122ch10_exer9_001

122ch10_exer9_001 - 398 Chapter 10 Gases Sections 10.5 and...

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Unformatted text preview: 398 Chapter 10 Gases Sections 10.5 and 10.6 Using the ideal-gas equation, we can relate the density of a gas to its molar mass: M = dRT/ P. We can also use the ideal—gas equation to solve problems involving gaSes as reactants or products in chemical reactions. In all applications of the ideal-gas equation we must remember to convert temperatures to the absolute—temperature scale (the Kelvin scale). In gas mixtures the total pressure is the sum of the partial pressures that each gas would exert if it were pres- ent alone under the same conditions (Dalton’s law of par- tial pressures). The partial pressure of a component of a mixture is equal to its mole fraction times the total pres- sure: P1 = X1 P,. The mole fraction is the ratio of the moles of one component of a mixture to the total moles of all components. In calculating the quantity of a gas collected over water, correction must be made for the partial pres- sure of water vapor in the gas mixture. Section 10.7 The kinetic-molecular theory accounts for the properties of an ideal gas in terms of a set of assump— tions about the nature of gases. Briefly, these assumptions are: Molecules are in continuous chaotic motion; the vol- ume of gas molecules is negligible compared to the vol- ume of their container; the gas molecules have no attractive forces for one another; their collisions are elastic; and the average kinetic energy of the gas molecules is proportion— al to the absolute temperature. The molecules of a gas do not all have the same kinet— ic energy at a given instant. Their speeds are distributed Exercises Gas Characteristics; Pressure 10.1 How does a gas differ from a liquid with respect to each CQ of the following properties: (a) density; (b) compressibil- ity; (c) ability to mix with other substances of the same phase to form homogeneous mixtures? 10.2 (a) Both a liquid and a gas are moved to larger contain— CQ ers. How does their behavior differ? Explain the differ- ence in molecular terms. (b) Although water and carbon tetrachloride, CCl4(l), do not mix, their vapors form homogeneous mixtures. Explain. (c) The densities of gases are generally reported in units of g/L, whereas those for liquids are reported as g/mL. Explain the molecular basis for this difference. 10.3 Consider two people of the same mass standing in a CQ room. One person is standing normally, and the other is standing on one foot. (a) Does one person exert a greater force on the floor than the other? (b) Does one person exert a greater pressure on the floor than the other? over a wide range; the distribution varies with the molar? mass of the gas and with temperature. The root-mam square (rms) speed, it, varies in proportion to the square j} root of the absolute temperature and inversely with the ,; square root of the molar mass: u = m . ’ Section 10.8 It follows from kinetic—molecular them}, I that the rate at which a gas undergoes effusion (escapeS through a tiny hole into a vacuum) is inversely propop tional to the square root of its molar mass (Graham’s law) The diffusion of one gas through the space occupied by a second gas is another phenomenon related to the speeds at which molecules move. Because molecules undergo fre_ quent collisions with one another, the mean free path\ the mean distance traveled between collisions—is short Collisions between molecules limit the rate at which a gas molecule can diffuse. Section 10.9 Departures from ideal behavior increase in magnitude as pressure increases and as temperature de- creases. The extent of nonideality of a real gas can be seen by examining the quantity PV/ RT for 1 mol of the gas as a function of pressure; for an ideal gas, this quantity is ex- actly 1 at all pressures. Real gases depart from ideal be- havior because the molecules possess finite volume and because the molecules experience attractive forces for one another upon collision. The van der Waals equation is an equation of state for gases that modifies the ideal-gas equa- tion to account for intrinsic molecular volume and inter- molecular forces. 10.4 The height of the mercury column in a barometer in Den- CQ ver, elevation 5000 feet, is less than that for a mercury col- umn in Los Angeles, elevation 13?. feet. Explain. 10.5 (a) How high in meters must a column of water be to exert a pressure equal to that of a 760—mm column of mer- cury? The density of water is 1.0 g/mL, whereas that of mercury is 13.6 g /mL. (b) What is the pressure in atmos- pheres on the body of a diver if he is 36 ft below the sur— face of the water when atmospheric pressure at the surface is 095 atm? 10.6 The compound laiodododecane 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 752 torr? 10.7 Each of the following statements concerns a mercury CQ barometer such as that shown in Figure 10.2. Identify any incorrect statements, and correct them. (a) The tube must 10.13 be 1 cm2 in cross-sectional area. (b) At equilibrium, the force of gravity per unit area acting on the mercury col- umn at the level of the outside mercury equals the force of gravity per unit area acting on the atmosphere. (C) The column of mercury is held up by the vacuum at the top of the column. Suppose you make a mercury barometer using a glass tube about 50 cm in length, closed at one end. What would you expect to see if the tube is filled with mercury and invert- ed in a mercury dish, as in Figure 10.2? Explain. 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. Perform the following conversions: (a) 2.44 atm to torr; (b) 682 torr to kilopascals; (c) 776 mm Hg to atmospheres; (d) 1.456 X 105 Pa to atmospheres; (e) 3.44 atm to bars. in the United States, barometric pressures are report— ed in inches of mercury (in. Hg). On a beautiful sum- mer day in Chicago the barometric pressure is 30.45 in. Hg. (a) Convert this pressure to torr. (b) A meteorolo- gist explains the nice weather by referring to a “high- pressure area.” In light of your answer to part (a), explain why this term makes sense. (a) On Titan, the largest moon of Saturn, the atmospheric pressure is 1.63105 Pa. What is the atmospheric pressure of Titan in atm? (b) On Venus the surface atmospheric pressure is about 90 Earth atmospheres. What is the Venu- sian atmospheric pressure in kilopascals? Suppose that a woman weighing 125 lb and wearing high-heeled 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 kilopascals. The Gas Laws 10.17 CQ Assume that 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 K to 500 K while the pressure is kept constant. (b) Redraw the container to show what it might look like if the pressure on the piston is increased from 1.0 atm to 2.0 atm while the temperature is kept constant. 10.14 10.15 10.16 10.18 CQ 10.19 10.20 Exercises 399 A set of bookshelves rests on a hard floor surface on the edges of the two vertical sides of the shelves, each of which has a cross—sectional dimension of 2,2 x 30 cm. 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. If the atmospheric pressure is 0.975 atm, what is the pres- sure of the enclosed gas in each of the three cases depict— ed in the drawing? h = 67 mm (1') (ii) (iii) An open-end manometer containing mercury is con- nected to a container of gas, as depicted in Sample Exer- cise 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 13.6 cm higher than in the one open to the atmosphere; atmospheric pressure is 1.05 atm. (b) The mercury in the arm attached to the gas is 12 mm lower than in the one open to the atmosphere; atmospheric pressure is 0.988 atm. Assume that you have a cylinder with a movable piston. What would happen to the gas pressure inside the cylin- der if you do the following? (a) Decrease the volume to one-third the original volume while holding the temper- ature constant (b) Reduce the Kelvin temperature to half its original value While holding the volume constant, (c) Reduce the amount of gas to half while keeping the volume and temperature constant. A fixed quantity of gas at 23°C exhibits a pressure of 748 torr and occupies a volume of 10.3 L. (a) Use Boyle’s law to calculate the volume the gas will occupy at 23°C if the pressure is increased to 1.88 atm. (b) Use Charles’s law to calculate the volume the gas will occupy if the tempera- ture is increased to 165°C while the pressure is held constant. A sample of gas occupies a volume of 1248 ft3 at 0.988 atm and 280°C. (a) Calculate the pressure of the gas if its volume is decreased to 978 ft3 while its temper— ature is held constant. (b) At what temperature in degrees 400 Chapter 10 Cases Celsius is the volume of the gas 1435 ft3 if the pressure is 10.22 Nitrogen and hydrogen gases react to form ammonia kept constant? CQ as follows: 10.21 (a) How is the law of combining volumes explained by N205.) + 3H2(g) w—a 2NH3(g) , . ? . _ _ CQ AVOgadrO S hypOtheSIS' (b) COHSIder a 1'0 L flaSk con At a certain temperature and pressure, 1.2 L of N2 reacts taming neon gas and a 1.5-L flask contammg xenon gas. with 3.6 L of H2. If all the N2 and H2 are consumed, What Both gases are at the same pressure and temperature. Ac- . , . volume of NH3, at the same temperature and Presgu cording to Avogadro 5 law, what can be said about the , Te, Wlll be produced? ratio of the number of atoms in the two flasks? gas it? The Ideal-Gas Equation 10.32 An aerosol spray can with a volume of 456 mL contains 3.18 g of propane gas (C3H8) as a propellant. (a) If the can is at 23°C, what is the pressure in the can? (b) What vol. ume would the propane occupy at STP? (c) The can says that exposure to temperatures above 130°F may cause the 10.23 (a) Write the ideal-gas equation, and give the units used for each term in the equation when R : 0.0821 L-atm/mol-K. (b) What is an ideal gas? 10.24 (a) What conditions are represented by the abbreviation 10.25 CQ STP? (b) What is the molar volume of an ideal gas at STP? (c) Room temperature is often assumed to be 25°C. Calcu- late the molar volume of an ideal gas at room temperature. 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 the flask is 1.2 g. Which flask contains gas of molar mass 30, and which contains the gas of molar mass 60? 10.33 can to burst. What is the pressure in the can at this temperature? Chlorine is widely used to purify municipal water sup. plies and to treat swimming pool waters. Suppose that the volume of a particular sample of C12 gas is 9.22 L at 1124 torr and 24°C. (a) How many grams of C12 are in the sample? (b) What volume will the C12 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 6.00 L if the temperature is 58°C? ‘ 10.26 Suppose you are given two flasks at the same tempera— 10.34 Many gases are shipped in high-pressure containers. Con- 51 CQ ture, one of Volume 2 L and the other Of VOlume 3 L. In the sider a steel tank whose volume is 68.0 L and which a 2-L flask the gas pressure is X atm, and the mass of gas in contains 02 gas at a pressure of 15,900 kPa at 23°C. 5 the flask is 4.8 g. In the 3—L flask the gas pressure is 0.1X, (a) What mass of 02 does the tank contain? (b) What vol- Eu-Eg and the mass of gas is 0.36 g. Do the two gases have the ume would the gas occupy at STP? (c) At what tempera- fi same molar mass? If not, which contains the gas of high- ture would the pressure in the tank equal 170 atm? er molar mass? (d) What would be the pressure of the gas, in kPa, if it were 10.27 Calculate each of the following quantities for an ideal gas: transferred t0 8 COH’fainer at 24°C Whose V01um€ is 52-6 L? (a) the VOIume of the gas’ m hterS' 1f2'46 m0] has a prcs— 10.35 In an experiment reported in the scientific literature, male 10.28 10.29 10.30 10.31 sure of 1.28 atm at a temperature of —6°C; (b) the absolute temperature of the gas at which 4.79 X 10'2 mol occu- pies 135 mL at 720 torr; (c) the pressure, in atmospheres, it 5.52 x 10*2 mol occupies 413 mL at 88°C; (d) the quan- tity of gas, in moles, if 88.4 L at 54°C has a pressure of 9.84 kPa. For an ideal gas, calculate the following quantities: (a) the pressure of the gas if 0.215 mol occupies 338 mL at 32°C; (b) the temperature (in kelvins) at which 0.0412 mol occu- pies 3.00 L at 1.05 atm, (c) the number of moles in 98.5 L at 236 K and 690 torr; (d) the volume occupied by 5.48 X 10‘3 mol at 55°C and a pressure of 3.87 kPa. The Hindenburg was a hydrogen—filled dirigible that ex- ploded in 1937. If the Hindenburg held 2.0 x 105 m3 of hydrogen gas at 23°C and 1.0 atm, what mass of hydro- gen was present? A neon sign is made of glass tubing whose inside diameter is 4.5 cm and whose length is 5.3 m. If the sign contains neon at a pressure of 2.03 torr at 35°C, how many grams of neon are in the sign? (The volume of a cylinder is 7rr2l1.) A scuba diver’s tank contains 0.29 kg of Oz compressed into a volume of 2.3 L. (a) Calculate the gas pressure in— side the tank at 9°C. (b) What volume would this oxygen occupy at 26°C and 0.95 atm? 10.36 cockroaches were made to run at different speeds on a miniature treadmill while their oxygen consumption was measured. In one hour the average cockroach running at 0.08 km/ hr consumed 0.8 mL of 02 at 1 atm pressure and 24°C per gram of insect weight. (a) How many moles of 02 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 02 in a 48-hr period? (Air is 21 mol percent 02.) After the large eruption of Mount St. Helens in 1980, gas samples from the volcano were taken by sampling the downwind gas plume. The unfiltered gas samples were passed over a gold-coated wire coil to absorb mercury (Hg) present in the gas. The mercury was recovered from the coil by heating it, and then analyzed. In one particu— lar set of experiments scientists found a mercury vapor level of 1800 ng of Hg per cubic meter in the plume, at a gas temperature of 10°C. Calculate (a) the partial pres— sure of Hg vapor in the plume; (b) the number of Hg atoms per cubic meter in the gas; (c) the total mass of Hg emitted per day by the volcano if the daily plume volume was 1600 kms. as IS in >l~ 1 S 16 is 61mm CL: '0' t—aQLLOQ r: :J\<1(D(DU: s» (D UH UH rther Applications of the Ideal-Gas Equation 3:10.37 f CQ " 10.38 CQ 10.39 «,CQ 10.40 CQ 10.41 10.42 10.43 Which gas is most dense at 1.00 atm and 298 K? (a) C02; Which gas is least dense at 1.00 atm and 298 K? (a) 503; (b) HCl; (c) C02. Explain Which of the following statements best explains why a closed balloon filled with helium gas rises in air? (a) Helium is an monatomic gas, whereas nearly all the molecules that make up air, such as nitrogen and oxy- gen, are diatomic. (b) The average speed of helium atoms is higher than the average speeds of air molecules, and the higher speed of collisions with the balloon walls propels the bal- loon upward. (c) Because the helium atoms are of lower mass than the average air molecule, the helium gas is less dense than air. The balloon thus weighs less than the air displaced by its volume. ((1) Because helium has a lower molar mass than the aver- age air molecule, the helium atoms are in faster motion. This means that the temperature of the helium is high- er 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 gas 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 N02 gas at 0.970 atm and 35°C. (b) Calculate the molar mass of a gas if 2.50 g oc- cupies 0.875 L at 685 torr and 35°C. (a) Calculate the density of sulfur hexafluoride gas at 455 torr and 32°C. (b) Calculate the molar mass of a vapor that has a density of 6.345 g/ L at 22°C and 743 torr. In the Dumas~bulb technique for determining the molar mass of an unknown liquid, you vaporize the sample of / Boiling water 10.44 10.45 10.46 10.47 10.48 10.49 10.50 Exercises 401 a liquid that boils below 100°C in a boiling-water bath and determine the mass of vapor required to fill the bulb (see drawing). 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. The molar mass of a volatile substance was determined by the Dumasvbulb method described in Exercise 10.43. The unknown vapor had a mass of 0.963 g,- the volume of the bulb was 418 cm3, pressure 752 torr, and temper- ature 100°C. Calculate the molar mass of the unknown vapor. Magnesium can be used as a “getter” in evacuated en— closures, to react with the last traces of oxygen. (The mag- nesium is usually heated by passing an electric current through a wire or ribbon of the metal.) If an enclosure of 0.382 L has a partial pressure of 02 of 3.5 X 10'6 torr at 27°C, what mass of magnesium will react according to the following equation? 2Mg(s) + 02(g) —> 2MgO(s) Calcium hydride, CaHZ, reacts with water to form hydrogen gas: CaH2(s) + 2H20(l) —> Ca(OH)2(aq) + 2H2(g) This reaction is sometimes used to inflate life rafts, weath- er balloons, and the like, where a simple, compact means of generating H2 is desired. How many grams of CaHz are needed to generate 64.5 L of H2 gas if the pressure of H2 is 814 torr at 32°C? Ammonium sulfate, an important fertilizer, can be pre- pared by the reaction of ammonia with sulfuric acid: 2NH3(g) + H2504(aq) ——> (NH4)2304(1111) Calculate the volume of NH3(g) needed at 42°C and 15.6 atm to react with 87 kg of H2504. The metabolic oxidation of glucose, C6H1206, in our bod- ies produces C02, which is expelled from our lungs as a gas: C6H1206W) + 602(3) —* 6C302(3) + 6H20(l) Calculate the volume of dry C02 produced at body tem— perature (37°C) and 0.970 atm when 24.5 g of glucose is consumed in this reaction. Hydrogen gas is produced when zinc reacts with sulfu— ric acid: Zn(s) + HZSO4(aq) —> ZnSO4(aq) + H2(g) 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.) it” Acetylene gas, C2H2(g), can be prepared by the reaction of calcium carbide with water: CaC2(S) + 2H200) —* Ca(OH)2(S) + C2H2(g) Calculate the volume of C2H2 that is collected over water at 21°C by reaction of 3.26 g of CaCz if the total pressure of the gas is 748 torr? (The vapor pressure of water is tab- ulated in Appendix B.) 402 . 10.51 CQ 10.52 CQ 3? 10.53 3" E13 ‘12: 5 1::- 1: :3! CD; 7.13: 11:13! (:5 13 at 10.61 CQ s; 1. .. mm. w "‘5: 10.62 CQ ‘ x 10.63 CQ 10.54 CQ Chapter 10 Gases Partial Pressures Consider the apparatus shown in the drawing. (a) When the stopcock 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 02 gas change when the gases mix? What is the partial pressure of 02 in the mixture? (c) What is the total pressure in the container after the gases mix? 2.0 L 3.0 L 1.0 atm 2.0 atm 25°C 25°C Consider a mixture of two gases, A and B, confined to a closed vessel. A quantity of a third gas, C, is added to the same vessel at the same temperature. How does the addi» tion 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 0.538 mol He(g), 0.315 mol Ne(g), and 0.103 mol Ar(g) is confined in a 7.00-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. 10.54 10.55 10.56 10.57 10.58 10.59 10.60 Amixture containing 3.15 g each of CH4(g), C2H4(g), and C4H]O(g) is contained in a 2.00—L flask at a temperature of 64°C. (a) Calculate the partial pressure of each of the gases in the mixture (b) Calculate the total pressure of the mixture. A mixture of gases contains 0.75 mol N2, 0.30 mo] 02, and 0.15 mol C02. If the total pressure of the mixture is 1.56 atm, what is the partial pressure of each component? A mixture of gases contains 12.47 g of N2, 1.98 g of H2, and 8.15 g of NH3. If the total pressure of the mixture is 2.35 atm, what is the partial pressure of each component? At an underwater depth of 250 ft, the pressure is 8.38 atm. What should the mole percent of oxygen be in the div. ing 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 6.55 g of 02, 4.92 g of N2, and 1.32 g of H2? (b) What is the partial pressure in atm of each compo. nent of this mixture if it is held in a 12.40—L vessel at 15°C? A quantity of N2 gas originally held at 3.80 atm pressure in a 1.00-L container at 26°C is transferred to a 10.0-L con~ tainer at 20°C. A quantity of 02 gas originally at 4.75 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 5.25 g of 802(3) originally in a 4.00-L vessel at 26°C is transferred to a 13.6—L vessel at 25°C. A sample of 2.35 g N2(g) originally in a 3.18-L vessel at 20°C is trans- ferred to this same 13.6—L vessel. (a) What is the partial pressure of SOZ(g) in the larger container? (b) What is the partial pressure of N2(g) in this vessel? (c) What is the total pressure in the vessel? Kinetic-Molecular Theory; Graham’s Law What change or changes in the state of a gas bring about each of the following effects? (a) The number of impacts per unit time on a given container wall increases. (b) The average energy of impact of molecules with the wall of the container decreases. (c) The average distance between gas molecules increases. (d) The average speed of mole- cules in the gas mixture is increased. Indicate which of the following statements regarding the kinetic-molecular theory of gases are correct. For those that are false, formulate a correct version of the statement. (a) The average kinetic energy of a collec- tion of gas molecules at a given temperature is propor- tional to «Ml/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 ener- gy. (d) The volume of the gas molecules is negligible in comparison to the total volume in which the gas is contained. What property or properties of gases can you point to that support the assumption that most of the volume in a gas is empty space? 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. 10.65 CQ 10.66 CQ 10.67 10.68 10.69 This repulsion gives rise to pressure. Explain why Charles's law argues for the kinetic-molecular theory and against Newton’s model. Vessel A contains CO(g) at 0°C and 1 atm. Vessel B con- tains 802(3) at 20°C and 05 atm. The two vessels have the same volume. (a) Which vessel contains more mole- cules? (b) Which contains more mass? (c) in which vessel is the average kinetic energy of molecules higher? (d)II1 which vessel is the rms speed of molecules higher? Suppose you have two 1—L flasks, one containing N; at STP, the other containing CH4 at STP. How do these sys- tems 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 aver- age molecular speed at 300 K: C02, N20, HF, F2,H2- (b) Calculate and compare the rms speeds of H2 and C02 molecules at 300 K. (a) Place the following gases in order of increasing aver' age molecular speed at 25°C: Ne, HBr, 502, NF3, CO- (b) Calculate the rms speed of NF3 molecules at 25°C. Hydrogen has two naturally occurring isotopes, 1H and 2H. Chlorine also has two naturally occurring isotopesr 35c1 and 370. Thus, hydrogen chloride gas consists of four distinct types of molecules: 111350, 1H37Cl, 2H35C1r and 2H370. Place these four molecules in order of in' creasing rate of effusion. 10.70 10.71 As discussed in the "Chemistry at Work" box in Section 10.9, enriched uranium is produced via gaseous diffusion of UF6. Suppose a process were developed to allow dif- fusion of gaseous uranium atoms, U(g). Calculate the ratio of diffusion rates for 235U and 238U, and compare it to the ratio for UF6 given in the essay. Arsenic(IlI) sulfide sublimes readily, even below its melt— ing point of 320°C. The molecules of the vapor phase are found to cffuse through a tiny hole at 0.28 times the rate of effusion of Ar atoms under the same conditions of tem— 10.72 403 Exercises perature 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 condi- tions. 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 02 gas to effuse. Calculate the molar mass of the unknown gas. (Remember that the faster the rate of effu- sion, the shorter the time required for effusion of 1.0 L; that is, rate and time are inversely proportional.) ____________________.___.__.....__———————————————- NonideaI-Gas Behavior 10.73 10.74 CQ 10.75 CQ 10.76 CQ (a) Under what experimental conditions of temperature and pressure do gases usually behave nonideally? (b) What two properties or characteristics of gas mole- cules cause them to behave nonideally? The planet Jupiter has a mass 318 times that of Earth, and its surface temperature is 140 K. Mercury has a mass 0.05 times that of Earth, and its surface temperature is between 600 and 700 K. On which planet is the atmosphere more likely to obey the ideal—gas law? Explain. Explain how the function PV/ RT can be used to show how gases behave nonideally at high pressures. For nearly all real gases, the quantity PV/RT decreases below the value of 1, which characterizes an ideal gas, as pressure on the gas increases. At much higher pressures, however, PV/ RT increases and rises above the value of 1. (a) Explain the initial drop in value of PV/RT below 1 and the fact that it rises above 1 for still higher pressures. 10.77 10.78 10.79 10.80 (b) The effects we have just noted are smaller for gases at higher temperature. Why is this so? Based on their respective van der Waals constants (Table 10.3), is Ar 0r C02 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. Calculate the pressure that CCl4 will exert at 400C if 1.00 mol occupies 28.0 L, assuming that (a) CCl4 obeys the ideal-gas equation; (b) CCl4 obeys the van der Waals equation. (Values for the van der Waals constants are given in Table 10.3.) It turns out that the van der Waals constant 1) 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 100 atm pressure and 0°C. (Assume for simplicity that the ideal—gas equation still holds.) Additional Exercises 10.81 CQ 10.82 CQ 10.83 10.84 Consider the apparatus below, which shows gases in two containers and a third empty container. When the stop- cocks are opened and the gases allowed to mix, what is the distribution of atoms in each container, assuming that the containers are of equal volume and ignoring the vol— ume of the tubing connecting them. Suppose the mercury used to make a barometer has a few small droplets of water trapped in it that rise to the top of the mercury in the tube. Will the barometer show the correct atmospheric pressure? 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 695 torr, assuming that the tem- perature doesn’t change. To minimize the rate of evaporation of the tungsten fila— ment, 1.4 X 10‘5 mol of argon is placed in a 600—cm3 lightbulb. What is the pressure of argon in the lightbulb at 23°C? 10.85 10.86 10.87 10.88 Propane, C3Hg, liquefies under modest pressure, allow— ing 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/InL. (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. What is the total mass (in grams) of 02 in a room meas— uring (10.0 X 8.0 X 8.0) ft3 if the air in the room is at STP and contains 20.95% 02. Nickel carbonyl, Ni(CO)4, is one of the most toxic sub— stances known. The present maximum allowable con— centration in laboratory air during an 8-hr workday is 1 part in 109. Assume 24°C and 100 atm pressure. What mass of Ni(CO)4 is allowable in a laboratory that is 54 m2 in area, with a ceiling height of 3.1 m? Consider the arrangement of bulbs shown in the drawing. 05L 1.0 L . 532 torr 800 torr 1.0 L 265 torr Volume Pressure Uiffiifi ##"c ‘ c c 4.. 404 Chapter 10 Gases 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 con- stant? (We can neglect the volume of the capillary tubing connecting the bulbs.) 10.89 Assume that a single cylinder of an automobile engine has a volume of 524 cms. (a) If the cylinder is full of air at 74°C and 0.980 atm, how many moles of 02 are present? (The mole fraction of OZ in dry air is 0.2095.) (b) How many grams of CngB could be combusted by this quan- tity of 02, assuming complete combustion with forma— tion of C02 and H20? [10.90] Ammonia, NH3(g), and hydrogen chloride, HCl(g), react to form solid ammonium chloride, NH4Cl(s): NH3(g) + HCl(g) —» NH4C1(s) Two 2.00-L flasks at 25°C are connected by a stopcock, as shown in the drawing. One flask contains 500 g NH3(g), and the other contains 500 g HCl(g). When the stopcock is opened, the gases react until one i‘ completely con- sumed. (a) Which gas will remain int e system after the reaction is complete? (b) What will be the final pressure of the system after the reaction is com lete? (Neglect the volume of the ammonium chloride f rmed.) 10.91 A sample of 1.42 g of helium andan unweighed quanti- ty of 02 are mixed in a flas at room temperature. The partial pressure of helium in the flask is 42.5 torr, and the partial pressure of oxygen is 158 torr. What is the mass of the oxygen in the container? [10.92] A gaseous mixture of 02 and Kr has a density of 1.104 g/ L at 435 torr and 300 K. What is the mole percent 02 in the mixture? [10.93] A glass vessel fitted with a stopcock 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 tem- perature and pressure, it weighs 339.076 g. What is the mole percent of Ne in the gas mixture? [10.94] The density of a gas of unknown molar mass was meas- ured as a function of pressure at 0°C, as in the table above. (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? W 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 10.95 Suppose that when Torricelli had his great idea for con. CQ structing a mercury manometer, he had rushed into the laboratory and found the following items of glass: 800 mm (a) (b) (C) (d) (6) Which of these would have been satisfactory for his use in forming the first manometer? Explain why the unsat- isfactory ones would not have worked. [10.96] Consider the apparatus used in Exercise 10.90. A gas at 1 atm pressure is contained in the left flask, and the right flask is evacuated. When the stopcock is opened, the gas expands to fill both flasks. A very small temperature change is noted when this expansion occurs. Explain how this observation relates to assumption 3 of the kinetic- molecular theory, Section 10.7. 10.97 ()n a single plot, qualitatively sketch the distribution of molecular speeds for (a) Kr(g) at 250°C; (b) Kr(g) at OUC; (c) Ar(g) at 03C. 10.98 Does the effect of intermolecular attraction on the prop- erties of a gas become more significant or less significant if (a) the gas is compressed to a smaller volume at con- stant temperature; (b) the temperature of the gas is in- creased at constant volume. [10.99] 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 ideal— gas behavior. (b) By using data in Table 10.3, calculate the pressure of the gas according to the van der Waals equa- tion. (c) Under the conditions of this problem, which cor- rection dominates, the one for finite volume of gas molecules or the one for attractive interactions? w.fl Integrative Exercises 10.100 Cyclopropane, a gas used with oxygen as a general anes- thetic, is composed of 85.7% C and 14.3% Hby mass. (a) If 1.56 g of cyclopropane has a volume of 1.00 L at 0.984 atm and 500°C, what is the molecular formula of cyclo- propane? (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. 10.101 in the “Chemistry at Work” box on pipelines, Section 10.5, it is mentioned that the total deliverability of natural gas (methane, CH4) to the various regions of the United States is on the order of 2.7 X 1012 L per day, measured at STP. Calculate the total enthalpy change for combus— tion of this quantity of methane. (Note: Less than 'tliiS amount of methane is actually combusted daily. Some Of the delivered gas is passed through to other regions.) [10.1021A gas forms when elemental sulfur is heated carefully with AgF. The initial product boils at 15°C. Experiments on several samples yielded a gas density 0f 0.803 :: 0.010 g/L for the gas at 150 mm pressure and 32°C. When the gas reacts with water, all the fluorine is 10.103 converted to aqueous HF. Other products are elemen- tal sulfur, 58, and other sulfur-containing compounds. A 480-mL sample of the dry gas at 126 mm pressure and 28°C, when reacted with 80 mL of water, yielded a 0.081 M solution of HF. The initial gaseous product under- goes a transformation over a period of time to a second compound with the same empirical and molecular for— mula, which boils at ——lO°C. (a) Determine the empirical and molecular formulas of the first compound formed. (b) Draw at least two reasonable Lewis structures that represent the initial compound and the one into which it is transformed over time. (c) Describe the likely geometries of these compounds, and estimate the sin- gle bond distances, given that the S —S bond distance in 58 is 2.04 A and the F—F distance in F2 is 1.43 A Chlorine dioxide gas (C102) is used as a commercial bleaching agent. It bleaches materials by oxidizing them. In the course of these reactions, the C102 is itself reduced. (a) What is the Lewis structure for C102? (b) Why do you think that C102 is reduced so readily? (c) When a C102 molecule gains an electron, the chlorite ion, ClOf, forms. Draw the Lewis structure for C102’. (d) Predict the 0* Cl —0 bond angle in the ClOf ion. (6) One method of preparing C102 is by the reaction of chlorine and sodi- um chlorite: Clz(g) + 2NaC102(s) —> 2002(3) + 2NaCl(s). If you allow 10.0 g of NaC102 to react with 2.00 L of chlorine gas at a pressure of 1.50 atm at 21 DC, how many grams of C102 can be prepared? [10.104] Natural gas is very abundant in many Middle Eastern oil 10.107 10.108 10.109 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 thus has a boiling point at atmospheric pressure of —164°C. One pos- sible strategy is to oxidize the methane to methanol, CH30H, which has a boiling point of 65°C, and which can eMedia Exercises 405 eMedia Exercises therefore be shipped more readily. Suppose that 10.7 X 109 ft3 of methane at atmospheric pressure and 25°C are oxidized to methanol. (a) What volume of methanol is formed if the density of CH3OH is 0.791 g/ L? (b) Write balanced chemical equations for the oxidations of methane and methanol to C02(g) and H200). Calculate the total enthalpy change for complete combustion of the 10.7 X 109 ft3 of methane described above and for complete combustion of the equivalent amount of methanol, as cal— culated in part (a). (c) Methane, when liquefied, has a den- sity of 0.466 g/mL; the density of methanol at 25°C is 0.791 g/ L. 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? [10.105] Gaseous iodine pentafluoride, IFS, can be prepared by the reaction of solid iodine and gaseous fluorine: 12(5) + 51%;) —> ZlFstsz) A 5.00—L flask containing 10.0 g 12 is charged with 10.0 g 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 IFS in the flask? (b) What is the mole fraction of IFS in the flask? [10.106] 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 chem- ical 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 reac— tions are complete, calculate the percentage by mass of magnesium carbonate in the mixture. Using the Gas Laws activity (eChapter 10.3), select a mass and a pressure to be held constant, and compare the vol- umes of N2 and Xe at various temperatures. Under iden— tical conditions—the same mass at the same pressure and temperature—are the volumes of N2 and Xe equal? If not, explain why. The P-V Relationships movie (eChapter 10.3) illustrates Boyle’s law and points out that this law holds only when temperature is constant. (a) Reproduce the pressure ver- sus volume graph presented in the movie. (b) Using the ideal-gas equation, deduce and superimpose on your graph from part (a) the line you would expect on the P~V plot at a temperature higher than the original and at a temperature lower than the original: (c) Do the same for the V versus 1 / P plot. Automobile air bags are inflated by the explosive decom- position of sodium azide, as shown in the Air Bags movie (eChapter 10.5). (a) If an air bag is to be inflated with 40.0 L of gas, initially at 110°C and 1.05 atm pressure, what mass of sodium azide must be available for decomposi- tion? (b) What does the notation 0(5) stand for in the decomposition reaction? (c) Why is it important that the 10.110 10.111 reactants include an oxidant to react with the sodium metal produced by the decomposition? Use the Density of Gases activity (eChapter 10.5) to com- pare the densities of two different gasesat the same pressure and temperature. Explain in terms of kinetic-molecular the- ory why the molar mass of a gas is necessary to calculate the density of a gas, but not to determine its pressure. , 2 at P = fl RT V The relative speeds of helium and neon atoms are shown in the Kinetic Energy in a Gas movie (eChupter 10.7). (a) If the average kinetic energies of both gases are the same at a given temperature, determine how much faster heli- um atoms are moving (on average) than neon atoms. (b) How does the fact that average kinetic energy of a gas is directly proportional to absolute temperature explain Boyle’s observation that pressure decreases with increas- ing volume at constant temperature? (c) How does it explain Charles’s observation that pressure increases with increasing temperature at constant volume? ...
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122ch10_exer9_001 - 398 Chapter 10 Gases Sections 10.5 and...

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