b. As you draw a vacuum in your mouth, atmospheric pressure pushing on the surface of the liquid forces the liquid up the straw.

Transcription

1 CHAPTER FIVE Questions 16. a. Heating the can will increase the pressure of the gas inside the can, P T, V and n constant. As the pressure increases, it may be enough to rupture the can. b. As you draw a vacuum in your mouth, atmospheric pressure pushing on the surface of the liquid forces the liquid up the straw. c. The external atmospheric pressure pushes on the can. Since there is no opposing pressure from the air inside, the can collapses. d. How "hard" the tennis ball is depends on the difference between the pressure of the air inside the tennis ball and atmospheric pressure. A "sea level" ball will be much "harder" at high altitude since the external pressure is lower at high altitude. A high altitude ball will be "soft" at sea level. 17. PV = nrt = constant at constant n and T. At two sets of conditions, P1V 1 = constant = P2V 2. P1V 1 = P2V 2 (Boyle's law). = constant at constant n and P. At two sets of conditions, = constant =. (Charles's law) 18. Boyle's law: P 1/V at constant n and T In the kinetic molecular theory (kmt), P is proportional to the collision frequency which is proportional to 1/V. As the volume increases there will be fewer collisions per unit area with the walls of the container and pressure will decrease (Boyle's law). Charles's law: V T at constant n and P When a gas is heated to a higher temperature, the speeds of the gas molecules increase and thus hit the walls of the container more often and with more force. In order to keep the pressure constant, the volume of the container must increase (this increases surface area which decreases the number of collisions per unit area which decreases the pressure). Therefore, volume and temperature are directly related at constant n and P (Charles s law). 19. The kinetic molecular theory assumes that gas particles do not exert forces on each other and that gas 97

2 98 CHAPTER 5 particles are volumeless. Real gas particles do exert attractive forces for each other, and real gas particles do have volumes. A gas behaves most ideally at low pressures and high temperatures. The effect of attractive forces is minimized at high temperatures since the gas particles are moving very rapidly. At low pressure, the container volume is relatively large (P and V are inversely related) so the volume of the container taken up by the gas particles is negligible. 20. Molecules in the condensed phases (liquids and solids) are very close together. Molecules in the gaseous phase are very far apart. A sample of gas is mostly empty space. Therefore, one would expect 1 mol of H O(g) to occupy a huge volume as compared to 1 mol of. 21. Method 1: molar mass = 2 Determine the density of a gas at a measurable temperature and pressure, then use the above equation to determine the molar mass. Method 2: Determine the effusion rate of the unknown gas relative to some known gas; then use Graham s law of effusion (the above equation) to determine the molar mass. 22. a. At constant temperature, the average kinetic energy of the He gas sample will equal the average kinetic energy of the Cl 2 gas sample. In order for the average kinetic energy to be the same, the smaller He atoms must move at a faster average velocity as compared to Cl 2. Therefore, plot A, with the slower average velocity, would be for the Cl 2 sample, and plot B would be for the He sample. Note the average velocity in each plot is a little past the top peak. b. As temperature increases, the average velocity of a gas will increase. Plot A would be for O 2(g) at 273 K and plot B, with the faster average velocity, would be for O (g) at 1273 K. 2 Since a gas behaves more ideally at higher temperatures, O 2(g) at 1273 K would behave most ideally. 23. Rigid container (constant volume): As reactants are converted to products, the mol of gas particles present decrease by one-half. As n decreases, the pressure will decrease (by one-half). Density is the mass per unit volume. Mass is conserved in a chemical reaction, so the density of the gas will not change since mass and volume do not change. Flexible container (constant pressure): Pressure is constant since the container changes volume in order to keep a constant pressure. As the mol of gas particles decrease by a factor of 2, the volume of the container will decrease (by one-half). We have the same mass of gas in a smaller volume, so the gas density will increase (is doubled). 24. a. Containers ii, iv, vi, and viii have volumes twice that of containers i, iii, v, and vii. Containers iii, iv, vii, and viii have twice the number of molecules (mol) present as compared to containers i, ii,

3 CHAPTER 5 99 v, and vi. The container with the lowest pressure will be the one which has the fewest mol of gas present in the largest volume (containers ii and vi both have the lowest P). The smallest container with the most mol of gas present will have the highest pressure (containers iii and vii both have the highest P). All the other containers (i, iv, v and viii) will have the same pressure between the two extremes. The order is: ii = vi < i = iv = v = viii < iii = vii. b. All have the same average kinetic energy since the temperature is the same in each container. Only the temperature determines the average kinetic energy. c. The least dense gas will be container ii since it has the fewest of the lighter Ne atoms present in the largest volume. Container vii has the most dense gas since the largest number of the heavier Ar atoms are present in the smallest volume. To figure out the ordering for the other containers, we will calculate the relative density of each. In the table below, m 1 equals the mass of Ne in container i, V 1 equals the volume of container i, and d 1 equals the density of the gas in container i. Containe r mass, volume density i ii iii iv v vi vii viii m 1, V1 m 1, 2V1 2m 1, V1 2m 1, 2V1 2m 1, V1 2m 1, 2V1 4m 1, V1 4m 1, 2V1 = d 1 = 2d 1 = d 1 = 2d1 = d1 = 4d 1 = 2d1 Exercises Pressure From the table, the order of gas density is: ii < i = iv = vi < iii = v = viii < vii 1/2 d. µ rms = (3 RT/M) ; the root mean square velocity only depends on the temperature and the molar mass. Since T is constant, the heavier argon molecules will have the slower root mean square velocity as compared to the neon molecules. The order is: v = vi = vii = viii < i = ii = iii = iv a. 4.8 atm = mm Hg; b mm Hg = torr 5 c. 4.8 atm = Pa; d. 4.8 atm = 71 psi 26. a psi = 150 atm; b. 150 atm = 15 MPa 5 c. 150 atm = torr cm = 65 mm Hg or 65 torr; 65 torr = atm

4 100 CHAPTER atm = = Pa in Hg = 508 mm Hg = 508 torr; 508 torr = atm 29. If the levels of Hg in each arm of the manometer are equal, the pressure in the flask is equal to atmospheric pressure. When they are unequal, the difference in height in mm will be equal to the difference in pressure in mm Hg between the flask and the atmosphere. Which level is higher will tell us whether the pressure in the flask is less than or greater than atmospheric. a. P flask < P atm; P flask = = 642 mm Hg = 642 torr; 642 torr = atm atm = Pa b. P flask > P atm; P flask = 760. torr torr = 975 torr; 975 torr = 1.28 atm atm = Pa c. P = = 517 torr; P = = 850. torr flask flask 30. a. The pressure is proportional to the mass of the fluid. The mass is proportional to the volume of the column of fluid (or to the height of the column assuming the area of the column of fluid is constant). ; In this case, the volume of silicon oil will be the same as the volume of Hg in Exercise V = ; V Hg = V oil,, m oil = Since P is proportional to the mass of liquid: P oil = P Hg = P Hg = PHg This conversion applies only to the column of liquid. P flask = 760. torr - ( ) torr = = 749 torr torr = atm; atm = Pa

5 CHAPTER P flask = 760. torr + ( ) torr = = 781 torr torr = 1.03 atm; 1.03 atm = Pa b. If we are measuring the same pressure, the height of the silicon oil column would be = 10.5 times the height of a mercury column. The advantage of using a less dense fluid than mercury is in measuring small pressures. The quantity measured (length) will be larger for the less dense fluid. Thus, the measurement will be more precise. Gas Laws 31. From Boyle s law, P1V 1 = P2V 2 at constant n and T. P 2 = = atm As expected, as the volume increased, the pressure decreased. 32. The pressure exerted on the balloon is constant and the moles of gas present is constant. From Charles s law, V /T = V /T at constant P and n V 2 = = 239 ml As expected, as the temperature decreased, the volume decreased. 33. From Avogadro s law, V 1/n 1 = V 2/n 2 at constant T and P. V 2 = = 44.8 L As expected, as the mol of gas present increases, volume increases. 34. As NO 2 is converted completely into N2O 4, the mol of gas present will decrease by one-half (from the 2:1 mol ratio in the balanced equation). Using Avogadro s law, N2O 4(g) will occupy one-half the original volume of NO 2(g). This is expected since the mol of gas present decrease by one-half when NO is converted into N O a. PV = nrt, V = = 14.0 L

6 102 CHAPTER 5-2 b. PV = nrt, n = = mol c. PV = nrt, T = = 678 K = 405 C d. PV = nrt, P = = 133 atm a. P = Pa = atm; T = = 298 K PV = nrt, n = -5 = mol b. PV = nrt, P = = 179 atm c. V = = 3.6 L d. T = = = 334 K = 61 C n = = mol 3 3 For He: mol = g He For H : mol = g H P = = atm

7 CHAPTER a. PV = nrt; 175 g Ar = 4.38 mol Ar T = = 69.6 K b. PV = nrt, P = = 32.3 atm ml = mol O 2 V = -2 = L = 46 ml 41. At constant n and T, PV = nrt = constant, P1V 1 = P2V 2; At sea level, P = 1.00 atm = 760. mm Hg. V 2 = = 3.0 L The balloon will burst at this pressure since the volume must expand beyond the 2.5 L limit of the balloon. Note: To solve this problem, we did not have to convert the pressure units into atm; the units of mm Hg canceled each other. In general, only convert units if you have to. Whenever the gas constant R is not used to solve a problem, pressure and volume units must only be consistent, and not necessarily in units of atm and L. The exception is temperature as T must always be converted to the Kelvin scale. 42. PV = nrt, n is constant. = nr = constant, V 2 = V 1, so P 2 = = 100. psi = 109 psi 43. PV = nrt, V and n constant, so = constant and. P 2 = = 13.7 MPa = 33.5 MPa

8 104 CHAPTER a. At constant n and V, = 40.0 atm = 46.6 atm b. = 273 K = K c. T 2 = = 273 K = 171 K 45. PV = nrt, n constant; = nr = constant, 4 P 2 = = 710. torr = torr 46. PV = nrt, V constant; = constant, ; mol molar mass = mass mass 2 = = 309 g Ar remains 47. PV = nrt, n is constant. = nr = constant,, V 2 = V 2 = 1.00 L = 2.82 L; V = = 1.82 L 48. PV = nrt, P is constant. = Gas Density, Molar Mass, and Reaction Stoichiometry STP: T = 273 K and P = 1.00 atm; n = = mol He

9 CHAPTER Or we can use the fact that at STP, 1 mol of an ideal gas occupies L L = mol He; mol He = 0.27 g He CO 2(s) CO 2(g); 4.00 g CO 2 = mol CO2-2 At STP, the molar volume of a gas is L mol CO 2 = 2.04 L 51. C6H12O 6(s) + 6 O 2(g) 6 CO 2(g) + 6 H2O(g) 5.00 g C6H12O 6 = mol O2 V = = = 4.23 L O 2 Since T and P are constant, the volume of each gas will be directly proportional to the mol of gas present. The balanced equation says that equal mol of CO 2 and H2O will be produced as mol of O2 reacted. So the volumes of CO and H O produced will equal the volume of O reacted. = 4.23 L Since the solution is 50.0% H2O 2 by mass, the mass of H2O 2 decomposed is 125/2 = 62.5 g g H2O 2 = mol O2 V = = = 23.0 L O = mol mol H 2 are in the balloon. This is 80.% of the total amount of H 2 that had to be generated:

10 106 CHAPTER (total mol H 2) = , total mol H 2 = mol H mol H 2 = g Fe mol H 2 = g of 98% sulfuric acid NaN 3(s) 2 Na(s) + 3 N 2(g) = 3.12 mol N 2 needed to fill air bag. mass NaN 3 reacted = 3.12 mol N 2 = 135 g NaN3 55. CH3OH + 3/2 O 2 CO H2O or 2 CH3OH(l) + 3 O 2(g) 2 CO 2(g) + 4 H2O(g) 50.0 ml = 1.33 mol CH3OH(l) available = 1.85 mol O 2 available 1.33 mol CH3OH = 2.00 mol O mol O 2are required to react completely with all of the CH3OH available. We only have 1.85 mol O, so O is limiting mol O 2 = 2.47 mol H2O 56. For ammonia (in one minute): 3 = mol NH 3 3 NH 3 flows into the reactor at a rate of mol/min. For CO 2 (in one minute): 2 = mol CO 2

11 CHAPTER CO 2 flows into the reactor at mol/min. 3 To react completely with mol NH 3/min, we need: 2 = mol CO 2/min Since 660 mol CO 2/min are present, ammonia is the limiting reagent. 4 = g urea/min 57. a. CH 4(g) + NH 3(g) + O 2(g) HCN(g) + H2O(g); Balancing H first, then O, gives: CH 4 + NH 3 + O 2 HCN + 3 H2O or 2 CH 4(g) + 2 NH 3(g) + 3 O 2(g) 2 HCN(g) + 6 H2O(g) b. PV = nrt, T and P constant; Since the volumes are all measured at constant T and P, the volumes of gas present are directly proportional to the mol of gas present (Avogadro s law). Because Avogadro s law applies, the balanced reaction gives mol relationships as well as volume relationships. Therefore, 2 L of CH 4, 2 L of NH 3 and 3 L of O 2are required by the balanced equation for the production of 2 L of HCN. The actual volume ratio is 20.0 L CH 4:20.0 L NH 3:20.0 L O 2 (or 1:1:1). The volume of O2 required to react with all of the CH 4 and NH 3 present is 20.0 L (3/2) = 30.0 L. Since only 20.0 L of O are present, O is the limiting reagent. The volume of HCN produced is: L O 2 = 13.3 L HCN 58. Since P and T are constant, V and n are directly proportional. The balanced equation requires 2 L of H 2 to react with 1 L of CO (2:1 volume ratio due to 2:1 mol ratio in balanced equation). The actual volume ratio present in one minute is 16.0 L/25.0 L = (0.640:1). Since the actual volume ratio present is smaller than the required volume ratio, H 2 is the limiting reactant. The volume of CH3OH produced at STP will be one-half the volume of H 2 reacted due to the 1:2 mol ratio in the balanced equation. In one minute, 16.0 L/2 = 8.00 L CH OH are produced (theoretical yield). = = mol CH3OH in one minute mol CH3OH = 11.4 g CH3OH (theoretical yield per minute) % yield = 100 = 46.5% yield

12 108 CHAPTER One of the equations developed in the text to determine molar mass is: molar mass = where d = density in units of g/l molar mass = = 42.1 g/mol The empirical formula mass of CH 2 = (1.008) = g/mol. = 3.00; Molecular formula = C3H6 60. P (molar mass) = drt, d =, P (molar mass) = RT Molar mass = M = = 96.9 g/mol Mass of CHCl = 48.5; = 2.00; Molecular formula is C2H2Cl P (molar mass) = drt, d = density = For SiCl 4, molar mass = M = (35.45) = g/mol d = = 5.77 g/l for SiCl 4 For SiHCl 3, molar mass = M = (35.45) = g/mol d = = 4.60 g/l for SiHCl = 12.6 g/l

13 CHAPTER Partial Pressure 63. = 1.1 atm With air present, the partial pressure of CO 2 will still be 1.1 atm. The total pressure will be the sum of the partial pressures, P = + P. total air P total = 1.1 atm + = = 2.1 atm 64. = 1.00 g H 2 = mol H 2; n He = 1.00 g He = mol He = 12.2 atm P He = = 6.15 atm; = 12.2 atm atm = 18.4 atm 65. Use the relationship P1V 1 = P2V 2 for each gas, since T and n for each gas is constant. For H 2: P 2 = = 475 torr = 317 torr For N 2: P 2 = atm = atm; atm = 50.7 torr P total = = = 368 torr 66. For H 2: P 2 = = 360. torr = 240. torr P TOT = = 320. torr torr = 80. torr For N 2: P 1 = = 80. torr = 240 torr 67. a. mol fraction CH 4 =

14 110 CHAPTER 5 b. PV = nrt, n total = = mol -2 c. = mol = mol CH mol CH 4 = 1.06 g CH = mol = mol O 2; mol O 2 = 3.03 g O2 68. If we had g of the gas, we would have 50.0 g He and 50.0 g Xe. P He = HeP total = torr = 582 torr; P Xe = = 18 torr 69., atm = = = atm -3 = = mol H mol H 2 = g Zn 70. To calculate the volume of gas, we can use P and n (V = n RT/P ) or we can use P and n (V = n RT/P ). Since is unknown, we will use P and n. total total tot tot He He He He He He P He + = 1.00 atm = 760. torr = P He torr, P He = 736 torr n He = g = mol He = 3.69 L NaClO 3(s) 2 NaCl(s) + 3 O 2(g)

15 CHAPTER = mol O 2 Mass NaClO decomposed = mol O Mass % NaClO 3 = 100 = 18.0% = g NaClO atm atm = 2.48 atm is the pressure of the amount of F 2 reacted. PV = nrt, V and T are constant. = constant, = 2.00; So Xe + 2 F 2 XeF4 Kinetic Molecular Theory and Real Gases (KE) = (3/2) RT; At 273 K: (KE) = 273 K = J/mol avg avg 3 At 546 K: (KE) avg = 546 K = J/mol 74. (KE) avg = (3/2) RT. Since the kinetic energy depends only on temperature, CH 4 (Exercise 5.73) and N 2 at the same temperature will have the same average kinetic energy. So, for N 2, the average kinetic 3 3 energy is J/mol (at 273 K) and J/mol (at 546 K) u rms =, where R = and M = molar mass in kg = kg/mol for CH4 For CH 4 at 273 K: u rms = = 652 m/s Similarly u rms for CH 4 at 546 K is 921 m/s. For N 2 at 273 K: u rms = = 493 m/s

16 112 CHAPTER 5 Similarly for N 2 at 546 K, u rms = 697 m/s. 76. u rms = ; = = We want the root mean square velocities to be equal, and this occurs when =. The ratio of the temperatures is: = = = The heavier UF 6 molecules would need a temperature times that of the He atoms in order for the root mean square velocities to be equal KE ave = (3/2) RT and KE = (1/2) mv ; As the temperature increases, the average kinetic energy of the gas sample will increase. The average kinetic energy increases because the increased temperature results in an increase in the average velocity of the gas molecules. 78. a b c d avg. KE inc dec same (KE T) same avg. velocity inc dec same ( same coll. freq wall inc dec inc inc Average kinetic energy and average velocity depend on T. As T increases, both average kinetic energy and average velocity increase. At constant T, both average kinetic energy and average velocity are constant. The collision frequency is proportional to the average velocity (as velocity increases it takes less time to move to the next collision) and to the quantity n/v (as molecules per volume increase, collision frequency increases). 79. a. They will all have the same average kinetic energy since they are all at the same temperature. b. Flask C; H 2 has the smallest molar mass. At constant T, the lightest molecules are the fastest (on the average). This must be true in order for the average kinetic energies to be constant. 80. a. All the gases have the same average kinetic energy since they are all at the same temperature. b. At constant T, the lighter the gas molecule, the faster the average velocity Xe (131.3 g/mol) < Cl (70.90 g/mol) < O (32.00 g/mol) < H (2.016 g/mol) slowest fastest

17 CHAPTER c. At constant T, the lighter H 2 molecules have a faster average velocity than the heavier O2 molecules. As temperature increases, the average velocity of the gas molecules increases. Separate samples of H 2 and O 2 can only have the same average velocities if the temperature of the O sample is greater than the temperature of the H sample Graham s law of effusion: where M = molar mass; = = 1.067, so M = g/mol; Of the choices, the gas would be NO, nitrogen monoxide = 0.502, = (0.502) M 1, M 1 = 83. = 1.02; = The relative rates of effusion of C O: C O: C O are 1.04: 1.02: Advantage: CO 2 isn't as toxic as CO. Major disadvantages of using CO 2 instead of CO: 1. Can get a mixture of oxygen isotopes in CO Some species, e.g., C O O and C O 2, would effuse (gaseously diffuse) at about the same rate since the masses are about equal. Thus, some species cannot be separated from each other. 84. where M = molar mass; Let Gas (1) = He, Gas (2) = Cl 2 = 4.209, t = 19 min

18 114 CHAPTER a. P = = atm 2 2 b. (V - nb) = nrt; For N 2: a = 1.39 atm L /mol and b = L/mol ( L L) = L atm (P atm) ( L) = L atm P = atm = = atm c. The ideal gas law is high by 0.11 atm or 100 = 0.91%. 86. a. P = = atm 2 2 b. (V - nb) = nrt; For N 2: a = 1.39 atm L /mol and b = L/mol ( L L) = L atm (P atm) ( L L) = L atm P atm = = atm, P = = atm c. The results agree to ± atm (0.08%). d. In Exercise 5.85, the pressure is relatively high and there is a significant disagreement. In 5.86, the pressure is around 1 atm, and both gas law equations show better agreement. The ideal gas law is valid at relatively low pressures. Atmospheric Chemistry NO = 5 10 from Table 5.4. P NO = NO P total = atm = 5 10 atm

19 CHAPTER PV = nrt, -8 = 2 10 mol NO/L 13 3 = 1 10 molecules NO/cm He = from Table 5.4. P He = He P total = atm = atm -7 = mol He/L 14 3 = atoms He/cm At 100. km, T - 75 C and P atm. PV = nrt, = nr = constant, V 2 = -4 = 4 10 L = 0.4 ml 90. At 15 km, T -50 C and P = 0.1 atm. Use since n is constant. V 2 = = 7 L 91. N 2(g) + O 2(g) 2 NO(g), automobile combustion or formed by lightning 2 NO(g) + O 2(g) 2 NO 2(g), reaction with atmospheric O2 2 NO 2(g) + H2O(l) HNO 3(aq) + HNO 2(aq), reaction with atmospheric H2O S(s) + O 2(g) SO 2(g), combustion of coal 2 SO 2(g) + O 2(g) 2SO 3(g), reaction with atmospheric O2 H2O(l) + SO 3(g) H2SO 4(aq), reaction with atmospheric H2O HNO 3(aq) + CaCO 3(s) Ca(NO 3) 2(aq) + H2O(l) + CO 2(g) H2SO 4(aq) + CaCO 3(s) CaSO 4(aq) + H2O(l) + CO 2(g)

20 116 CHAPTER 5 Additional Exercises 93. a. PV = nrt b. PV = nrt c. PV = nrt PV = Constant P = T = Const T T = V = Const V d. PV = nrt e. P = f. PV = nrt PV = Constant P = Constant = nr = Constant 94. At constant T and P, Avogadro s law applies; that is, equal volumes contain equal moles of molecules. In terms of balanced equations, we can say that mol ratios and volume ratios between the various reactants and products will be equal to each other. Br F 2 2 X; Two moles of X must contain two moles of Br and 6 moles of F; X must have the formula BrF. 95. Mn(s) + x HCl(g) MnCl x(s) + H 2(g) 3 = mol Cl in compound = mol HCl = mol H 2 = mol Cl = = = 4.00

21 CHAPTER The formula of compound is MnCl H 2(g) + O 2(g) 2 H2O(g); Since P and T are constant, volume ratios will equal mol ratios (V f /V i = n f /n i). Let x = mol H 2 = mol O 2 present initially. H 2 will be limiting since a 2:1 H2 to O 2 mol ratio is required by the balanced equation, but only a 1:1 mol ratio is present. Therefore, no H 2 will be present after the reaction goes to completion. However, excess O 2(g) will be present as well as the H O(g) produced. 2 mol O 2 reacted = x mol H 2 = x/2 mol O2 mol O 2 remaining = x mol O 2 initially - x/2 mol O 2 reacted = x/2 mol O2 mol H2O produced = x mol H 2 = x mol H2O Total mol gas initially = x mol H 2 + x mol O 2 = 2 x Total mol gas after reaction = x/2 mol O 2 + x mol H2O = 1.5 x = 0.75; V /V = 0.75:l or 3:4 f i 97. We will apply Boyle s law to solve. PV = nrt = contstant, P1V 1 = P2V2 Let condition (1) correspond to He from the tank that can be used to fill balloons. We must leave 1.0 atm of He in the tank, so P 1 = 200. atm = 199 atm and V 1 = 15.0 L. Condition (2) will correspond to the filled balloons with P 2 = 1.00 atm and V 2 = N(2.00 L) where N is the number of filled balloons, each at a volume of 2.00 L. 199 atm 15.0 L = 1.00 atm N(2.00 L), N = ; We can t fill 0.5 of a balloon, so N = 1492 balloons or to 3 significant figures, 1490 balloons mol of He removed = = mol -5 In the original flask, mol of He exerted a partial pressure of = atm. V = -3 = L = 7.00 ml 99. For O 2, n and T are constant, so P1V 1 = P2V 2. P 1 = = 785 torr = 761 torr = P tot =, = = 24 torr

22 118 CHAPTER C3H5N3O 9(s) 12 CO 2(g) + 6 N 2(g) + 10 H2O(g) + O 2(g); For every 4 mol of nitroglycerin reacted, = 29 mol of gas are produced. mol gas produced = 25.0 g C3H5N3O 9 = mol P tot = = = 5.06 atm kg Mo = mol Mo mol Mo = mol O 2 5 = L of O L O 2 = L air mol Mo = mol H 2 5 = L of H For NH 3: P 2 = = atm = atm For O 2: P 2 = = 1.50 atm = atm After the stopcock is opened, V and T will be constant, so P n. The balanced equation requires: = = 1.25 The actual ratio present is: = = 1.50

23 CHAPTER The actual ratio is larger than the required ratio, so NH 3 in the denominator is limiting. Since equal mol of NO will be produced as NH 3 reacted, the partial pressure of NO produced is atm (the same as reacted) ml juice = 90. ml C2H5OH present 90. ml C2H5OH = 1.5 mol CO2 The CO 2 will occupy ( =) 75 ml not occupied by the liquid (headspace). = 490 atm Actually, enough CO 2 will dissolve in the wine to lower the pressure of CO 2 to a much more reasonable value PV = nrt, V and T are constant. When V and T are constant, pressure is directly proportional to moles of gas present, and pressure ratios are identical to mol ratios. At 25 C: 2 H 2(g) + O 2(g) 2 H2O(l); H2O(l) is produced. The balanced equation requires 2 mol H 2 for every mol O 2 reacted. The same ratio (2:1) holds true for pressure units. The actual pressure ratio present is 2 atm H 2 to 3 atm O 2, well below the required 2:1 ratio. Therefore, H 2 is the limiting reactant. The only gas present at 25 C after the reaction goes to completion will be the excess O. 2 (reacted) = 2.00 atm H 2 = 1.00 atm O2 (excess) = (initially) - (reacted) = 3.00 atm atm = 2.00 atm O 2 = Ptotal At 125 C: 2 H 2(g) + O 2(g) 2 H2O(g); H2O(g) is produced. The major difference in the problem is that gaseous water is now a product, which will increase the

24 120 CHAPTER 5 total pressure. (produced) = 2.00 atm H 2 = 2.00 atm H2O P total = (excess) + (produced) = 2.00 atm O atm H2O = 4.00 atm If Be, the formula is Be(C5H7O 2) 3 and M (12) + 21(1) + 6(16) = 311 g/mol. 2+ If Be, the formula is Be(C5H7O 2) 2 and M (12) + 14(1) + 4(16) = 207 g/mol. Data Set I (M = drt/p and d = mass/v): M = = 209 g/mol Data Set II: M = = 202 g/mol These results are close to the expected value of 207 g/mol for Be(C5H7O 2) 2. Thus, we conclude from these data that beryllium is a divalent element with an atomic mass of 9.0 amu Out of g compounds, there are: g C = mol C; = g H = 7.31 mol H; = g N = mol N; = Empirical formula: C2H3N ; Let Gas (1) = He; 3.20 =, M 2 = 41.0 g/mol Empirical formula mass of C2H3N 2(12.0) + 3(1.0) + 1(14.0) = So, the molecular formula is also C H N , = 726 torr torr = 702 torr = atm

25 CHAPTER PV = nrt, = mol N 2 Mass of N in compound = mol = g -3-2 % N = 100 = 13.3% N g CO 2 = g C; % C = 100 = 73.78% C g H2O = g H; % H = 100 = 10.9% H -3 PV = nrt, = mol N mol N 2 = g nitrogen % N = 100 = 7.14% N % O = ( ) = 8.2% O Out of g of compound, there are: g C = mol C; 7.14 g N = mol N 10.9 g H = 10.8 mol H; 8.2 g O = 0.51 mol O Dividing all values by 0.51 gives an empirical formula of C12H21NO. = 392 g/mol Empirical formula mass of C12H21NO 195 g/mol and Thus, the molecular formula is C24H42N2O At constant T, the lighter the gas molecules, the faster the average velocity. Therefore, the pressure

26 122 CHAPTER 5 will increase initially because the lighter H 2 molecules will effuse into container A faster than air will escape. However, the pressures will eventually equalize once the gases have had time to mix thoroughly The van der Waals' constant b is a measure of the size of the molecule. Thus, C3H 8 should have the largest value of b since it has the largest molar mass (size) The values of a are: H 2, ; CO 2, 3.59; N 2, 1.39; CH 4, 2.25 Since a is a measure of interparticle attractions, the attractions are greatest for CO 2. Challenge Problems 112. PV = nrt, V and T are constant. We will do this limiting reagent problem using an alternative method. Let's calculate the partial pressure of C3H3N that can be produced from each of the starting materials assuming each reactant is limiting. The reactant that produces the smallest amount of product will run out first and is the limiting reagent. = MPa C3H 6 = MPa if C3H 6 is limiting. = MPa NH 3 = MPa if NH 3 is limiting. = MPa O 2 = MPa if O 2 is limiting. Thus, C3H 6 is limiting. Although more product could be produced from NH 3 and O 2, there is only enough C H to produce MPa of C H N. The partial pressure of C H N after the reaction is: Pa = 4.94 atm n = = 30.3 mol C H N mol = g C3H3N can be produced BaO(s) + CO 2(g) BaCO 3(s); CaO(s) + CO 2(g) CaCO 3(s) n i = = initial moles of CO 2 = = mol CO2

27 CHAPTER n f = = final moles of CO 2 = = mol CO = mol CO2 reacted. Since each metal reacts 1:1 with CO 2, the mixture contains mol of BaO and CaO. The molar masses of BaO and CaO are g/mol and g/mol, respectively. Let x = g BaO and y = g CaO, so: x + y = 5.14 g and mol Solving by simultaneous equations: x y = x -y = y = 1.19 y = g CaO and y = x = 4.45 g BaO % BaO = 100 = 86.6% BaO; % CaO = = 13.4% CaO 114. Cr(s) + 3 HCl(aq) CrCl 3(aq) + 3/2 H 2(g); Zn(s) + 2 HCl(aq) ZnCl 2(aq) + H 2(g) mol H produced = n = = mol H mol H 2 = mol H 2 from Cr reaction + mol H 2 from Zn reaction -3 From the balanced equation: mol H 2 = mol Cr (3/2) + mol Zn 1 Let x = mass of Cr and y = mass of Zn, then: -3 x + y = g and = We have two equations and two unknowns. Solving by simultaneous equations: = x y

28 124 CHAPTER = x y = x x = mass Cr = = g y = mass Zn = g g = g Zn; mass % Zn = 100 = 29.0% Zn 115. a. The reaction is: CH 4(g) + 2 O 2(g) CO 2(g) + 2 H2O(g) PV = nrt, = RT = constant, The balanced equation requires 2 mol O 2 for every mol of CH 4 that reacts. For three times as much oxygen, we would need 6 mol O 2 per mol of CH 4 reacted. Air is 21% mol percent O 2, so = 0.21 n air. Therefore, the mol of air we would need to delivery the excess O2 are: = 0.21 n = 6, n = 29 = 29 air air In one minute: 3 = 200. L 29 = L air/min b. If x moles of CH 4 were reacted, then 6 x mol O 2 were added, producing x mol CO 2 and x mol of CO. In addition, 2 x mol H O must be produced to balance the hydrogens. 2 CH 4(g) + 2 O 2(g) CO 2(g) + 2 H2O(g); CH 4(g) + 3/2 O 2(g) CO(g) + 2 H2O(g) Amount O 2 reacted: x mol CO 2 = 1.90 x mol O x mol CO = x mol O 2 Amount of O 2 left in reaction mixture = 6.00 x x x = 4.03 x mol O2 Amount of N 2 = 6.00 x mol O 2 = 22.6 x 23 x mol N2 The reaction mixture contains: x mol CO x mol CO x mol O x mol H2O + 23 x mol N 2 = 30. x total mol of gas = ; = 0.032; = 0.13;

29 CHAPTER = 0.067; = The reactions are: C(s) + 1/2 O 2(g) CO(g) and C(s) + O 2(g) CO 2(g) PV = nrt, P = n = n (constant) Since the pressure has increased by 17.0%, the number of moles of gas has also increased by 17.0%. n = n = (5.00) = 5.85 mol gas = final initial = 5.00 (balancing moles of C) = 0.85 If all C was converted to CO 2, no O 2 would be left. If all C was converted to CO, we would get 5 mol CO and 2.5 mol excess O in the reaction mixture. In the final mixture: 2 = 1.70 mol CO; = 5.00, = 3.30 mol CO 2 = 0.291; = 0.564; = a. Volume of hot air: V = r = (2.50 m) = 65.4 m (Note: radius = diameter/2 = 5.00/2 = 2.50 m) m = L n = 3 = mol air Mass of hot air = mol Mass of air displaced: = g 3 4

30 126 CHAPTER 5 n = 3 = mol air Mass = mol Lift = g g = g = g of air displaced 4 b. Mass of air displaced is the same, g. Moles of He in balloon will be the same as moles 3 of air displaced, mol, since P, V and T are the same. Mass of He = mol = g Lift = g g = g c. Mass of hot air: n = 3 = mol air mol = g of hot air Mass of air displaced: n = 3 = mol air mol = g of air displaced Lift = g g = g At low P and high T, the molar volume of a gas will be relatively large. The an /V and an b/v terms become negligible because V is large. Since nb is the actual volume of the gas molecules themselves, then nb << V and the -nbp term is negligible compared to PV. Thus PV = nrt a. If we have L of air, then there are L of CO.

31 CHAPTER P CO = CO P total; CO = since V n; P CO = 628 torr = 0.19 torr 3-3 b. n CO = ; Assuming 1.0 cm of air = 1.0 ml = L: -8 n CO = = mol CO mol = molecules CO in the 1.0 cm of air 120. a. Initially, = 1.00 atm and the total pressure is 2.00 atm (P to t = ). The total pressure after reaction will also be 2.00 atm since we have a constant pressure container. Since V and T are constant before the reaction takes place, there must be equal moles of N 2 and H2 present initially. Let x = mol N = mol H that are present initially. From the balanced equation, 2 2 N 2(g) + 3 H 2(g) 2 NH 3(g), H 2 will be limiting since three times as many mol of H 2 are required to react as compared to mol of N 2. After the reaction occurs, none of the H 2 remains (it is the limiting reagent). mol NH 3 produced = x mol H 2 = 2x/3 mol N 2 reacted = x mol H 2 = x/3 mol N 2 remaining = x mol N 2 present initially - x/3 mol N 2 reacted = 2x/3 mol N 2 remaining After the reaction goes to completion, equal mol of N 2(g) and NH 3(g) are present (2x/3). Since equal mol are present, then the partial pressure of each gas must be equal P tot = 2.00 atm = ; Solving: b. V n since P and T are constant. The mol of gas present initially are: = x + x = 2x mol After reaction, the mol of gas present are: = = 4x/3 mol =

32 128 CHAPTER 5 The volume of the container will be two-thirds the original volume so: V = 2/3(15.0 L) = 10.0 L