# Version 001 HW03-Non Ideal, Gas Mixtures & KMT vandenbout (52130) 1. = torr

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1 Version 001 HW03-Non Ideal, Gas Mixtures & KMT vandenbout (52130) 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. Nlib points Two gases are contained in gas bulbs connected byavalve. GasAispresent ina1liter bulb at a pressure of 811 torr. Gas B exerts a pressure of 277 torr in a 1 liter bulb. The valve is opened and the two gases equilibrate. What is the partial pressure of gas A expressed after equilibration? Correct answer: torr. V A 1 L P A 811 torr V total 2 L P A V A P t V t P t P AV A V t (811 torr)(1 L) 2 L V B 1 L P B 277 torr torr ChemPrin3e T points A reminder... partial pressures are calculated from the total pressure via mole fractions, not percent by mass. So you WILL have to convert the percent by mass to mole fraction BEFORE you answer this problem. A mixture of oxygen and helium is 92.3% by mass oxygen. It is collected at atmospheric pressure (745 torr). What is the partial pressure of oxygen in this mixture? Torr Torr correct Torr Torr Torr Assume you have 100 g of this mixture; calculate the number of moles: 1 mol O 2 n O2 (92.3 g O 2 ) g O mol O 2. 1 mol He n He (7.7 g He) g He mol He. n tot n O2 +n He mol O mol He mol gas Dalton s Law: P O2 P tot χ O2 P tot n O 2 n tot (745 Torr) mol O mol gas Torr ChemPrin3e T points If the average speed of a water molecule at 25 C is 640 m s 1, what is the average speed at 100 C? m/s correct m/s m/s m/s m/s T C K

2 Version 001 HW03-Non Ideal, Gas Mixtures & KMT vandenbout (52130) 2 T 2 25 C K From kinetic molecular theory, the temperature is directly proportional to mean KE. KE mean 1 (MW)(average molecular speed)2 2 and knowing MW is constant (it s the same gas)wegetaveragespeedv T ofgasmolecules: v T1 v T2 T1 T2 v T2 v T1 T2 T1 (640 m/s) m/s K K ChemPrin3e (part 1 of 2) 10.0 points Consider (calculate) ONLY the nitrogen gas that comes from the azide in this problem. Air bags in automobiles contain crystals of sodium azide (NaN 3 ) which during a collision decompose rapidly to give nitrogen gas and sodium metal. Potassium nitrate and silicon dioxide are added to remove the sodium metal by converting it into a harmless material. First, the sodium reacts with potassium nitrate to produce potassium oxide (K 2 O), sodium oxide (Na 2 O), and additional nitrogen gas. The metal oxides (K 2 O and Na 2 O) react with silicon dioxide in a final reaction to produce silicate glass, which is harmless and stable. The nitrogen gas liberated by this process instantly inflates the air bag. Assume that the nitrogen gas liberated behaves as an ideal gas and that any solid produced has a negligible volume (which may be ignored). Calculate the mass of sodium azide required to generate enough nitrogen gas to fill a 46 L air bag at 1.45 atm and 39 C. Correct answer: g. P 1.45 atm T 39 C K R L atm/k/mol V N2 46 L MW g Applying the ideal gas law, n N2 P V (1.45 atm)(46 L) ( L atm/k/mol)(312 K) mol N 2. The balanced reaction is 2 NaN 3 (s) 3 N 2 (g)+2 Na(s) ( ) 2 mol NaN3 m NaN3 ( mol N 2 ) 3 mol N ( ) g NaN3 1 mol NaN gnan (part 2 of 2) 10.0 points What isthe rootmean square speed of the N 2 gas molecules generated? Correct answer: m/s. MW N2 28 g/mol V rms 3 MW N2 R J/K/mol 3(8.314 J/K/mol)(312 K) (28 g/mol) (kg/m 2 /s 2 ) ( ) 1000 g J kg m/s. Mlib points Which of the following statements about the Kinetic-Molecular Theory of gases is false? 1. The average kinetic energy of a gas molecule is independent of the temperature. correct 2. Collisions between molecules are elastic.

3 Version 001 HW03-Non Ideal, Gas Mixtures & KMT vandenbout (52130) 3 3. Gases consist of molecules in continuous, random motion. 4. The distance between molecules is much larger than the diameter of each molecule. The average kinetic energy of gas molecules is very much dependent on temperature. The higher the temperature, the larger is the average kinetic energy of the gas molecules. ChemPrin3e T points A plot of the Maxwell distribution for the same gas against temperature shows that 1. at low temperatures, most molecules have speeds close to their average speed. correct 2. at high temperatures, most molecules have speeds close to their average speed. 3. as the temperature decreases, the spread of speeds widens. 4. as the temperature decreases, a high proportion of molecules have very high speeds. 5. as the temperature increases, a high proportion of molecules have very slow speeds. The Maxwell distribution of speeds for a particular sample of gas at a given temperature shows the following characteristics if one of the following variables is changed: Mass: The distribution of speeds for a given sample of gas is narrower and the average speed is lower for a gas of higher molecular weight. Temperature: The distribution of speeds for a given sample of gas is wider and the average speed is higher as the temperature of a gas increases. Msci ran points Given the gases Ne, N 2, Cl 2, CO 2 put them in order of their DECREASING rate of effusion. 1. N 2 > Ne > Cl 2 > CO 2 2. Ne > N 2 > CO 2 > Cl 2 correct 3. CO 2 > Cl 2 > Ne > N 2 4. Cl 2 > CO 2 > N 2 > Ne Effusion is when gas molecules escape through the tiny holes in their container. Lighter, faster molecules effuse more quickly than heavy, slow ones. Ne (MW20 g/mol) > N 2(MW28 g/mol) > CO 2(MW44 g/mol) > Cl 2(MW71 g/mol) Msci points Calculate the ratio of the rate of effusion of CO 2 to that of He : : : : : 1 correct Eff CO2 Eff He MWHC 4 MWCO DVB Kinetic Theory of Gases points A sample of He gas and O 2 have the same temperature, pressure, and volume. Which gas has a greater number of collision of gas molecules with the walls of the container? 1. The O 2 since it has a higher average kinetic energy because it is more massive

4 Version 001 HW03-Non Ideal, Gas Mixtures & KMT vandenbout (52130) 4 2. The He gas because it is less massive and moving with a higher average velocity correct 3. The O 2 since it has a higher average momentum since it is more massive 4. They are the same since the pressure is the same Both gases have the same temperature so both have the same average kinetic energy. The lighter mass of He means it will have a higher velocity. The higher velocity will mean the He gas will have more collisions. However, thenetresultwillbethesamepressureaseach collision will have less force as the molecules will have a smaller momentum. Ostwald process points Nitric acid is produced commercially by the Ostwald process. In the first step, ammonia is oxidized to nitric oxide: 4NH 3 (g)+5o 2 (g) 4NO(g)+6H 2 O(g) Assume this reaction is carried out in the apparatus diagramed below atm atm atm correct First,calculatethepartialpressuresofNH 3 and O 2 after the stopcock is opened (and before the reaction). Use Boyle s Law... new volume is 3 L so that... P NH3 (2L/3L)(1/2atm) 1/3 atm P O2 (1L/3L)(3/2atm) 1/2 atm You must have at least 5/4 more moles of O 2 than NH 3 for complete reaction. That means you need 5/12 atm of O 2. You have more than enough (0.5 atm 6/12 atm) so the oxygen is in excess. Theeasypart... YoumaketheSAMEnumberofmolesofNOasyouuseNH 3,sothefinal partial pressure of the NO will be the same as the initial partial pressure of the NH 3 which is 1/3 atm or atm. Brodbelt points A 5.0 L flask containing O 2 at 2.00 atm is connected to a 3.0 L flask containing H 2 at 4.00 atm and the gases are allowed to mix. What is the mole fraction of H 2? L NH atm 1.00 L O atm The stopcock between the two reaction containers is opened, and the reaction proceeds using proper catalysts. Calculate the partial pressure of NO after the reaction is complete. Assume 100% yield for the reaction, assume the final container volume is 3.00 L, and assume the temperature is constant atm atm correct Cannot be determined Applying the ideal gas law P V n P V

5 Version 001 HW03-Non Ideal, Gas Mixtures & KMT vandenbout (52130) 5 (2 atm)(5 L) N O2 (4 atm)(3 L) N H2 Assume the temperature of the two gases remains the same before and after the mixing occurs. The mole fraction of H 2 is n H2 χ H2 n H 2 n total n H2 +n O2 (4 atm)(3 L) (4 atm)(3 L) (2 atm)(5 L) + (4 atm)(3 L) (4 atm)(3 L)+(2 atm)(5 L) ChemPrin3e (part 1 of 2) 10.0 points A gas mixture being used to simulate the atmosphere of another planet consists of 359 mg of methane, 176 mg of argon, and 241 mg of nitrogen. The partial pressure of nitrogen at 297 K is 10 kpa. Calculate the total pressure of the mixture. Correct answer: kpa. m N2 241 mg g m CH4 359 mg g m Ar 176 mg g P N2 10 kpa n CH g mol g/mol n Ar g mol g/mol n N g mol g/mol P V n, so P n and the partial pressures are P N2 10 kpa P CH4 n CH 4 n N2 P N mol 10 kpa mol kpa P Ar n Ar P N2 n N mol 10 kpa mol kpa P total kpa kpa +10 kpa kpa. 014 (part 2 of 2) 10.0 points Calculate the volume. Correct answer: L. R L atm T 297 K K mol Using the total moles and pressure, n total mol mol mol mol. P V n V nt R P ( mol)(297 K) V kpa L atm K mol kpa 1 atm V L. Note: You can also obtain the same result using any of the three separate gases and its partial pressure. DVB Dalton s Law RXN points When heated, solid mercury oxide HgO will decompose into mercury and oxygen gas 2HgO(s) 2Hg(g)+O 2 (g)

6 Version 001 HW03-Non Ideal, Gas Mixtures & KMT vandenbout (52130) 6 You start with a container that has only HgO solid in it. The temperature is raised to 700K and you find that all of the solid has decomposed (and all the mercury is vapor). The total pressure in the container is 0.75 bar. What is the partial pressure of oxygen?? bar bar bar correct bar bar Thenumber ofmolesofmercuryvaporthat is formed is twice the number of moles of O 2. Therefore the partial pressure of Hg(g) will will twice that of O 2. So P Hg 2P O2 The total pressure is the sum of the partial pressures, P Hg + P O2 2P O2 +P O2 3 x P O bar P O bar DVB Ideal Gas Model points In the limit of low pressure, all gases exhibit ideal behavior because when the pressure is very low the gas particles are 1. far apart and rarely interacting correct 2. undergoing only elastic collisions 3. experiencing a balance of kinetic and potential energy 4. slightly attracted to one another 5. moving very slowly At very low pressures the average distance between gas particles is large and therefore the particles are rarely interacting with each other. As such, all gases appear to have the same behavior since they are essentially invisible to one another. Gases move slower at lower temperatures Generally all substances are slightly attracted to themselves. This does not vary with pressure. In a real gas attraction are generally important at intermediate pressure as attractive forces are longer range than repulsive forces. DVB Ideal Gas Model points Deviations from ideal gas behavior can be modeled with other equations of state. One such equation that attempts to account for the repulsive interactions of gas particles is the hard sphere model P(V nb) n A 1 mole sample of He gas at 1000K and 500 bar has a volume of L. Estimate the value of the constant b in the hard sphere model for He? L mol 1 correct L mol L mol L mol L mol 1 Rearranging the hard sphere model gives V (n/p)+nb V V IG +nb That is the volume of the ideal gas + nb nb V V IG V IG (1)(.08314)(1000)/(500) nb L 0.01 L/1 mol 0.01 L mol 1 DVB Ideal Gas Model points The ideal gas equation models the gas behavior observed in the real world 1. perfectly for some gases but not for oth-

7 Version 001 HW03-Non Ideal, Gas Mixtures & KMT vandenbout (52130) 7 ers 2. perfectly for pressures under 20 atm 3. very well under some conditions but shows large errors in others correct 4. perfectly under all conditions for all gases 5. perfectly for temperatures under 1000 K The ideal gasmodel isnever perfect. In the limit that the pressure goes to zero all gases exhibit ideal behavior. But at finite pressure there are always deviations (albeit very small at low pressures). ChemPrin3e T points Which of the following gases would you predict to have the largest value of the van der Waals coefficient b? 1. C 2 F 6 Gas a, L 2 atm mol 2 b, L mol 1 helium hydrogen neon krypton xenon chlorine CO ammonia water Which of the following gases has the largest attractive forces? 1. chlorine correct 2. helium 3. neon 4. ammonia 5. water The larger the Van der Waals coefficient a, the larger the attractive forces. 2. Cl 2 3. CO 2 4. C 2 FCl 5 correct 5. C 2 F 2 Cl 4 The larger the van der Waals coefficient b, the larger the molecule. The largest molecules have 8 atoms. Of these, C 2 FCl 5 is larger than C 2 F 2 Cl 4 and C 2 F 6, because Cl is larger than F. ChemPrin3e T points Consider the following van der Waals coefficients:

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