Chapter 5 CRS s The Gaseous State Equal volumes of propane, C 3 H 8, and carbon monoxide at the same temperature and pressure have the same a. density. b.. c. number of atoms. 1) a only 2) b only 3) c only 4) a and b only 5) a, b, and c Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 2 2) b only Section 5.2 Empirical Gas Laws (p. 143) Avogadro s Law states that equal volumes of gas at the same pressure and temperature have equal numbers of particles. The valve between the 2.00-L bulb, in which the gas pressure is 1.00 atm, and the 3.00-L bulb, in which the gas pressure is 1.50 atm, is opened. What is the final pressure in the two bulbs, the temperature remaining constant? Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 3 Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 4 (continued) 1) 0.900 atm 2) 1.25 atm 3) 1.30 atm 4) 2.25 atm 5) 2.50 atm 3) 1.30 atm Section 5.3 The Ideal Gas Law (pp. 144 145) The number of moles of particles must be constant (assuming no leaks!). So, n initial = n left, initial + n right, intial = n final. Use n = P/RT to rewrite each term in this equation: (P left, initial)( left )/RT + (P right, initial) ( right )/RT = P final ( left + right )/RT. Cancel the RT terms, plug in the given values, and solve to get P final = 1.30 atm. Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 5 Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 6 1
Absolute zero is the temperature at which 1) gaseous helium liquefies. 2) a straight-line graph of P versus 1/ intersects the 1/ axis. 3) a straight-line graph of versus 1/P intersects the 1/P axis. 4) a graph of P versus at constant T intersects the axis. 5) a straight-line graph of versus T intersects the T axis. 5) a straight-line graph of versus T intersects the T axis. Section 5.2 Empirical Gas Laws (p. 141) Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 7 Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 8 The temperature of a gas in a sealed container changes from 40.0 to 80.0 C. If the volume remains constant, the pressure will change from 750 mmhg to 1) 375 mmhg. 2) 665 mmhg. 3) 846 mmhg. 4) 893 mmhg. 5) 1500 mmhg. 3) 846 mmhg. Section 5.2 Empirical Gas Laws (pp. 142 143) Solve the combined gas law for P 2 : P 2 = P 1 ( 1 / 2 )(T 2 /T 1 ) = P 1 (1)(T 2 /T 1 ) = (750 mm Hg)(353 K/333 K) = 846 mm Hg. REMEMBER: You must always convert temperatures to Kelvin before using them in the gas law expressions! Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 9 Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 10 The pressure of 4.0 L of nitrogen in a flexible container is decreased to one-half its original pressure, and its absolute temperature is increased to double the original temperature. The volume is now 1) 2.0 L. 2) 4.0 L. 3) 8.0 L. 4) 16.0 L. 5) 32.0 L. 4) 16.0 L. Section 5.2 Empirical Gas Laws (pp. 142 143) Solve the combined gas law for 2 : 2 = 1 (P 1 /P 2 )(T 2 /T 1 ) = (4.0 L)[1/(1/2)](2/1) = 16 L. Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 11 Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 12 2
Calcium nitrate will react with ammonium chloride at slightly elevated temperatures, as represented in the equation Ca(NO 3 ) 2 (s) + 2NH 4 Cl(s) 2N 2 O(g) + CaCl 2 (s) + 4H 2 O(g) A 3.00-mol sample of each reactant will give what volume of N 2 O at STP? 1) 11.2 L 2) 22.4 L 3) 33.6 L 4) 44.8 L 5) 67.2 L Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 13 5) 67.2 L Section 5.4 Stoichiometry Problems Involving Gas olumes (pp. 148 149) Three moles of calcium nitrate will produce (22.4 L/mol)(2 3 mol) = 134 L of dinitrogen monoxide. Three moles of ammonium chloride will produce (22.4 L/mol)(3 mol) = 67.2 L of dinitrogen monoxide. Ammonium chloride is the limiting reactant, and the volume will be 67.2 L. Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 14 Which of the following gases has the greatest density at 2.5 atm and 25 C? 1) N 2 O 2) F 2 3) HNF 2 4) C 3 H 8 5) NF 3 5) NF 3 Section 5.3 The Ideal Gas Law (pp. 146 147) The density of a sample of gas is D = M/ = [n (molar mass)]/ = (molar mass) (n/). According to Avogadro s Law, the ratio n/ will be a constant. So, the most dense sample is the one with the largest molar mass. The molar masses of the samples are: N 2 O = 44 g/mol; F 2 = 38 g/mol; HNF 2 = 53 g/mol; C 3 H 8 = 44 g/mol; NF 3 = 71 g/mol. Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 15 Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 16 All the following statements describe 64 g of gaseous sulfur dioxide at 0ºC and 76 cmhg pressure EXCEPT 1) one mole of gas. 2) 22.4 L of gas. 3) the amount of gas that contains 32 g of sulfur. 4) the amount of gas that contains 32 g of oxygen. 5) the amount of gas that contains 64 6.02 10 23 molecules of SO 2. Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 17 5) the amount of gas that contains 64 6.02 10 23 molecules of SO 2. Section 5.3 The Ideal Gas Law (pp. 144 147) Note that 0 C and 76 cmhg = 760 mmhg are STP conditions. Further note that 64 g SO 2 = 1 mol SO 2. According to Avogadro s Law, the volume of the sample will be about 22.4 L. One-half the mass of SO 2 is in the single S atom (32 amu) and the other half is in the two O atoms (2 16 = 32 amu), so the sample is 32 g sulfur and 32 g oxygen. The number of gas particles is 1 mol = 6.02 10 23 molecules. Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 18 3
Which of the following statements concerning equal volumes of the gases dinitrogen monoxide, N 2 O, and propane, C 3 H 8, at the same temperature and pressure, is (are) true? a. They have the same number of atoms. b. They have the same. c. They have the same density. 1) a only 2) b only 3) a and b only 4) b and c only 5) a, b, and c Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 19 4) b and c only Section 5.2 Empirical Gas Laws (pp. 143 144) Avogadro s Law indicates that the samples will contain the same number of moles of particles and therefore the same particle density. The molar masses of the two gases are nearly equal (44.1 g/mol), which means their mass densities will also be nearly equal. But, the C 3 H 8 sample will contain 1/3 more atoms than the N 2 O sample. Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 20 The partial pressures of CH 4, N 2, and O 2 in a sample of gas were found to be 100., 450., and 200. mmhg, respectively. Calculate the mole fraction of nitrogen. 1) 0.133 2) 0.267 3) 0.333 4) 0.600 5) 0.733 4) 0.600 Section 5.5 Gas Mixtures; Law of Partial Pressures (pp. 149 150) Mole fraction of N 2 = (450.)/(100. + 450. + 200.) = 0.600. Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 21 Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 22 A sample of hydrogen was collected by water displacement at 23.0 C and an atmospheric pressure of 735 mmhg. Its volume is 568 ml. After water vapor is removed, what volume would the hydrogen occupy at the same conditions of pressure and temperature? (The vapor pressure of water at 23.0 C is 21 mmhg.) 1) 509 ml 2) 539 ml 3) 552 ml 4) 568 ml 5) 585 ml 3) 552 ml Section 5.5 Gas Mixtures; Law of Partial Pressures (pp. 151 152) The ratio of volumes of H 2 to H 2 O in the gas mixture will be equal to the ratios of the pressures: (H 2 )/(H 2 O) = x/(568 ml x) = (735 mmhg 21 mmhg)/(21 mmhg)). Solving for x gives x = 552 ml. Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 23 Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 24 4
A given mass of gas in a rigid container is heated from 100 C to 500 C. Which of the following assumptions of the kinetic molecular theory of gases is stated correctly? 1) The pressure will remain the same. 2) The pressure exerted by the gas particles will decrease by a factor of five. 3) The average kinetic energy of the gas particles will increase by a factor of five. 4) The pressure will increase by a factor less than five. 5) The volume occupied by the gas particles will increase by a factor greater than five. Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 25 4) The pressure will increase by a factor less than five. Section 5.3 The Ideal Gas Law (p. 144) According to the ideal gas law, pressure is directly proportional to the Kelvin temperature for a fixed amount of gas at fixed volume. A fivefold increase in the Kelvin temperature should correspond to a fivefold increase in pressure. But, the temperatures given are Celsius temperatures and represent less than a fivefold increase on the Kelvin scale. The pressure increase will thus be less than fivefold. REMEMBER: always convert to Kelvin when working with the gas laws! Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 26 All the following statements concerning a sample of oxygen gas at 1.00 atm pressure are true EXCEPT 1) the molecules are in constant rapid random motion. 2) the pressure exerted by gaseous oxygen is due to the impact of the molecules with the walls of the container. 3) the average kinetic energy of the gaseous oxygen is inversely proportional to the absolute temperature of the gas. 4) collisions between the gaseous molecules are elastic. 5) the volume occupied by the oxygen molecules is negligible compared with the size of the container. 3) the average kinetic energy of the gaseous oxygen is inversely proportional to the absolute temperature of the gas. Section 5.6 Kinetic Theory of an Ideal Gas (p. 153) The average kinetic energy of the particles is assumed to be directly proportional to the absolute temperature. Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 27 Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 28 If 250 ml of methane, CH 4, effuses through a small hole in 48 s, the time required for the same volume of helium to pass through the hole will be 1) 12 s. 2) 24 s. 3) 48 s. 4) 96 s. 5) 192 s. 2) 24 s. Section 5.7 Molecular Speeds; Diffusion and Effusion (pp. 157 158) According to Graham s Law, rate of effusion of He Mm(CH 4 ) 16 = = 2. rate of effusion of CH 4 Mm(He) 4 Since helium effuses 2 times faster, it will take only one-half the time: (48 s)/2 = 24 s. Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 29 Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 30 5
In the van der Waals equation of state for 1 mol of gas, a P + ( b) 2 = RT the effect of intermolecular forces is accounted for by a 1) 2. 2) P. 3) b. 4) the term b. a 5) P + ( b) 2. a 1) P + 2. Section 5.8 Real Gases (pp. 160 161) The intermolecular forces effectively reduce the pressure of a real gas, and a/ 2 is the correction term needed to bump the real gas pressure P back up to its ideal value. Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 31 Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 32 (continued) Each of the following containers represents a cylinder at 25 C of some theoretical gas, X: A C B D The cylinder containing the gas at the highest pressure is: 1) A. 2) B. 3) C. 4) D. 5) Cannot be determined (some of the concentrations are the same). Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 33 Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 34 3) C. Section 5.3 The Ideal Gas Law (pp. 144 147) Which of the following graphs does NOT correctly describe the ideal gas law 1) For an ideal gas, pressure increases directly with n and decreases inversely with : P = k(n/) Define a pressure score for each container as (# of particles)/(# volume units). The pressure scores of the containers are as follows: A: 5/5; B: 5/3; C: 3/1 = 3; D: 8/3. The largest score is for container C. It has the highest pressure. n constant T, P Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 35 Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 36 6
(continued) (continued) 2) 4) R 3) P T constant P, n 5) They all correctly represent the ideal gas law. constant T, n Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 37 Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 38 5) They all correctly represent the ideal gas law. Section 5.3 The Ideal Gas Law (pp. 144) At constant T and P: = (RT/P)n = kn; at constant P and n, = (nr/p)t = kt; at constant T and n, P = (nrt)/ = k/. In which of the following reactions will the pressure increase after the reaction returns to its original temperature? 1) Cl 2 (g) + 3 F 2 (g) 2 ClF 3 (g) 2) 4 NH 3 (g) + 5 O 2 (g) 4 NO(g) + 6 H 2 O(g) 3) 2 NO(g) + O 2 (g) 2 NO 2 (g) 4) C 2 H 6 O(l) + 3 O 2 (g) 2 CO 2 (g) + 3 H 2 O(l) 5) C(s) + O 2 (g) CO 2 (g) Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 39 Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 40 2) 4 NH 3 (g) + 5 O 2 (g) 4 NO(g) + 6 H 2 O(g) Section 5.5 Gas Mixtures; Law of Partial Pressures (pp. 149 150) Only in reaction (2) is there a net increase in the number of gas particles. Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 41 1) 2) Molecular speed distributions for a gas at two different temperatures are shown below. Which of the following graphs correctly describes the distributions at the two temperatures, where T 2 > T 1? NOTE: the small vertical lines indicate average T2 speed. 3) T1 T2 T2 molecular speed molecular speed T1 Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 42 4) T1 molecular speed molecular speed 5) none of the above. T1 T2 7
1) T 1 T 2 m olecular speed Section 5.7 M olecular Speeds; D iffusion and Effusion (pp. 155 156) N one of the responses (2) (4) can be correct because the T 2 curve must be broader and flatter than the T 1 curve. Also, (4) incorrectly indicates that the T 2 curve has a y-intercept at a point other than (0, 0). Copyright Houghton Mifflin Company.All rights reserved. CRS, 5 43 8