres, (b) torr, and (c) inches of Hg.

If the atmospheric pressure is 0.995 atm, what is the pressure of the enclosed gas in each of the three cases depicted in the drawing? Assume that the gray liquid is mercury. Closed end Gas (i) (ii) (iii) Gas h = 52 cm h = 67 cm h = 10.3 cm Gas Open end Open end h h h

An open-end manometer containing mercury is connected to a container of gas, as depicted in Sample Exercise 10.2. What is the pressure of the enclosed gas in torr in each of the following situations? (a) The mercury in the arm attached to the gas is 15.4 mm higher than in the one open to the atmosphere; atmospheric pressure is 0.985 atm. (b) The mercury in the arm attached to the gas is 12.3 mm lower than in the one open to the atmosphere; atmospheric pressure is 0.99 atm.

You have a gas at 25 C confined to a cylinder with a movable piston. Which of the following actions would double the gas pressure? (a) Lifting up on the piston to double the volume while keeping the temperature constant; (b) Heating the gas so that its temperature rises from 25 C to 50 C, while keeping the volume constant; (c) Pushing down on the piston to halve the volume while keeping the temperature constant.

A fixed quantity of gas at 21 C exhibits a pressure of 752 torr and occupies a volume of 5.12 L. (a) Calculate the volume the gas will occupy if the pressure is increased to 1.88 atm while the temperature is held constant. (b) Calculate the volume the gas will occupy if the temperature is increased to 175 C while the pressure is held constant.

(a) Amontons law expresses the relationship between pressure and temperature. Use Charless law and Boyles law to derive the proportionality relationship between P and T.

(b) If a car tire is filled to a pressure of 32.0 lbs>in. 2 1psi2 measured at 75 F, what will be the tire pressure if the tires heat up to 120 F during driving?

Nitrogen and hydrogen gases react to form ammonia gas as follows: N21g2 + 3 H21g2 2 NH31g2 At a certain temperature and pressure, 1.2 L of N2 reacts with 3.6 L of H2. If all the N2 and H2 are consumed, what volume of NH3, at the same temperature and pressure, will be produced?

(c) Room temperature is often assumed to be 25 C. Calculate the molar volume of an ideal gas at 25 C and 1 atm pressure

If you measure pressure in bars instead of atmospheres, calculate the corresponding value of R in L-bar/mol-K.

To derive the ideal-gas equation, we assume that the volume of the gas atoms/molecules can be neglected. Given the atomic radius of neon, 0.69 , and knowing that a sphere has a volume of 4pr 3>3, calculate the fraction of space that Ne atoms occupy in a sample of neon at STP.

Suppose you are given two 1-L flasks and told that one contains a gas of molar mass 30, the other a gas of molar mass 60, both at the same temperature. The pressure in flask A is X atm, and the mass of gas in the flask is 1.2 g. The pressure in flask B is 0.5X atm, and the mass of gas in that flask is 1.2 g. Which flask contains the gas of molar mass 30, and which contains the gas of molar mass 60?

Suppose you are given two flasks at the same temperature, one of volume 2 L and the other of volume 3 L. The 2-L flask contains 4.8 g of gas, and the gas pressure is X atm. The 3-L flask contains 0.36 g of gas, and the gas pressure is 0.1X. Do the two gases have the same molar mass? If not, which contains the gas of higher molar mass?

Complete the following table for an ideal gas: P V n T 2.00 atm 1.00 L 0.500 mol ? K 0.300 atm 0.250 L ? mol 27 C 650 torr ? L 0.333 mol 350 K ? atm 585 mL 0.250 mol 295 K

Calculate each of the following quantities for an ideal gas: (a) the volume of the gas, in liters, if 1.50 mol has a pressure of 1.25 atm at a temperature of -6 C; (b) the absolute temperature of the gas at which 3.33 * 10-3 mol occupies 478 mL at 750 torr; (c) the pressure, in atmospheres, if 0.00245 mol occupies 413 mL at 138 C; (d) the quantity of gas, in moles, if 126.5 L at 54 C has a pressure of 11.25 kPa

The Goodyear blimps, which frequently fly over sporting events, hold approximately 175,000 ft 3 of helium. If the gas is at 23 C and 1.0 atm, what mass of helium is in a blimp?

A neon sign is made of glass tubing whose inside diameter is 2.5 cm and whose length is 5.5 m. If the sign contains neon at a pressure of 1.78 torr at 35 C, how many grams of neon are in the sign? (The volume of a cylinder is pr 2 h.)

(a) Calculate the number of molecules in a deep breath of air whose volume is 2.25 L at body temperature, 37 C, and a pressure of 735 torr.

(b) The adult blue whale has a lung capacity of 5.0 * 103 L. Calculate the mass of air (assume an average molar mass of 28.98 g>mol) contained in an adult blue whales lungs at 0.0 C and 1.00 atm, assuming the air behaves ideally

(a) If the pressure exerted by ozone, O3, in the stratosphere is 3.0 * 10-3 atm and the temperature is 250 K, how many ozone molecules are in a liter?

(b) Carbon dioxide makes up approximately 0.04% of Earths atmosphere. If you collect a 2.0-L sample from the atmosphere at sea level (1.00 atm) on a warm day 127 C2, how many CO2 molecules are in your sample?

A scuba divers tank contains 0.29 kg of O2 compressed into a volume of 2.3 L. (a) Calculate the gas pressure inside the tank at 9 C. (b) What volume would this oxygen occupy at 26 C and 0.95 atm?

An aerosol spray can with a volume of 250 mL contains 2.30 g of propane gas 1C3H82 as a propellant. (a) If the can is at 23 C, what is the pressure in the can? (b) What volume would the propane occupy at STP? (c) The cans label says that exposure to temperatures above 130 F may cause the can to burst. What is the pressure in the can at this temperature?

A 35.1 g sample of solid CO2 (dry ice) is added to a container at a temperature of 100 K with a volume of 4.0 L. If the container is evacuated (all of the gas removed), sealed and then allowed to warm to room temperature 1T = 298 K2 so that all of the solid CO2 is converted to a gas, what is the pressure inside the container?

A 334-mL cylinder for use in chemistry lectures contains 5.225 g of helium at 23 C. How many grams of helium must be released to reduce the pressure to 75 atm assuming ideal gas behavior

Chlorine is widely used to purify municipal water supplies and to treat swimming pool waters. Suppose that the volume of a particular sample of Cl2 gas is 8.70 L at 895 torr and 24 C. (a) How many grams of Cl2 are in the sample? (b) What volume will the Cl2 occupy at STP? (c) At what temperature will the volume be 15.00 L if the pressure is 8.76 * 102 torr? (d) At what pressure will the volume equal 5.00 L if the temperature is 58 C?

Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is 55.0 gallons that contains O2 gas at a pressure of 16,500 kPa at 23 C. (a) What mass of O2 does the tank contain? (b) What volume would the gas occupy at STP? (c) At what temperature would the pressure in the tank equal 150.0 atm? (d) What would be the pressure of the gas, in kPa, if it were transferred to a container at 24 C whose volume is 55.0 L?

In an experiment reported in the scientific literature, male cockroaches were made to run at different speeds on a miniature treadmill while their oxygen consumption was measured. In 1 hr the average cockroach running at 0.08 km>hr consumed 0.8 mL of O2 at 1 atm pressure and 24 C per gram of insect mass. (a) How many moles of O2 would be consumed in 1 hr by a 5.2-g cockroach moving at this speed? (b) This same cockroach is caught by a child and placed in a 1-qt fruit jar with a tight lid. Assuming the same level of continuous activity as in the research, will the cockroach consume more than 20% of the available O2 in a 48-hr period? (Air is 21 mol % O2.)

The physical fitness of athletes is measured by VO2 max, which is the maximum volume of oxygen consumed by an individual during incremental exercise (for example, on a treadmill). An average male has a VO2 max of 45 mL O2>kg body mass/min, but a world-class male athlete can have a VO2 max reading of 88.0 mL O2>kg body mass/min. (a) Calculate the volume of oxygen, in mL, consumed in 1 hr by an average man who weighs 185 lbs and has a VO2 max reading of 47.5 mL O2>kg body mass/min. (b) If this man lost 20 lb, exercised, and increased his VO2 max to 65.0 mL O2>kg body mass/min, how many mL of oxygen would he consume in 1 hr?

Which gas is most dense at 1.00 atm and 298 K: CO2, N2O, or Cl2? Explain

Rank the following gases from least dense to most dense at 1.00 atm and 298 K: SO2, HBr, CO2. Explain.

Which of the following statements best explains why a closed balloon filled with helium gas rises in air? (a) Helium is a monatomic gas, whereas nearly all the molecules that make up air, such as nitrogen and oxygen, are diatomic. (b) The average speed of helium atoms is greater than the average speed of air molecules, and the greater speed of collisions with the balloon walls propels the balloon upward. (c) Because the helium atoms are of lower mass than the average air molecule, the helium gas is less dense than air. The mass of the balloon is thus less than the mass of the air displaced by its volume. (d) Because helium has a lower molar mass than the average air molecule, the helium atoms are in faster motion. This means that the temperature of the helium is greater than the air temperature. Hot gases tend to rise.

Which of the following statements best explains why nitrogen gas at STP is less dense than Xe gas at STP? (a) Because Xe is a noble gas, there is less tendency for the Xe atoms to repel one another, so they pack more densely in the gaseous state. (b) Xe atoms have a higher mass than N2 molecules. Because both gases at STP have the same number of molecules per unit volume, the Xe gas must be denser. (c) The Xe atoms are larger than N2 molecules and thus take up a larger fraction of the space occupied by the gas. (d) Because the Xe atoms are much more massive than the N2 molecules, they move more slowly and thus exert less upward force on the gas container and make the gas appear denser.

(a) Calculate the density of NO2 gas at 0.970 atm and 35 C

(b) Calculate the molar mass of a gas if 2.50 g occupies 0.875 L at 685 torr and 35 C.

(a) Calculate the density of sulfur hexafluoride gas at 707 torr and 21 C

(b) Calculate the molar mass of a vapor that has a density of 7.135 g>L at 12 C and 743 torr

In the Dumas-bulb technique for determining the molar mass of an unknown liquid, you vaporize the sample of a liquid that boils below 100 C in a boiling-water bath and determine the mass of vapor required to fill the bulb. From the following data, calculate the molar mass of the unknown liquid: mass of unknown vapor, 1.012 g; volume of bulb, 354 cm3 ; pressure, 742 torr; temperature, 99 C. Dumas bulb Boiling water l? led with vaporized unknown substance

The molar mass of a volatile substance was determined by the Dumas-bulb method described in Exercise 10.53. The unknown vapor had a mass of 0.846 g; the volume of the bulb was 354 cm3 , pressure 752 torr, and temperature 100 C. Calculate the molar mass of the unknown vapor.

Magnesium can be used as a getter in evacuated enclosures to react with the last traces of oxygen. (The magnesium is usually heated by passing an electric current through a wire or ribbon of the metal.) If an enclosure of 0.452 L has a partial pressure of O2 of 3.5 * 10-6 torr at 27 C, what mass of magnesium will react according to the following equation? 2 Mg1s2 + O21g2 2 MgO1s2

Calcium hydride, CaH2, reacts with water to form hydrogen gas: CaH21s2 + 2 H2O1l2 Ca1OH221aq2 + 2 H21g2 This reaction is sometimes used to inflate life rafts, weather balloons, and the like, when a simple, compact means of generating H2 is desired. How many grams of CaH2 are needed to generate 145 L of H2 gas if the pressure of H2 is 825 torr at 21 C?

The metabolic oxidation of glucose, C6H12O6, in our bodies produces CO2, which is expelled from our lungs as a gas: C6H12O61aq2 + 6 O21g2 6 CO21g2 + 6 H2O1l2 (a) Calculate the volume of dry CO2 produced at body temperature 137 C2 and 0.970 atm when 24.5 g of glucose is consumed in this reaction. (b) Calculate the volume of oxygen you would need, at 1.00 atm and 298 K, to completely oxidize 50.0 g of glucose.

Both Jacques Charles and Joseph Louis Guy-Lussac were avid balloonists. In his original flight in 1783, Jacques Charles used a balloon that contained approximately 31,150 L of H2. He generated the H2 using the reaction between iron and hydrochloric acid: Fe1s2 + 2 HCl1aq2 FeCl21aq2 + H21g2 How many kilograms of iron were needed to produce this volume of H2 if the temperature was 22 C?

Hydrogen gas is produced when zinc reacts with sulfuric acid: Zn1s2 + H2SO41aq2 ZnSO41aq2 + H21g2 If 159 mL of wet H2 is collected over water at 24 C and a barometric pressure of 738 torr, how many grams of Zn have been consumed? (The vapor pressure of water is tabulated in Appendix B.)

Acetylene gas, C2H21g2, can be prepared by the reaction of calcium carbide with water: CaC21s2 + 2 H2O1l2 Ca1OH221aq2 + C2H21g2 Calculate the volume of C2H2 that is collected over water at 23 C by reaction of 1.524 g of CaC2 if the total pressure of the gas is 753 torr. (The vapor pressure of water is tabulated in Appendix B.

Consider the apparatus shown in the following drawing. (a) When the valve between the two containers is opened and the gases allowed to mix, how does the volume occupied by the N2 gas change? What is the partial pressure of N2 after mixing? (b) How does the volume of the O2 gas change when the gases mix? What is the partial pressure of O2 in the mixture? (c) What is the total pressure in the container after the gases mix? 2.0 L 1.0 atm 25 C 3.0 L 2.0 atm 25 C N2 O2

Consider a mixture of two gases, A and B, confined in a closed vessel. A quantity of a third gas, C, is added to the same vessel at the same temperature. How does the addition of gas C affect the following: (a) the partial pressure of gas A, (b) the total pressure in the vessel, (c) the mole fraction of gas B?

A mixture containing 0.765 mol He(g), 0.330 mol Ne(g), and 0.110 mol Ar(g) is confined in a 10.00-L vessel at 25 C. (a) Calculate the partial pressure of each of the gases in the mixture. (b) Calculate the total pressure of the mixture.

A deep-sea diver uses a gas cylinder with a volume of 10.0 L and a content of 51.2 g of O2 and 32.6 g of He. Calculate the partial pressure of each gas and the total pressure if the temperature of the gas is 19 C.

The atmospheric concentration of CO2 gas is presently 390 ppm (parts per million, by volume; that is, 390 L of every 106 L of the atmosphere are CO2). What is the mole fraction of CO2 in the atmosphere?

A plasma-screen TV contains thousands of tiny cells filled with a mixture of Xe, Ne, and He gases that emits light of specific wavelengths when a voltage is applied. A particular plasma cell, 0.900 mm * 0.300 mm * 10.0 mm, contains 4% Xe in a 1:1 Ne:He mixture at a total pressure of 500 torr. Calculate the number of Xe, Ne, and He atoms in the cell and state the assumptions you need to make in your calculation.

A piece of dry ice (solid carbon dioxide) with a mass of 5.50 g is placed in a 10.0-L vessel that already contains air at 705 torr and 24 C. After the carbon dioxide has totally sublimed, what is the partial pressure of the resultant CO2 gas, and the total pressure in the container at 24 C

A sample of 5.00 mL of diethylether 1C2H5OC2H5, density = 0.7134 g>mL2 is introduced into a 6.00- L vessel that already contains a mixture of N2 and O2, whose partial pressures are PN2 = 0.751 atm and PO2 = 0.208 atm. The temperature is held at 35.0 C, and the diethylether totally evaporates. (a) Calculate the partial pressure of the diethylether. (b) Calculate the total pressure in the container

A rigid vessel containing a 3:1 mol ratio of carbon dioxide and water vapor is held at 200 C where it has a total pressure of 2.00 atm. If the vessel is cooled to 10 C so that all of the water vapor condenses, what is the pressure of carbon dioxide? Neglect the volume of the liquid water that forms on cooling.

If 5.15 g of Ag2O is sealed in a 75.0-mL tube filled with 760 torr of N2 gas at 32 C, and the tube is heated to 320 C, the Ag2O decomposes to form oxygen and silver. What is the total pressure inside the tube assuming the volume of the tube remains constant?

At an underwater depth of 250 ft, the pressure is 8.38 atm. What should the mole percent of oxygen be in the diving gas for the partial pressure of oxygen in the mixture to be 0.21 atm, the same as in air at 1 atm?

(a) What are the mole fractions of each component in a mixture of 15.08 g of O2, 8.17 g of N2, and 2.64 g of H2?

(b) What is the partial pressure in atm of each component of this mixture if it is held in a 15.50-L vessel at 15 C?

A quantity of N2 gas originally held at 5.25 atm pressure in a 1.00-L container at 26 C is transferred to a 12.5-L container at 20 C. A quantity of O2 gas originally at 5.25 atm and 26 C in a 5.00-L container is transferred to this same container. What is the total pressure in the new container?

A sample of 3.00 g of SO21g2 originally in a 5.00-L vessel at 21 C is transferred to a 10.0-L vessel at 26 C. A sample of 2.35 g of N21g2 originally in a 2.50-L vessel at 20 C is transferred to this same 10.0-L vessel. (a) What is the partial pressure of SO21g2 in the larger container? (b) What is the partial pressure of N21g2 in this vessel? (c) What is the total pressure in the vessel?

Determine whether each of the following changes will increase, decrease, or not affect the rate with which gas molecules collide with the walls of their container: (a) increasing the volume of the container, (b) increasing the temperature, (c) increasing the molar mass of the gas.

Indicate which of the following statements regarding the kinetic-molecular theory of gases are correct. (a) The average kinetic energy of a collection of gas molecules at a given temperature is proportional to m1>2 . (b) The gas molecules are assumed to exert no forces on each other. (c) All the molecules of a gas at a given temperature have the same kinetic energy. (d) The volume of the gas molecules is negligible in comparison to the total volume in which the gas is contained. (e) All gas molecules move with the same speed if they are at the same temperature.

Which assumptions are common to both kinetic-molecular theory and the ideal-gas equation?

Newton had an incorrect theory of gases in which he assumed that all gas molecules repel one another and the walls of their container. Thus, the molecules of a gas are statically and uniformly distributed, trying to get as far apart as possible from one another and the vessel walls. This repulsion gives rise to pressure. Explain why Charless law argues for the kineticmolecular theory and against Newtons model.

WF6 is one of the heaviest known gases. How much slower is the root-mean-square speed of WF6 than He at 300 K?

You have an evacuated container of fixed volume and known mass and introduce a known mass of a gas sample. Measuring the pressure at constant temperature over time, you are surprised to see it slowly dropping. You measure the mass of the gas-filled container and find that the mass is what it should begas plus containerand the mass does not change over time, so you do not have a leak. Suggest an explanation for your observations.

The temperature of a 5.00-L container of N2 gas is increased from 20 C to 250 C. If the volume is held constant, predict qualitatively how this change affects the following: (a) the average kinetic energy of the molecules; (b) the root-meansquare speed of the molecules; (c) the strength of the impact of an average molecule with the container walls; (d) the total number of collisions of molecules with walls per second.

Suppose you have two 1-L flasks, one containing N2 at STP, the other containing CH4 at STP. How do these systems compare with respect to (a) number of molecules, (b) density, (c) average kinetic energy of the molecules, (d) rate of effusion through a pinhole leak?

(a) Place the following gases in order of increasing average molecular speed at 25 C: Ne, HBr, SO2, NF3, CO.

(b) Calculate the rms speed of NF3 molecules at 25 C.

(c) Calculate the most probable speed of an ozone molecule in the stratosphere, where the temperature is 270 K.

(a) Place the following gases in order of increasing average molecular speed at 300 K: CO, SF6, H2S, Cl2, HBr.

(b) Calculate the rms speeds of CO and Cl2 molecules at 300 K.

(c) Calculate the most probable speeds of CO and Cl2 molecules at 300 K.

Explain the difference between effusion and diffusion.

At constant pressure, the mean free path 1l2 of a gas molecule is directly proportional to temperature. At constant temperature, l is inversely proportional to pressure. If you compare two different gas molecules at the same temperature and pressure, l is inversely proportional to the square of the diameter of the gas molecules. Put these facts together to create a formula for the mean free path of a gas molecule with a proportionality constant (call it Rmfp, like the ideal-gas constant) and define units for Rmfp

Hydrogen has two naturally occurring isotopes, 1 H and 2 H. Chlorine also has two naturally occurring isotopes, 35 Cl and 37 Cl. Thus, hydrogen chloride gas consists of four distinct types of molecules: 1 H35 Cl, 1 H37 Cl, 2 H35 Cl, and 2 H37 Cl. Place these four molecules in order of increasing rate of effusion.

As discussed in the Chemistry Put to Work box in Section 10.8, enriched uranium can be produced by effusion of gaseous UF6 across a porous membrane. Suppose a process were developed to allow effusion of gaseous uranium atoms, U(g). Calculate the ratio of effusion rates for 235 U and 238 U, and compare it to the ratio for UF6 given in the essay.

Arsenic(III) sulfide sublimes readily, even below its melting point of 320 C. The molecules of the vapor phase are found to effuse through a tiny hole at 0.28 times the rate of effusion of Ar atoms under the same conditions of temperature and pressure. What is the molecular formula of arsenic(III) sulfide in the gas phase?

A gas of unknown molecular mass was allowed to effuse through a small opening under constant- pressure conditions. It required 105 s for 1.0 L of the gas to effuse. Under identical experimental conditions it required 31 s for 1.0 L of O2 gas to effuse. Calculate the molar mass of the unknown gas. (Remember that the faster the rate of effusion, the shorter the time required for effusion of 1.0 L; in other words, rate is the amount that diffuses over the time it takes to diffuse.)

(a) List two experimental conditions under which gases deviate from ideal behavior.

(b) List two reasons why the gases deviate from ideal behavior

The planet Jupiter has a surface temperature of 140 K and a mass 318 times that of Earth. Mercury (the planet) has a surface temperature between 600 K and 700 K and a mass 0.05 times that of Earth. On which planet is the atmosphere more likely to obey the ideal-gas law? Explain.

Based on their respective van der Waals constants (Table 10.3), is Ar or CO2 expected to behave more nearly like an ideal gas at high pressures? Explain.

Briefly explain the significance of the constants a and b in the van der Waals equation.

In Sample Exercise 10.16, we found that one mole of Cl2 confined to 22.41 L at 0 C deviated slightly from ideal behavior. Calculate the pressure exerted by 1.00 mol Cl2 confined to a smaller volume, 5.00 L, at 25 C. (a) First use the ideal-gas equation and (b) then use the van der Waals equation for your calculation. (Values for the van der Waals constants are given in Table 10.3.) (c) Why is the difference between the result for an ideal gas and that calculated using the van der Waals equation greater when the gas is confined to 5.00 L compared to 22.4 L?

Calculate the pressure that CCl4 will exert at 40 C if 1.00 mol occupies 33.3 L, assuming that (a) CCl4 obeys the idealgas equation; (b) CCl4 obeys the van der Waals equation. (Values for the van der Waals constants are given in Table 10.3.) (c) Which would you expect to deviate more from ideal behavior under these conditions, Cl2 or CCl4? Explain

Table 10.3 shows that the van der Waals b parameter has units of L/mol. This implies that we can calculate the size of atoms or molecules from b. Using the value of b for Xe, calculate the radius of a Xe atom and compare it to the value found in Figure 7.7, that is, 1.40 . Recall that the volume of a sphere is 14>32pr 3

Table 10.3 shows that the van der Waals b parameter has units of L/mol. This means that we can calculate the sizes of atoms or molecules from the b parameter. Refer back to the discussion in Section 7.3. Is the van der Waals radius we calculate from the b parameter of Table 10.3 more closely associated with the bonding or nonbonding atomic radius discussed there? Explain.

A gas bubble with a volume of 1.0 mm3 originates at the bottom of a lake where the pressure is 3.0 atm. Calculate its volume when the bubble reaches the surface of the lake where the pressure is 730 torr, assuming that the temperature doesnt change

A 15.0-L tank is filled with helium gas at a pressure of 1.00 * 102 atm. How many balloons (each 2.00 L) can be inflated to a pressure of 1.00 atm, assuming that the temperature remains constant and that the tank cannot be emptied below 1.00 atm?

To minimize the rate of evaporation of the tungsten filament, 1.4 * 10-5 mol of argon is placed in a 600@cm3 lightbulb. What is the pressure of argon in the lightbulb at 23 C?

Carbon dioxide, which is recognized as the major contributor to global warming as a greenhouse gas, is formed when fossil fuels are combusted, as in electrical power plants fueled by coal, oil, or natural gas. One potential way to reduce the amount of CO2 added to the atmosphere is to store it as a compressed gas in underground formations. Consider a 1000-megawatt coal-fired power plant that produces about 6 * 106 tons of CO2 per year. (a) Assuming ideal-gas behavior, 1.00 atm, and 27 C, calculate the volume of CO2 produced by this power plant. (b) If the CO2 is stored underground as a liquid at 10 C and 120 atm and a density of 1.2 g>cm3 , what volume does it possess? (c) If it is stored underground as a gas at 36 C and 90 atm, what volume does it occupy?

Propane, C3H8, liquefies under modest pressure, allowing a large amount to be stored in a container. (a) Calculate the number of moles of propane gas in a 110-L container at 3.00 atm and 27 C. (b) Calculate the number of moles of liquid propane that can be stored in the same volume if the density of the liquid is 0.590 g>mL. (c) Calculate the ratio of the number of moles of liquid to moles of gas. Discuss this ratio in light of the kinetic-molecular theory of gases.

Nickel carbonyl, Ni1CO24, is one of the most toxic substances known. The present maximum allowable concentration in laboratory air during an 8-hr workday is 1 ppb (parts per billion) by volume, which means that there is one mole of Ni1CO24 for every 109 moles of gas. Assume 24 C and 1.00 atm pressure. What mass of Ni1CO24 is allowable in a laboratory room that is 12 ft * 20 ft * 9 ft?

When a large evacuated flask is filled with argon gas, its mass increases by 3.224 g. When the same flask is again evacuated and then filled with a gas of unknown molar mass, the mass increase is 8.102 g. (a) Based on the molar mass of argon, estimate the molar mass of the unknown gas. (b) What assumptions did you make in arriving at your answer?

Consider the arrangement of bulbs shown in the drawing. Each of the bulbs contains a gas at the pressure shown. What is the pressure of the system when all the stopcocks are opened, assuming that the temperature remains constant? (We can neglect the volume of the capillary tubing connecting the bulbs.) 1.0 L 265 torr 1.0 L 800 torr H2 N2 Ne 0.5 L 532 tor

Assume that a single cylinder of an automobile engine has a volume of 524 cm3 . (a) If the cylinder is full of air at 74 C and 0.980 atm, how many moles of O2 are present? (The mole fraction of O2 in dry air is 0.2095.) (b) How many grams of C8H18 could be combusted by this quantity of O2, assuming complete combustion with formation of CO2 and H2O?

Assume that an exhaled breath of air consists of 74.8% N2, 15.3% O2, 3.7% CO2, and 6.2% water vapor. (a) If the total pressure of the gases is 0.985 atm, calculate the partial pressure of each component of the mixture. (b) If the volume of the exhaled gas is 455 mL and its temperature is 37 C, calculate the number of moles of CO2 exhaled. (c) How many grams of glucose 1C6H12O62 would need to be metabolized to produce this quantity of CO2? (The chemical reaction is the same as that for combustion of C6H12O6. See Section 3.2 and Problem 10.57.)

A 1.42-g sample of helium and an unknown mass of O2 are mixed in a flask at room temperature. The partial pressure of the helium is 42.5 torr, and that of the oxygen is 158 torr. What is the mass of the oxygen?

An ideal gas at a pressure of 1.50 atm is contained in a bulb of unknown volume. A stopcock is used to connect this bulb with a previously evacuated bulb that has a volume of 0.800 L as shown here. When the stopcock is opened the gas expands into the empty bulb. If the temperature is held constant during this process and the final pressure is 695 torr, what is the volume of the bulb that was originally filled with gas?

The density of a gas of unknown molar mass was measured as a function of pressure at 0 C, as in the table that follows. (a) Determine a precise molar mass for the gas. [Hint: Graph d>P versus P.] (b) Why is d>P not a constant as a function of pressure? Pressure (atm) 1.00 0.666 0.500 0.333 0.250 Density (g/L) 2.3074 1.5263 1.1401 0.7571 0.5660

A glass vessel fitted with a stopcock valve has a mass of 337.428 g when evacuated. When filled with Ar, it has a mass of 339.854 g. When evacuated and refilled with a mixture of Ne and Ar, under the same conditions of temperature and pressure, it has a mass of 339.076 g. What is the mole percent of Ne in the gas mixture?

You have a sample of gas at -33 C. You wish to increase the rms speed by a factor of 2. To what temperature should the gas be heated?

Consider the following gases, all at STP: Ne, SF6, N2, CH4. (a) Which gas is most likely to depart from the assumption of the kinetic-molecular theory that says there are no attractive or repulsive forces between molecules? (b) Which one is closest to an ideal gas in its behavior? (c) Which one has the highest root-mean-square molecular speed at a given temperature? (d) Which one has the highest total molecular volume relative to the space occupied by the gas? (e) Which has the highest average kinetic-molecular energy? (f) Which one would effuse more rapidly than N2? (g) Which one would have the largest van der Waals b parameter?

Does the effect of intermolecular attraction on the properties of a gas become more significant or less significant if (a) the gas is compressed to a smaller volume at constant temperature; (b) the temperature of the gas is increased at constant volume?

Which of the noble gases other than radon would you expect to depart most readily from ideal behavior? Use the density data in Table 7.8 to show evidence in support of your answer.

It turns out that the van der Waals constant b equals four times the total volume actually occupied by the molecules of a mole of gas. Using this figure, calculate the fraction of the volume in a container actually occupied by Ar atoms (a) at STP, (b) at 200 atm pressure and 0 C. (Assume for simplicity that the ideal-gas equation still holds.)

Large amounts of nitrogen gas are used in the manufacture of ammonia, principally for use in fertilizers. Suppose 120.00 kg of N21g2 is stored in a 1100.0-L metal cylinder at 280 C. (a) Calculate the pressure of the gas, assuming idealgas behavior. (b) By using the data in Table 10.3, calculate the pressure of the gas according to the van der Waals equation. (c) Under the conditions of this problem, which correction dominates, the one for finite volume of gas molecules or the one for attractive interactions?

Cyclopropane, a gas used with oxygen as a general anesthetic, is composed of 85.7% C and 14.3% H by mass. (a) If 1.56 g of cyclopropane has a volume of 1.00 L at 0.984 atm and 50.0 C, what is the molecular formula of cyclopropane? (b) Judging from its molecular formula, would you expect cyclopropane to deviate more or less than Ar from ideal-gas behavior at moderately high pressures and room temperature? Explain. (c) Would cyclopropane effuse through a pinhole faster or more slowly than methane, CH4?

Consider the combustion reaction between 25.0 mL of liquid methanol 1density = 0.850 g>mL2 and 12.5 L of oxygen gas measured at STP. The products of the reaction are CO21g2 and H2O1g2. Calculate the volume of liquid H2O formed if the reaction goes to completion and you condense the water vapor.

An herbicide is found to contain only C, H, N, and Cl. The complete combustion of a 100.0-mg sample of the herbicide in excess oxygen produces 83.16 mL of CO2 and 73.30 mL of H2O vapor at STP. A separate analysis shows that the sample also contains 16.44 mg of Cl. (a) Determine the percentage of the composition of the substance. (b) Calculate its empirical formula. (c) What other information would you need to know about this compound to calculate its true molecular formula?

A 4.00-g sample of a mixture of CaO and BaO is placed in a 1.00-L vessel containing CO2 gas at a pressure of 730 torr and a temperature of 25 C. The CO2 reacts with the CaO and BaO, forming CaCO3 and BaCO3. When the reaction is complete, the pressure of the remaining CO2 is 150 torr. (a) Calculate the number of moles of CO2 that have reacted. (b) Calculate the mass percentage of CaO in the mixture.

Ammonia and hydrogen chloride react to form solid ammonium chloride: NH31g2 + HCl1g2 NH4Cl1s2 Two 2.00-L flasks at 25 C are connected by a valve, as shown in the drawing on the next page. One flask contains 5.00 g of NH31g2, and the other contains 5.00 g of HCl(g). When the valve is opened, the gases react until one is completely consumed. (a) Which gas will remain in the system after the reaction is complete? (b) What will be the final pressure of the system after the reaction is complete? (Neglect the volume of the ammonium chloride formed.) (c) What mass of ammonium chloride will be formed? 5.00 g 2.00 L 25 C 5.00 g 2.00 L 25 C NH3(g) HCl(g)

Gas pipelines are used to deliver natural gas (methane, CH4) to the various regions of the United States. The total volume of natural gas that is delivered is on the order of 2.7 * 1012 L per day, measured at STP. Calculate the total enthalpy change for combustion of this quantity of methane.

Chlorine dioxide gas 1ClO22 is used as a commercial bleaching agent. It bleaches materials by oxidizing them. In the course of these reactions, the ClO2 is itself reduced. (a) What is the Lewis structure for ClO2? (b) Why do you think that ClO2 is reduced so readily? (c) When a ClO2 molecule gains an electron, the chlorite ion, ClO2 -, forms. Draw the Lewis structure for ClO2 -. (d) Predict the OClO bond angle in the ClO2 - ion. (e) One method of preparing ClO2 is by the reaction of chlorine and sodium chlorite: Cl21g2 + 2 NaClO21s2 2 ClO21g2 + 2 NaCl1s2 If you allow 15.0 g of NaClO2 to react with 2.00 L of chlorine gas at a pressure of 1.50 atm at 21 C, how many grams of ClO2 can be prepared?

Natural gas is very abundant in many Middle Eastern oil fields. However, the costs of shipping the gas to markets in other parts of the world are high because it is necessary to liquefy the gas, which is mainly methane and has a boiling point at atmospheric pressure of -164 C. One possible strategy is to oxidize the methane to methanol, CH3OH, which has a boiling point of 65 C and can therefore be shipped more readily. Suppose that 10.7 * 109 ft 3 of methane at atmospheric pressure and 25 C is oxidized to methanol. (a) What volume of methanol is formed if the density of CH3OH is 0.791 g>mL? (b) Write balanced chemical equations for the oxidations of methane and methanol to CO21g2 and H2O1l2. Calculate the total enthalpy change for complete combustion of the 10.7 * 109 ft 3 of methane just described and for complete combustion of the equivalent amount of methanol, as calculated in part (a). (c) Methane, when liquefied, has a density of 0.466 g>mL; the density of methanol at 25 C is 0.791 g>mL. Compare the enthalpy change upon combustion of a unit volume of liquid methane and liquid methanol. From the standpoint of energy production, which substance has the higher enthalpy of combustion per unit volume?

Gaseous iodine pentafluoride, IF5, can be prepared by the reaction of solid iodine and gaseous fluorine: I21s2 + 5 F21g2 2 IF51g2 A 5.00-L flask containing 10.0 g of I2 is charged with 10.0 g of F2, and the reaction proceeds until one of the reagents is completely consumed. After the reaction is complete, the temperature in the flask is 125 C. (a) What is the partial pressure of IF5 in the flask? (b) What is the mole fraction of IF5 in the flask (c) Draw the Lewis structure of IF5. (d) What is the total mass of reactants and products in the flask?

A 6.53-g sample of a mixture of magnesium carbonate and calcium carbonate is treated with excess hydrochloric acid. The resulting reaction produces 1.72 L of carbon dioxide gas at 28 C and 743 torr pressure. (a) Write balanced chemical equations for the reactions that occur between hydrochloric acid and each component of the mixture. (b) Calculate the total number of moles of carbon dioxide that forms from these reactions. (c) Assuming that the reactions are complete, calculate the percentage by mass of magnesium carbonate in the mixture.

Problem 1DE You are given a cylinder of an unknown, non-radioactive, noble gas and tasked to determine its molar mass and use that value to identify the gas. The tools available to you are several empty mylar balloons that are about the size of a grapefruit when inflated (gases diffuse through mylar much more slowly than conventional latex balloons), an analytical balance, and three graduated glass beakers of different sizes (100 mL, 500 mL, and 2 L). (a) To how many significant figures would you need to determine the molar mass to identify the gas? (b) Propose an experiment or series of experiments that would allow you to determine the molar mass of the unknown gas. Describe the tools, calculations, and assumptions you would need to use. (c) If you had access to a broader range of analytical instruments, describe an alternative way you could identify the gas using any experimental methods that you have learned about in the earlier chapters.

Problem 1E Visualizing Concepts Mars has an average atmospheric pressure of 0.007 atm. Would it be easier or harder to drink from a straw on Mars than on Earth? Explain. [Section]

Problem 5E Visualizing Concepts Suppose you have a fixed amount of an ideal gas at a constant volume. If the pressure of the gas is doubled while the volume is held constant, what happens to its temperature? [Section]

Problem 4E Visualizing Concepts Imagine that the reaction 2 CO(g) + O2(g)?2 CO2(g) occurs in a container that has a piston that moves to maintain a constant pressure when the reaction occurs at constant temperature. Which of the following statements describes how the volume of the container changes due to the reaction: (a) the volume increases by 50%, (b) the volume increases by 33%, (c) the volume remains constant, (d) the volume decreases by 33%, (e) the volume decreases by 50%. [Sections]

You have a sample of gas in a container with a movable piston, such as the one in the drawing. (a) Redraw the container to show what it might look like if the temperature of the gas is increased from \(300 \text { to } 50 \mathrm{~K}\) while the pressure is kept constant. (b) Redraw the container to show what it might look like if the external pressure on the piston is increased from \(\text { 1. atm to } 2.0 \mathrm{~atm}\) while the temperature is kept constant. (c) Redraw the container to show what it might look like if the temperature of the gas decreases from \(300 \text { to } 200 \mathrm{~K}\) while the pressure is kept constant (assume the gas does not liquefy). [Section 10.3] Equation Transcription: Text Transcription: 300 to 50 K 1. atm to 2.0 atm 300 to 200 K

Consider the sample of gas depicted here. What would the drawing look like if the volume and temperature remained constant while you removed enough of the gas to decrease the pressure by a factor of 2? [Section 10.3]

The apparatus shown here has two gas-filled containers and one empty container, all attached to a hollow horizontal tube. When the valves are opened and the gases are allowed to mix at constant temperature, what is the distribution of atoms in each container? Assume that the containers are of equal volume and ignore the volume of the connecting tube. Which gas has the greater partial pressure after the valves are opened? [Section 10.6]

Problem 8E Visualizing Concepts On a single plot, qualitatively sketch the distribution of molecular speeds for (a) Kr(g) at -50 °C, (b) Kr(g) at 0 °C, (c) Ar(g) at 0 °C. [Section]

Consider the following graph. (a) If curves A and B refer to two different gases, \(\mathrm{He} \text { and } \mathrm{O}_{2}\) at the same temperature, which curve corresponds to He? (b) If A and B refer to the same gas at two different temperatures, which represents the higher temperature? (c) For each curve which speed is highest: the most probable speed, the root-mean-square speed, or the average speed? [Section10.7] \(\mathrm{HCl}\) gas is introduced at one end of the tube, and simultaneously \(\mathrm{NH}_{3}\) gas is introduced at the other end. When the two gases diffuse through the cotton plugs down the tube and meet, a white ring appears due to the formation of \(\mathrm{NH}_{4} \mathrm{Cl}(\mathrm{s})\). At which location \(a, b, \text { or } c\) - do you expect the ring to form? [Section Equation Transcription: Text Transcription: He and O2 HCl NH3 NH4Cl(s) a,b, or c

The accompanying drawing represents a mixture of three different gases. (a) Rank the three components in order of increasing partial pressure. (b) If the total pressure of the mixture is \(1.40 \mathrm{~atm}\), calculate the partial pressure of each gas. [Section 10.6] Equation Transcription: Text Transcription: 1.40 atm

A thin glass tube \(1 \mathrm{~m}\) long is filled with Ar gas at \(1 \mathrm{~atm}\), and the ends are stoppered with cotton plugs: \(\mathrm{HCl}\) gas is introduced at one end of the tube, and simultaneously \(\mathrm{NH}_{3}\) gas is introduced at the otherend. When the two gases diffuse through the cotton plugs down the tube and meet, a white ring appears due to the formation of \(\mathrm{NH}_{4} \mathrm{Cl}(\mathrm{s})\). At which location a,b,or c -do you expect the ring to form? [Section Equation Transcription: Text Transcription: 1 m 1 atm HCl NH3 NH4Cl(s)

Consider the following samples of gases: If the three samples are all at the same temperature, rank them with respect to (a) total pressure, (b) partial pressure of helium, (c) density, (d) average kinetic energy of particles.[Section 10.6 and 10.7] Equation Transcription: Text Transcription: =He =N2

Problem 13E Gas Characteristics; Pressure (Sections) How does a gas compare with a liquid for each of the following properties: (a) density, (b) compressibility, (c) ability to mix with other substances of the same phase to form homogeneous mixtures, (d) ability to conform to the shape of its container?

The graph below shows the change in pressure as the temperature increases for a \(1-\text { mol }\) sample of a gas confined to a \(1-L\) container. The four plots correspond to an ideal gas and three real gases: \(\mathrm{CO}_{2}, N_{2}, \text { and } \mathrm{Cl}_{2}\). (a) At room temperature, all three real gases have a pressure less than the ideal gas. Which van der Waals constant, \(a \text { or } b \text\), accounts for the influence intermolecular forces have in lowering the pressure of a real gas? (b) Use the van der Waals constants in Table to match the labels in the plot \((A, B, \text { and } C)\) with the respective gases \(\left(\mathrm{CO}_{2}, \mathrm{~N}_{2}, \text { and } \mathrm{Cl}_{2}\right)\).[Section 10.9 Equation Transcription: Text Transcription: 1-mol 1-L CO2, N2, and Cl2 a or b (A,B and C) (C02, N2, and Cl2)

Problem 14E Gas Characteristics; Pressure (Sections) (a) A liquid and a gas are moved to larger containers. How does their behavior differ once they are in the larger containers? Explain the difference in molecular terms. (b) Although liquid water and carbon tetrachloride, CCl4(l), do not mix, their vapors form a homogeneous mixture. Explain. (c) Gas densities are generally reported in grams per liter, whereas liquid densities are reported in grams per milliliter. Explain the molecular basis for this difference.

Problem 16E Gas Characteristics: Pressure (Sections) A set of bookshelves rests on a hard floor surface on four legs, each having a cross-sectional dimension of 3.0 * 4.1 cm in contact with the floor. The total mass of the shelves plus the books stacked on them is 262 kg. Calculate the pressure in pascals exerted by the shelf footings on the surface.

Problem 15E Gas Characteristics: Pressure (Sections) Suppose that a woman weighing 130 lb and wearing highheeled shoes momentarily places all her weight on the heel of one foot. If the area of the heel is 0.50 in.2. calculate the pressure exerted on the underlying surface in (a) kilopascals. (b) atmospheres, and (c) pounds per square inch.

Problem 18E Gas Characteristics: Pressure (Sections) The compound 1-iodododecane is a nonvolatile liquid with a density of 1.20 g/mL. The density of mercury is 13.6 g/mL. What do you predict for the height of a barometer column based on 1-iodododecane. when the atmospheric pressure is 749 torr?

Problem 17E Gas Characteristics: Pressure (Sections) (a) How high in meters must a column of water be to exert a pressure equal to that of a 760-mm column of mercury? The density of water is 1.0 g/mL. whereas that of mercury is 13.6 g/mL. (b) What is the pressure, in atmospheres, on the body of a diver if he or she is 39 ft below the surface of the water when atmospheric pressure at the surface is 0.97 atm?

Problem 19E Gas Characteristics: Pressure (Sections) The typical atmospheric pressure on top of Ml Everest (29.028 ft) is about 265 torr. Convert this pressure to (a) atm. (b) mm Hg. (c) pascals, (d) bars, (e) psi.

Problem 20E Gas Characteristics: Pressure (Sections) Perform the foDov/ing conversions: (a) 0.912 atm to torr. (b) 0.685 bar to kSopascab, (c) 655 mm Hg to atmospheres, (d) 1.323 * 105 Pa to atmospheres, (e) 2.50 atm to psi.

Problem 21E Gas Characteristics: Pressure (Sections) In the United States, barometric pressures are generally reported in inches of mercury (in. Hg). On a beautiful summer day in Chicago, the barometric pressure is 30.45 in. Hg. (a) Convert this pressure to torr. (b) Convert this pressure to atm

Problem 22E Gas Characteristics: Pressure (Sections) Hurricane Wilma of 2005 is the most intense hurricane on record in the Atlantic basin, with a low-pressure reading of &82 mbar (millibars). Convert this reading into (a) atmospheres, (b) torr. and (c) inches of Hg.

If the atmospheric pressure is \(0.995 \mathrm{~atm}\), what is the pressure of the enclosed gas in each of the three cases depicted in the drawing? Assume that the gray liquid is mercury. Equation Transcription: Text Transcription: 0.995 atm h=52 cm h=67 cm h=10.3 cm

An open-end manometer containing mercury is connected to a container of gas, as depicted in Sample Exercise 10.2. What is the pressure of the enclosed gas in torr in each of the following situations? (a) The mercury in the arm attached to the gas is \(15.4 \mathrm{~mm}\) higher than in the one open to the atmosphere; atmospheric pressure is \(0.985 \mathrm{~atm}\). (b) The mercury in the arm attached to the gas is \(12.3 \mathrm{~mm}\) lower than in the one open to the atmosphere; atmospheric pressure is \(0.99 \mathrm{~atm}\). Equation Transcription: Text Transcription: 15.4 mm 0.985 atm 12.3 mm 0.99 atm

Problem 25E The Gas Laws (Section) You have a gas at 25 °C confined to a cylinder with a movable piston. Which of the following actions would double the gas pressure? (a) Lifting up on the piston to double the volume while keeping the temperature constant: (b) Heating the gas so that its temperature rises from 25 5C to 50 5C. while keeping the volume constant: (c) Pushing down on the piston to halve the volume while keeping the temperature constant.

Problem 26E The Gas Laws (Section) A fixed quantity of gas at 21 °C exhibits a pressure of 752 torr and occupies a volume of 5.12 L. (a) Calculate the volume the gas will occupy if the pressure is increased to 1.88 atm while the temperature is held constant, (b) Calculate the volume the gas will occupy if the temperature is increased to 175 °C while the pressure is held constant.

Problem 28E The Gas Laws (Section) Nitrogen and hydrogen gases react to form ammonia gas as follows: N2(g) + 3 H2(g)-»2 NH3(g) At a certain temperature and pressure. 1.2 L of N2 reacts with 3.6 L of H2. If all the N2 and H2 are consumed, what volume of NH3. at the same temperature and pressure, will be produced?

Problem 29E The Ideal-Gas Equation (Section) (a) What conditions are represented by the abbreviation STP? (b) What is the molar volume of an ideal gas at STP? (c) Room temperature is often assumed to be 25 °C. Calculate the molar volume of an ideal gas at 25 °C and 1 atm pressure, (d) If you measure pressure in bars instead of atmospheres, calculate the corresponding value of R in L-ban'mol-K.

Problem 27E The Gas Laws (Section) (a) Amonton s law expresses the relationship between pressure and temperature. Use Charless law and Boyle s law to derive the proportionality relationship between P and T. (b) If a car tire is filled to a pressure of 32.0 lbs/in.2 (psi) measured at 75 5F. what will be the tire pressure if the tires heat up to 120 :F during driving?

Problem 30E The Ideal-Gas Equation (Section) To derive the ideal-gas equation, we assume that the volume of the gas atoms/molecules can be neglected. Given the atomic radius of neon. 0.69 A. and knowing that a sphere has a volume of 4ttt3/3. calculate the fraction of space that Ne atoms occupy in a sample of neon at STP.

Problem 31E The Ideal-Gas Equation (Section) Suppose you are given two 1-L flasks and told that one contains a gas of molar mass 30. the other a gas of molar mass 60. both at the same temperature. The pressure in flask A is X atm. and the mass of gas in the flask is 1.2 g. The pressure in flask B is 0.5X atm. and the mass of gas in that flask is 1.2 g. Which flask contains the gas of molar mass 30. and which contains the gas of molar mass 60?

Problem 32E The Ideal-Gas Equation (Section) Suppose you are given two flasks at the same temperature, one of volume 2 L and the other of volume 3 L. The 2-L flask contains 4.8 g of gas. and the gas pressure is X atm. The 3-L flask contains 0.36 g of gas. and the gas pressure is 0.1X. Do the two gases have the same molar mass? If not. which contains the gas of higher molar mass?

Problem 33E The Ideal-Gas Equation (Section) Complete the following table for an ideal gas: P V n T 2.00 atm 1.00 L 0.500 mol ? K 0.300 atm 0.250 L ? mol 27 °C 650 torr ? L 0.333 mol 350 K ? atm 585 mL 0.250 mol 295 K

Problem 34E The Ideal-Gas Equation (Section) Calculate each of the foDov/ing quantities for an ideal gas: (a) the volume of the gas. in liters, if 1.50 mol has a pressure of 1.25 atm at a temperature of -6 SC: (b) the absolute temperature of the gas at which 3.33 * 10-3 mol occupies 478 mL at 750 torr: (c) the pressure, in atmospheres, if 0.00245 mol occupies 413 mL at 138 =C; (d) the quantity of gas. in moles, if 126.5 L at 54 SC has a pressure of 11.25 kPa

Problem 35E The Ideal-Gas Equation (Section) The Goodyear blimps, which frequently fly over sporting events, hold approximately 175.000 ft3 of helium. If the gas is at 23 SC and 1.0 atm. what mass of helium is in a blimp?

Problem 36E The Ideal-Gas Equation (Section) A neon sign is made of glass tubing whose inside diameter is 2.5 cm and whose length is 5.5 m. If the sign contains neon at a pressure of 1.78 torr at 35 SC. how many grams of neon are in the sign? (The volume of a cylinder is irr2h.)

Problem 37E The Ideal-Gas Equation (Section) (a) Calculate the number of molecules in a deep breath of air whose volume is 2.25 L at body temperature. 37 SC. and a pressure of 735 torr. (b) The adult blue whale has a lung capacity of 5.0 x 103 L. Calculate the mass of air (assume an average molar mass of 28.98 g/mol) contained in an adult blue whale's lungs at 0.0 SC and 1.00 atm. assuming the air behaves ideally-

Problem 38E The Ideal-Gas Equation (Section) (a) If the pressure exerted by ozone. 03. in the stratosphere is 3.0 x 10-3 atm and the temperature is 250 K. how many ozone molecules are in a liter7 (b) Carbon dioxide makes up approximately 0.04% of Earth s atmosphere. If you collect a 2.0-L sample from the atmosphere at sea level (1.00 atm) on a warm day (27 °C), how many C02 molecules are in your sample?

Problem 39E The Ideal-Gas Equation (Section) A scuba diver's tank contains 0.29 kg of 02 compressed into a volume of 2.3 L. (a) Calculate the gas pressure inside the tank at 9 SC. (b) What volume would this oxygen occupy at 26 SC and 0.95 atm’

Problem 41E The Ideal-Gas Equation (Section) A 35.1 g sample of solid C02 (dry ice) is added to a container at a temperature of 100 K with a volume of 4.0 L. If the container is evacuated (all of the gas removed), sealed and then allowed to warm to room temperature (T = 298 K) so that all of the solid C02 is converted to a gas. what is the pressure inside the container

Problem 42E The Ideal-Gas Equation (Section) A 334-mL cylinder for use in chemistry lectures contains 5.225 g of helium at 23 SC. How many grams of helium must be released to reduce the pressure to 75 atm assuming ideal gas behavior?

Problem 40E The Ideal-Gas Equation (Section) An aerosol spray can with a volume of 250 mL contains 2.30 g of propane gas (C3H8) as a propellant, (a) If the can is at 23 SC. what is the pressure in the can? (b) What volume would the propane occupy at STP? (c) The can's label says that exposure to temperatures above 130 =F may cause the can to burst. What is the pressure in the can at this temperature?

Problem 44E The Ideal-Gas Equation (Section) Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is 55.0 gallons that contains 02 gas at a pressure of 16.500 kPa at 23 SC. (a) What mass of 02 does the tank contain? (b) What volume would the gas occupy at STP7 (c) At what temperature would the pressure in the tank equal 150.0 atm7 (d) What would be the pressure of the gas. in kPa. if it were transferred to a container at 24 =C whose volume is 55.0 L?

Problem 43E The Ideal-Gas Equation (Section) Chlorine is widely used to purify municipal water supplies and to treat swimming pool waters. Suppose that the volume of a particular sample of CI2 gas is 8.70 L at 895 torr and 24 5C. (a) How many grams of CI2 are in the sample7 (b) What volume will the CI2 occupy at STP? (c) At what temperature will the volume be 15.00 L if the pressure is 8.76 x 102 torr? (d) At what pressure will the volume equal 5.00 L if the temperature is 58 °C?

Problem 45E The Ideal-Gas Equation (Section) In an experiment reported in the scientific literature, male cockroaches were made to run at different speeds on a miniature treadmill while their oxygen consumption was measured. In 1 average cockroach running at 0.08 km>hr consumed 0.8 mL of 02 at 1 atm pressure and 2^ per gram of insect mass, (a) How many moles of 02 would be consumed in 1 hr by a 5.2-g cockroach moving at this speed7 (b) This same cockroach is caught by a child and placed ii qt fruit jar with a tight lid. Assuming the same level of continuous activity as in the research.« cockroach consume more than 20% of the available 02 in a 4&-hr period7 (Air is 21 mol % C

Problem 46E The Ideal-Gas Equation (Section) The physical fitness of athletes is measured by "1/02 max.’ which is the maximum volume of oxygen consumed by an individual during incremental exercise (for example, on a treadmill. An average male has a V02 max of 45 mL 02/kg body mass/min. but a world-class male athlete can have a V02 max reading of &8.0 mL 02/kg body mass/min (a) Calculate the volume of oxygen, in mL. consumed in 1 hr by an average man who weighs 185 lbs and has a VO 2 max reading of 47.5 mL 02/kg body mass/min. (b) If this man lost 20 b. exercised, and increased his V02 max to 65.0 mL 02/kg body mass/min. how many mL of oxygen would he consume in 1 hr

Further Applications of the Ideal-Gas Equation (Section) Which gas is most dense at 1.00 atm and 298 K: . or ? Explain

Further Applications of the Ideal-Gas Equation (Section) Rank the (blowing gases from least dense to most dense at 1.00 atm and 298 K: . Explain.

Further Applications of the Ideal-Gas Equation (Section) Which of the following statements best explains why nitrogen gas at STP is less dense than Xe gas at STP? (a) Because Xe is a noble gas. There is less tendency for the Xe atoms to repel one another, so they pack more densely in the gaseous state. (b) Xe atoms have a higher mass than molecules. Because both gases at STP have the same number of molecules per unit volume, the Xe gas must be denser. (c) The Xe atoms are larger than molecules and thus take up a larger fraction of the space occupied by the gas. (d) Because the Xe atoms are much more massive than the molecules, they move more slowly and thus exert less upward force on the gas container and make the gas appear denser.

Further Applications of the Ideal-Gas Equation (Section) Which of the following statements best explains why a closed balloon filled with helium gas rises in air’ (a) Helium is a monatomic gas. whereas nearly all the molecules that make up air. such as nitrogen and oxygen, are diatomic. (b) The average speed of helium atoms is greater than the average speed of air molecules, and the greater speed of collisions with the balloon walls propels the balloon upward. (c) Because the helium atoms are of lower mass than the average air molecule, the helium gas is less dense than air. The mass of the balloon is thus less than the mass of the air displaced by its volume. (d) Because helium has a lower molar mass than the average air molecule, the helium atoms are in faster motion. This means that the temperature of the helium is greater than the air temperature. Hot gases tend to rise.

Further Applications of the Ideal-Gas Equation (Section) (a) Calculate the density of gas at 0.970 atm and . (b) Calculate the molar mass of a gas if 2.50 g occupies 0.875 L at 685 torr and .

Further Applications of the Ideal-Gas Equation (Section) (a) Calculate the density of sulfur hexafluoride gas at 707 torr and . (b) Calculate the molar mass of a vapor that has a density of 7.135 g/L at and 743 torr.

In the Dumas-bulb technique for determining the molar mass of an unknown liquid, you vaporize the sample of a liquid that boils below \(100^{\circ} \mathrm{C}\) in a boiling-water bath and determine the mass of vapor required to fill the bulb. From the following data, calculate the molar mass of the unknown liquid: mass of unknown vapor, \(1.012 \mathrm{~g}\); volume of bulb, \(354 \mathrm{~cm}^{3}\); pressure, 742 torr; temperature, \(99^{\circ} \mathrm{C}\). Equation Transcription: Text Transcription: 100°C 1.012 g 354 cm3 99°C

Further Applications of the Ideal-Gas Equation (Section) The molar mass of a volatile substance was determined by the Dumas-bulb method described in Exercise 10.53. The unknown vapor had a mass of 0.846 g: the volume of the bulb was , pressure 752 torr. and temperature . Calculate the molar mass of the unknown vapor.

What is the molecularity of each of the following elementary reactions? Write the rate law for each.

Reaction Mechanisms (Section) (a) Based on the following reaction profile, how many intermediates are formed in the reaction A?D? (b) How many transition states are there? (c) Which step is the fastest? (d) For the reaction A?D, is ????E positive, negative, or zero?

Reaction Mechanisms (Section) Consider the following energy profile. (a) How many elementary reactions are in the reaction mechanism? (b) How many intermediates are formed in the reaction? (c) Which step is rate limiting? (d) For the overall reaction, is AE positive, negative, or zero?

Reaction Mechanisms (Section) The following mechanism has been proposed for the gas phase reaction of with : (a) Write the balanced equation for the overall reaction, (b) Identify any intermediates in the mechanism, (c) If the first step is slow and the second one is fast, which rate law do you expect to be observed for the overall reaction?

Reaction Mechanisms (Section) The decomposition of hydrogen peroxide is catalyzed by iodide ion. The catalyzed reaction is thought to proceed by a two-step mechanism: (slow step) (fast step) (a) Write the chemical equation for the overall process, (b) Identify the intermediate, if any, in the mechanism, (c) Assuming that the first step of the mechanism is rate determining, predict the rate law for the overall process.

Reaction Mechanisms (Section) The reaction was performed and the following data obtained under conditions of constant : (b) Does the linear plot guarantee that the overall rate law is second order?

Consider the apparatus shown in the following drawing. (a) When the valve between the two containers is opened and the gases allowed to mix, how does the volume occupied by the \(N_{2}\) gas change? What is the partial pressure of \(N_{2}\) after mixing? (b) How does the volume of the \(O_{2}\) gas change when the gases mix? What is the partial pressure of \(O_{2}\) in the mixture? (c) What is the total pressure in the container after the gases mix? Equation Transcription: Text Transcription: N2 N2 O2 O2 2.0 L 1.0 atm 25°C 3.0 L 2.0 atm 25°C

Problem 62e Partial Pressures (Section) Consider a mixture of two gases. A and B. confined in a closed vessel. A quantity of a third gas. C. is added to the same vessel at the same temperature. How does the addition of gas C affect the following: (a) the partial pressure of gas A. (b) the total pressure in the vessel, (c) the mole fraction of gas B?

Problem 63e Partial Pressures (Section) Consider a mixture of two gases. A and B. confined in a closed vessel. A quantity of a third gas. C, is added to the same vessel at the same temperature. How does the addition of gas C affect the following: (a) the partial pressure of gas A, (b) the total pressure in the vessel, (c) the mole fraction of gas B?

The atmospheric concentration of gas is presently 390 ppm (parts per million, by volume: that is. 390 L of every 106 L of the atmosphere are ). What is the mole fraction of in the atmosphere?

Partial Pressures (Section) A mixture containing 0.765 mol He(g). 0.330 mol Ne(g). and 0.110 mol Ar(g) is confined in a 10.00-L vessel at . (a) Calculate the partial pressure of each of the gases in the mixture, (b) Calculate the total pressure of the mixture.

Problem 66e Partial Pressures (Section) A plasma-screen TV contains thousands of tiny cells filled with a mixture of Xe. Ne. and He gases that emits light of specific wavelengths when a voltage is applied. A particular plasma cell. 0.900 mm x 0.300 mm x 10.0 mm. contains 4% Xe in a 1:1 Ne:He mixture at a total pressure of 500 torr. Calculate the number of Xe. Ne. and He atoms in the cell and state the assumptions you need to make in your calculation.

A piece of dry ice (Solid carbon dioxide) with a mass of 5.50 g is placed in a 10.0-L vessel that already contains air at 705 torr and 24 SC. After the carbon dioxide has totally sublimed, what is the partial pressure of the resultant C02 gas. and the total pressure in the container at ?

A rigid vessel containing a 3:1 mol ratio of carbon dioxide and water vapor is held at 200 SC where it has a total pressure of 2.00 atm. If the vessel is cooled to 10 SC so that all of the water vapor condenses, what is the pressure of carbon dioxide? Neglect the volume of the liquid water that forms on cooling.

Partial Pressures (Section) A sample of 5.00 mL of diethyl ether is introduced into a 6.00-L vessel that already contains a mixture of N2 and O2, whose partial pressures are and . The temperature is held at 35.0 °C, and the diethylether totally evaporates. (a) Calculate the partial pressure of the diethylether. (b) Calculate the total pressure in the container.

Problem 70e Partial Pressures (Section) If 5.15 g of Ag20 is sealed in a 75.0-mL tube filled with 760 torr of N2 gas at 32 SC. and the tube is heated to 320 SC. the Ag20 decomposes to form oxygen and silver. What is the total pressure inside the tube assuming the volume of the tube remains constant?

At an underwater depth of 250 ft. the pressure is 8.38 atm. What should the mole percent of oxygen be in the diving gas for the partial pressure of oxygen in the mixture to be 0.21 atm. the same as in air at 1 atm?

Problem 72e Partial Pressures (Section) (a) What are the mole fractions of each component in a mixture of 15.08 g of 02. 8.17 g of N2. and 2.64 g of H2? (b) What is the partial pressure in atm of each component of this mixture if it is held in a 15.50-L vessel at 15C?

Problem 73e Partial Pressures (Section) A quantity of N2 gas originally held at 5.25 atm pressure in a 1.00-L container at 26 SC is transferred to a 12.5-L container at 20 SC. A quantity of 02 gas originally at 5.25 atm and 26 SC in a 5.00-L container is transferred to this same container. What is the total pressure in the new container?

Problem 74e Partial Pressures (Section) A sample of 3.00 g of S02(g; originally in a 5.00-L vessel at 21 SC is transferred to a 10.0-L vessel at 26 SC. A sample of 2.35 g of N2(gj originally in a 2.50-L vessel at 20 SC is transferred to this same 10.0-L vessel, (a) What is the partial pressure of S02(g; in the larger container7 (b) What is the partial pressure of N2(g; in this vessel? (c) What is the total pressure in the vessel?

Determine whether each of the following changes wfl increase, decrease, or not affect the rate with which gas molecules collide with the walls of their container: (a) increasing the volume of the container, (b) increasing the temperature, (c) increasing the molar mass of the gas.

Kinetic-Molecular Theory of Gases: Effusion and Diffusion (Sections) Indicate which of the (blowing statements regarding the kinetic-molecular theory of gases are correct, (a) The average kinetic energy of a collection of gas molecules at a given temperature is proportional to . (b) The gas molecules are assumed to exert no forces on each other, (c) All the molecules of a gas at a given temperature have the same kinetic energy, (d) The volume of the gas molecules is negligible in comparison to the total volume in which the gas is contained, (e) All gas molecules move with the same speed if they are at the same temperature.

Problem 77e Kinetic-Molecular Theory of Gases; Effusion and Diffusion (Sections) Which assumptions are common to both kinetic-molecular theory and the ideal-gas equation?

Problem 78e Kinetic-Molecular Theory of Gases: Effusion and Diffusion (Sections) Newton had an incorrect theory of gases in which he assumed that an gas molecules repel one another and the walls of their container. Thus, the molecules of a gas are statically and uniformly distributed, trying to get as far apart as possible from one another and the vessel walls. This repulsion gives rise to pressure. Explain why Charles s law argues for the kineticmolecular theory and against Newton’s model.

Problem 79e Kinetic-Molecular Theory of Gases: Effusion and Diffusion (Sections) WF6 is one of the heaviest known gases. How much slower is the root-mean-square speed of WF6 than He at 300 K?

Problem 80e Kinetic-Molecular Theory of Gases: Effusion and Diffusion (Sections) You have an evacuated container of fixed volume and known mass and introduce a known mass of a gas sample. Measuring the pressure at constant temperature over time, you are surprised to see it sknvty dropping. You measure the mass of the gas-filled container and find that the mass is what it should be—gas plus container—and the mass does not change over time, so you do not have a leak. Suggest an explanation for your observations.

Problem 81e Kinetic-Molecular Theory of Gases: Effusion and Diffusion (Sections) The temperature of a 5.00-L container of N2 gas is increased from 20 SC to 250 =C. If the volume held constant, predict qualitatively how this change affects the foDowing: (a) the average kinetic energy of the molecules: (b) the root-meansquare speed of the molecules; (c) the strength of the impact of an average molecule with the container walls: (d) the total number of collisions of molecules with walls per second.

Problem 82e Kinetic-Molecular Theory of Gases: Effusion and Diffusion (Sections) Suppose you have two 1-L flasks, one containing N2 at STP. the other containing CH4 at STP How do these systems compare with respect to (a) number of molecules, (b) density, (c) average kinetic energy of the molecules, (d) rate of effusion through a pinhole leak?

Problem 83e Kinetic-Molecular Theory of Gases; Effusion and Diffusion (Sections) (a) Place the following gases in order of increasing average molecular speed at 25 SC: Ne. HBr. S02. NF3. CO. (b) Calculate the rms speed of NF3 molecules at 25 =C. (c) Calculate the most probable speed of an ozone molecule in the stratosphere, where the temperature is 270 K.

Problem 84e Kinetic-Molecular Theory of Gases; Effusion and Diffusion (Sections) (a) Place the following gases in order of increasing average molecular speed at 300 K: CO. SF6, H2S. C12. HBr. (b) Calculate the rms speeds of CO and C12 molecules at 300 K. (c) Calculate the most probable speeds of CO and C12 molecules at 300 K.

Problem 85e Kinetic-Molecular Theory of Gases; Effusion and Diffusion (Sections) Explain the difference between effusion and diffusion.

Problem 87e Kinetic-Molecular Theory of Gases: Effusion and Diffusion (Sections) Hydrogen has two naturally occurring isotopes. 1H and 2H. Chlorine also has two naturally occurring isotopes. 35CI and 37CI. Thus, hydrogen chloride gas consists of four distinct types of molecules: 1H35CI. 1H37CI. 2H35CI. and 2H37CI. Place these four molecules in order of increasing rate of effusion.

Problem 86e Kinetic-Molecular Theory of Gases: Effusion and Diffusion (Sections) At constant pressure, the mean free path (A) of a gas molecule is directly proportional to temperature. At constant temperature, A is inversely proportional to pressure. If you compare two different gas molecules at the same temperature and pressure, A is inversely proportional to the square of the diameter of the gas molecules. Put these facts together to create a formula for the mean free path of a gas molecule with a proportionality constant (call it Pmfp. Ike the ideal-gas constant) and define units for Pmfp.

Problem 88E Kinetic-Molecular Theory of Gases; Effusion and Diffusion (Sections) As discussed in the “Chemistry Put to Work” box in Section, enriched uranium can be produced by effusion of gaseous UF6 across a porous membrane. Suppose a process were developed to allow effusion of gaseous uranium atoms, U(g). Calculate the ratio of effusion rates for 235U and 238U, and compare it to the ratio for UF6 given in the essay.

Problem 89E Kinetic-Molecular Theory of Gases; Effusion and Diffusion (Sections) Arsenic(III) sulfide sublimes readily, even below its melting point of 320 °C. The molecules of the vapor phase are found to effuse through a tiny hole at 0.28 times the rate of effusion of Ar atoms under the same conditions of temperature and pressure. What is the molecular formula of arsenic(III) sulfide in the gas phase?

Problem 90E Kinetic-Molecular Theory of Gases; Effusion and Diffusion (Sections) A gas of unknown molecular mass was allowed to effuse through a small opening under constant-pressure conditions. It required 105 s for 1.0 L of the gas to effuse. Under identical experimental conditions it required 31 s for 1.0 L of O2 gas to effuse. Calculate the molar mass of the unknown gas. (Remember that the faster the rate of effusion, the shorter the time required for effusion of 1.0 L; in other words, rate is the amount that diffuses over the time it takes to diffuse.)

Problem 91E Nonideal-Gas Behavior (Section) (a) List two experimental conditions under which gases deviate from ideal behavior. (b) List two reasons why the gases deviate from ideal behavior.

Problem 92E Nonideal-Gas Behavior (Section) The planet Jupiter has a surface temperature of 140 K and a mass 318 times that of Earth. Mercury (the planet) has a surface temperature between 600 K and 700 K and a mass 0.05 times that of Earth. On which planet is the atmosphere more likely to obey the ideal-gas law? Explain.

Problem 94E Nonideal-Gas Behavior (Section) Briefly explain the significance of the constants a and b in the van der Waals equation.

Problem 93E Nonideal-Gas Behavior (Section) Based on their respective van der Waals constants (Table), is Ar or CO2 expected to behave more nearly like an ideal gas at high pressures? Explain. Table Van der Waals Constants for Gas Molecules Substance a(L2@atm/mol2) b(L/mol) He 0.0341 0.02370 Ne 0.211 0.0171 Ar 1.34 0.0322 Kr 2.32 0.0398 Xe 4.19 0.0510 H2 0.244 0.0266 N2 1.39 0.0391 O2 1.36 0.0318 F2 1.06 0.0290 Cl2 6.49 0.0562 H2O 5.46 0.0305 NH3 4.17 0.0371 CH4 2.25 0.0428 CO2 3.59 0.0427 CCl4 20.4 0.1383

Problem 95E Nonideal-Gas Behavior (Section) In Sample Exercise 10.16, we found that one mole of Cl2 confined to 22.41 L at 0 °C deviated slightly from ideal behavior. Calculate the pressure exerted by 1.00 mol Cl2 confined to a smaller volume, 5.00 L, at 25 °C. (a) First use the ideal-gas equation and (b) then use the van der Waals equation for your calculation. (Values for the van der Waals constants are given in Table) (c) Why is the difference between the result for an ideal gas and that calculated using the van der Waals equation greater when the gas is confined to 5.00 L compared to 22.4 L? Table Van der Waals Constants for Gas Molecules Substance a(L2@atm/mol2) b(L/mol) He 0.0341 0.02370 Ne 0.211 0.0171 Ar 1.34 0.0322 Kr 2.32 0.0398 Xe 4.19 0.0510 H2 0.244 0.0266 N2 1.39 0.0391 O2 1.36 0.0318 F2 1.06 0.0290 Cl2 6.49 0.0562 H2O 5.46 0.0305 NH3 4.17 0.0371 CH4 2.25 0.0428 CO2 3.59 0.0427 CCl4 20.4 0.1383

Problem 96E Nonideal-Gas Behavior (Section) Calculate the pressure that CCl4 will exert at 40 °C if 1.00 mol occupies 33.3 L, assuming that (a) CCl4 obeys the idealgas equation; (b) CCl4 obeys the van der Waals equation. (Values for the van der Waals constants are given in Table) (c) Which would you expect to deviate more from ideal behavior under these conditions, Cl2 or CCl4? Explain. Table Van der Waals Constants for Gas Molecules Substance a(L2@atm/mol2) b(L/mol) He 0.0341 0.02370 Ne 0.211 0.0171 Ar 1.34 0.0322 Kr 2.32 0.0398 Xe 4.19 0.0510 H2 0.244 0.0266 N2 1.39 0.0391 O2 1.36 0.0318 F2 1.06 0.0290 Cl2 6.49 0.0562 H2O 5.46 0.0305 NH3 4.17 0.0371 CH4 2.25 0.0428 CO2 3.59 0.0427 CCl4 20.4 0.1383

Table shows that the van der Waals \(b\) parameter has units of \(L / m o l\). This implies that we can calculate the size of atoms or molecules from \(b\). Using the value of \(b\) for \(X e\), calculate the radius of a \(X e\) atom and compare it to the value found in Figure , that is, \(1.40 \AA\). Recall that the volume of a sphere is \((4 / 3) \pi r^{3}\) Equation Transcription: Å Text Transcription: b L / m o l b X e X e 1.40 \AA (4 / 3) \pi r^{3}

Problem 98E Nonideal-Gas Behavior (Section) Table shows that the van der Waals b parameter has units of L/mol. This means that we can calculate the sizes of atoms or molecules from the b parameter. Refer back to the discussion in Section. Is the van der Waals radius we calculate from the b parameter of Table 10.3 more closely associated with the bonding or nonbonding atomic radius discussed there? Explain. Table Van der Waals Constants for Gas Molecules Substance a(L2@atm/mol2) b(L/mol) He 0.0341 0.02370 Ne 0.211 0.0171 Ar 1.34 0.0322 Kr 2.32 0.0398 Xe 4.19 0.0510 H2 0.244 0.0266 N2 1.39 0.0391 O2 1.36 0.0318 F2 1.06 0.0290 Cl2 6.49 0.0562 H2O 5.46 0.0305 NH3 4.17 0.0371 CH4 2.25 0.0428 CO2 3.59 0.0427 CCl4 20.4 0.1383

Problem 99AE A gas bubble with a volume of 1.0 mm3 originates at the bottom of a lake where the pressure is 3.0 atm. Calculate its volume when the bubble reaches the surface of the lake where the pressure is 730 torr, assuming that the temperature doesn’t change.

Problem 100AE A 15.0-L tank is filled with helium gas at a pressure of 1.00 × 102 atm. How many balloons (each 2.00 L) can be inflated to a pressure of 1.00 atm, assuming that the temperature remains constant and that the tank cannot be emptied below 1.00 atm?

Problem 101AE To minimize the rate of evaporation of the tungsten filament, 1.4 × 10-5 mol of argon is placed in a 600–cm3 lightbulb. What is the pressure of argon in the lightbulb at 23 °C?

Problem 103AE Propane, C3H8, liquefies under modest pressure, allowing a large amount to be stored in a container. (a) Calculate the number of moles of propane gas in a 110-L container at 3.00 atm and 27 °C. (b) Calculate the number of moles of liquid propane that can be stored in the same volume if the density of the liquid is 0.590 g/mL. (c) Calculate the ratio of the number of moles of liquid to moles of gas. Discuss this ratio in light of the kinetic-molecular theory of gases.

Problem 102AE Carbon dioxide, which is recognized as the major contributor to global warming as a “greenhouse gas,” is formed when fossil fuels are combusted, as in electrical power plantsfueled by coal, oil, or natural gas. One potential way to reduce the amount of CO2 added to the atmosphere is to store it as a compressed gas in underground formations. Consider a 1000-megawatt coal-fired power plant that produces about 6 × 106 tons of CO2 per year. (a) Assuming ideal-gas behavior, 1.00 atm, and 27 °C, calculate the volume of CO2 produced by this power plant. (b) If the CO2 is stored underground as a liquid at 10 °C and 120 atm and a density of 1.2 g/cm3, what volume does it possess? (c) If it is stored underground as a gas at 36 °C and 90 atm, what volume does it occupy?

Problem 104AE Nickel carbonyl, Ni(CO)4, is one of the most toxic substances known. The present maximum allowable concentration in laboratory air during an 8-hr workday is 1 ppb (parts per billion) by volume, which means that there is one mole of Ni(CO)4for every 109 moles of gas. Assume 24 °C and 1.00 atm pressure. What mass of Ni(CO)4 is allowable in a laboratory room that is 12 ft × 20 ft × 9 ft?

Problem 105AE When a large evacuated flask is filled with argon gas, its mass increases by 3.224 g. When the same flask is again evacuated and then filled with a gas of unknown molar mass, the mass increase is 8.102 g. (a) Based on the molar mass of argon, estimate the molar mass of the unknown gas. (b) What assumptions did you make in arriving at your answer?

Consider the arrangement of bulbs shown in the drawing. Each of the bulbs contains a gas at the pressure shown. What is the pressure of the system when all the stopcocks are opened, assuming that the temperature remains constant? (We can neglect the volume of the capillary tubing connecting the bulbs.) Equation Transcription: Text Transcription: N2 Ne H2 1.0 L 265 torr 1.0 L 800 torr 0.5 L 532 torr

Problem 107AE Assume that a single cylinder of an automobile engine has a volume of 524 cm3. (a) If the cylinder is full of air at 74 °C and 0.980 atm, how many moles of O2 are present? (The mole fraction of O2 in dry air is 0.2095.) (b) How many grams of C8H18 could be combusted by this quantity of O2, assuming complete combustion with formation of CO2 and H2O?

Problem 108AE Assume that an exhaled breath of air consists of 74.8% N2, 15.3% O2, 3.7% CO2, and 6.2% water vapor. (a) If the total pressure of the gases is 0.985 atm, calculate the partial pressure of each component of the mixture. (b) If the volume of the exhaled gas is 455 mL and its temperature is 37 °C, calculate the number of moles of CO2 exhaled. (c) How many grams of glucose (C6H12O6) would need to be metabolized to produce this quantity of CO2? (The chemical reaction is the same as that for combustion of C6H12O6. See Section and Problem) Problem The metabolic oxidation of glucose, C6H12O6, in our bodies produces CO2, which is expelled from our lungs as a gas: C6H12O6(aq) + 6 O2(g)?6 CO2(g) + 6 H2O(l) (a) Calculate the volume of dry CO2 produced at body temperature (37 °C) and 0.970 atm when 24.5 g of glucose is consumed in this reaction. (b) Calculate the volume of oxygen you would need, at 1.00 atm and 298 K, to completely oxidize 50.0 g of glucose

Problem 109AE A 1.42-g sample of helium and an unknown mass of O2 are mixed in a flask at room temperature. The partial pressure of the helium is 42.5 torr, and that of the oxygen is 158 torr. What is the mass of the oxygen?

An ideal gas at a pressure of \(1.50 \mathrm{~atm}\) is contained in a bulb of unknown volume. A stopcock is used to connect this bulb with a previously evacuated bulb that has a volume of \(0.800 \mathrm{~L}\) as shown here. When the stopcock is opened the gas expands into the empty bulb. If the temperature is held constant during this process and the final pressure is \(695 \text { torr }\), what is the volume of the bulb that was originally filled with gas? Equation Transcription: Text Transcription: 1.50 atm 0.800 L 695 torr

Problem 111AE The density of a gas of unknown molar mass was measured as a function of pressure at 0 °C, as in the table that follows. (a) Determine a precise molar mass for the gas. [Hint: Graph d/P versus P.] (b) Why is d/P not a constant as a function of pressure? Pressure (atm) 1.00 0.666 0.500 0.333 0.250 Density (g/L) 2.3074 1.5263 1.1401 0.7571 0.5660

Problem 113AE You have a sample of gas at -33 °C. You wish to increase the rms speed by a factor of 2. To what temperature should thegas be heated?

Problem 112AE A glass vessel fitted with a stopcock valve has a mass of 337.428 g when evacuated. When filled with Ar, it has a mass of 339.854 g. When evacuated and refilled with a mixture of Ne and Ar, under the same conditions of temperature and pressure, it has a mass of 339.076 g. What is the mole percent of Ne in the gas mixture?

Problem 114AE Consider the following gases, all at STP: Ne, SF6, N2, CH4. (a) Which gas is most likely to depart from the assumption of the kinetic-molecular theory that says there are no attractive or repulsive forces between molecules? (b) Which one is closest to an ideal gas in its behavior? (c) Which one has the highest root-mean-square molecular speed at a given temperature? (d) Which one has the highest total molecular volume relative to the space occupied by the gas? (e) Which has the highest average kinetic-molecular energy? (f) Which one would effuse more rapidly than N2? (g) Which one would have the largest van der Waals b parameter?

Problem 115AE Does the effect of intermolecular attraction on the properties of a gas become more significant or less significant if (a) the gas is compressed to a smaller volume at constant temperature; (b) the temperature of the gas is increased at constant volume?

Problem 116AE Which of the noble gases other than radon would you expect to depart most readily from ideal behavior? Use the density data in Table to show evidence in support of your answer. Table Some Properties of the Noble Gases Element Electron Configuration Boiling Point (K) Density (g/L) Atomic Radius*(Å) I1(kJ/mol) Helium 1(s) 4.2 0.18 0.28 2372 Neon [He]2s22p6 27.1 0.90 0.58 2081 Argon [Ne]3s23p6 87.3 1.78 1.06 1521 Krypton [Ar]4s23d104p6 120 3.75 1.16 1351 Xenon [Kr]5s24d105p6 165 5.90 1.40 1170 Radon [Xe]6s24f 145d106p6 211 9.73 1.50 1037

Problem 117AE It turns out that the van der Waals constant b equals four times the total volume actually occupied by the molecules of a mole of gas. Using this figure, calculate the fraction of the volume in a container actually occupied by Ar atoms (a) at STP, (b) at 200 atm pressure and 0 °C. (Assume for simplicity that the ideal-gas equation still holds.)

Problem 118AE Large amounts of nitrogen gas are used in the manufacture of ammonia, principally for use in fertilizers. Suppose 120.00 kg of N2(g) is stored in a 1100.0-L metal cylinder at 280 °C. (a) Calculate the pressure of the gas, assuming idealgas behavior. (b) By using the data in Table calculate the pressure of the gas according to the van der Waals equation. (c) Under the conditions of this problem, which correction dominates, the one for finite volume of gas molecules or the one for attractive interactions? Table Van der Waals Constants for Gas Molecules Substance a(L2@atm/mol2) b(L/mol) He 0.0341 0.02370 Ne 0.211 0.0171 Ar 1.34 0.0322 Kr 2.32 0.0398 Xe 4.19 0.0510 H2 0.244 0.0266 N2 1.39 0.0391 O2 1.36 0.0318 F2 1.06 0.0290 Cl2 6.49 0.0562 H2O 5.46 0.0305 NH3 4.17 0.0371 CH4 2.25 0.0428 CO2 3.59 0.0427 CCl4 20.4 0.1383

Problem 119IE Cyclopropane, a gas used with oxygen as a general anesthetic, is composed of 85.7% C and 14.3% H by mass. (a) If 1.56 g of cyclopropane has a volume of 1.00 L at 0.984 atm and 50.0 °C, what is the molecular formula of cyclopropane? (b) Judging from its molecular formula, would you expect cyclopropane to deviate more or less than Ar from ideal-gas behavior at moderately high pressures and room temperature? Explain. (c) Would cyclopropane effuse through a pinhole faster or more slowly than methane, CH4?

Problem 121IE An herbicide is found to contain only C, H, N, and Cl. The complete combustion of a 100.0-mg sample of the herbicide in excess oxygen produces 83.16 mL of CO2 and 73.30 mL of H2O vapor at STP. A separate analysis shows that the sample also contains 16.44 mg of Cl. (a) Determine the percentage of the composition of the substance. (b) Calculate its empirical formula. (c) What other information would you need to know about this compound to calculate its true molecular formula?

Problem 120IE Consider the combustion reaction between 25.0 mL of liquid methanol (density = 0.850 g>mL) and 12.5 L of oxygen gas measured at STP. The products of the reaction are CO2(g) and H2O(g). Calculate the volume of liquid H2O formed if the reaction goes to completion and you condense the water vapor.

Problem 122IE A 4.00-g sample of a mixture of CaO and BaO is placed in a 1.00-L vessel containing CO2 gas at a pressure of 730 torr and a temperature of 25 °C. The CO2 reacts with the CaO and BaO, forming CaCO3 and BaCO3. When the reaction is complete, the pressure of the remaining CO2 is 150 torr. (a) Calculate the number of moles of CO2 that have reacted. (b) Calculate the mass percentage of CaO in the mixture.

Ammonia and hydrogen chloride react to form solid ammonium chloride: \(\mathrm{NH}_{3}(\mathrm{~g})+\mathrm{HCl}(\mathrm{g}) \rightarrow \mathrm{NH}_{4} \mathrm{Cl}(\mathrm{s}\) Two \(2.00-\mathrm{L}\) flasks at \(25^{\circ} \mathrm{C}\) are connected by a valve, as shown in the drawing on the next page. One flask contains \(5.00 \mathrm{~g} \text { of } \mathrm{NH}_{3}(\mathrm{~g})\), and the other contains \(5.00 \mathrm{~g} \text { of } \mathrm{HCl}(\mathrm{g})\). When the valve is opened, the gases react until one is completely consumed. (a) Which gas will remain in the system after the reaction is complete? (b) What will be the final pressure of the system after the reaction is complete? (Neglect the volume of the ammonium chloride formed.) (c) What mass of ammonium chloride will be formed? Equation Transcription: Text Transcription: NH3(g)+HCl(g)NH4Cl(s) 2.00-L 25°C 5.00 g of NH3(g) 5.00 g of HCl(g)

Problem 126IE Natural gas is very abundant in many Middle Eastern oil fields. However, the costs of shipping the gas to markets in other parts of the world are high because it is necessary to liquefy the gas, which is mainly methane and has a boiling point at atmospheric pressure of -164 °C. One possible strategy is to oxidize the methane to methanol, CH3OH, which has a boiling point of 65 °C and can therefore be shipped more readily. Suppose that 10.7 × 109 ft3 of methane at atmospheric pressure and 25 °C is oxidized to methanol. (a) What volume of methanol is formed if the density of CH3OH is 0.791 g/>mL? (b) Write balanced chemical equations for the oxidations of methane and methanol to CO2(g) and H2O(l). Calculate the total enthalpy change for complete combustion of the 10.7 × 109 ft3 of methane just described and for complete combustion of the equivalent amount of methanol, as calculated in part (a). (c) Methane, when liquefied, has a density of 0.466 g>mL; the density of methanol at 25 °C is 0.791 g/mL. Compare the enthalpy change upon combustion of a unit volume of liquid methane and liquid methanol. From the standpoint of energy production, which substance has the higher enthalpy of combustion per unit volume?

Gas pipelines are used to deliver natural gas (methane, \(\mathrm{CH}_{4}\) ) to the various regions of the United States. The total volume of natural gas that is delivered is on the order of \(2.7 \times 10^{12} \mathrm{~L}\) per day, measured at STP. Calculate the total enthalpy change for combustion of this quantity of methane.(Note: Less than this amount of methane is actually combusted daily. Some of the delivered gas is passed through to other regions.) Equation Transcription: Text Transcription: CH4 2.7 x 1012L

Problem 125IE Chlorine dioxide gas (ClO2) is used as a commercial bleaching agent. It bleaches materials by oxidizing them. In the course of these reactions, the ClO2 is itself reduced. (a) What is the Lewis structure for ClO2? (b) Why do you think that ClO2 is reduced so readily? (c) When a ClO2 molecule gains an electron, the chlorite ion, ClO2 -, forms. Draw the Lewis structure for ClO2 -. (d) Predict the O—Cl—O bond angle in the ClO2 - ion. (e) One method of preparing ClO2 is by the reaction of chlorine and sodium chlorite: Cl2(g) + 2 NaClO2(s)?2 ClO2(g) + 2 NaCl(s) If you allow 15.0 g of NaClO2 to react with 2.00 L of chlorine gas at a pressure of 1.50 atm at 21 °C, how many grams of ClO2 can be prepared?

Problem 127IE Gaseous iodine pentafluoride, IF5, can be prepared by the reaction of solid iodine and gaseous fluorine: I2(s) + 5 F2(g)?2 IF5(g) A 5.00-L flask containing 10.0 g of I2 is charged with 10.0 g of F2, and the reaction proceeds until one of the reagents is completely consumed. After the reaction is complete, the temperature in the flask is 125 °C. (a) What is the partial pressure of IF5 in the flask? (b) What is the mole fraction of IF5 in the flask (c) Draw the Lewis structure of IF5. (d) What is the total mass of reactants and products in the flask?

Problem 128IE A 6.53-g sample of a mixture of magnesium carbonate and calcium carbonate is treated with excess hydrochloric acid. The resulting reaction produces 1.72 L of carbon dioxide gas at 28 °C and 743 torr pressure.(a) Write balanced chemical equations for the reactions that occur between hydrochloric acid and each component of the mixture. (b) Calculate the total number of moles of carbon dioxide that forms from these reactions. (c) Assuming that the reactions are complete, calculate the percentage by mass of magnesium carbonate in the mixture.