Version 001 HW04Ideal Gas Laws, Gas Mixtures and KMT sparks (52100) 1


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1 Version 001 HW04Ideal Gas Laws, Gas Mixtures and KMT sparks (52100) 1 This printout should have 15 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. Holt da 11 review points One method of estimating the temperature of the center of the sun is based on the assumptionthatthecenterconsistsofgasesthathave an average molar mass of 2.00 g/mol. If the density of the center of the sun is 1.40 g/cm 3 at a pressure of atm, calculate the temperature. Correct answer: C. d 1.4 g/cm 3 P atm M 2.00 g/mol T? M d R T P T M P dr (2.00 g/mol)( atm ) (1.4 g/cm 3 ) ( mol K L atm ) 1 ml 1 cm 3 1 L 1000 ml C ChemPrin3e points The analysis of a hydrocarbon revealed that it was % C and % H by mass. When 1.51 g of the gas was stored in a 1 L flask at C, it exerted a pressure of 484 Torr. What is the molecular formula of the hydrocarbon? 1. C 3 H 8 2. C 2 H 4 correct 3. C 7 H C 4 H C 4 H 6 6. C 3 H 5 7. C 5 H C 6 H C 8 H 16 m 1.51 g V 1 L T K P 484 Torr R L atm/k/mol The empirical formula derived from the elemental analyses is (CH 2 ) n. Applying the ideal gas law, P V n m MW MW mt R P V ( ) (1.51 g)( K) 760 Torr (484 Torr)(1 L) 1 atm L atm/k/mol g/mol. The empirical formula mass is g/mol. The value of nintheformula (CH 2 ) n is, therefore, equalto 2. Brodbelt 12 04a points For the reaction 2 HCl+Na 2 CO 3 2 NaCl+H 2 O+CO liters of CO 2 is collected at STP. How many moles of NaCl are also formed? moles moles moles moles moles
2 Version 001 HW04Ideal Gas Laws, Gas Mixtures and KMT sparks (52100) moles correct V CO L At STP we can use the standard molar volume, 22.4 L/mol mol CO L 22.4 L/mol 8.00 mol CO 2 2 mol NaCl 1 mol CO mol NaCl Nlib points Two gases are contained in gas bulbs connected byavalve. GasAispresent ina1liter bulb at a pressure of 935 torr. Gas B exerts a pressure of 334 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 935 torr V total 2 L P A V A P t V t P t P AV A V t (935 torr)(1 L) 2 L V B 1 L P B 334 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 Torr Torr correct 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 m/s
3 Version 001 HW04Ideal Gas Laws, Gas Mixtures and KMT sparks (52100) m/s m/s m/s correct T C K 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 Hint: Consider ONLY the nitrogen gas that comes from the azide in this problem. Your chemical equation should be the decomposition of sodium azide into sodium metal and nitrogen gas. (You will need to balance this!) 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 55 L air bag at 1.95 atm and 17 C. Correct answer: g. P 1.95 atm T 17 C K R L atm/k/mol V N2 55 L MW g Applying the ideal gas law, n N2 P V (1.95 atm)(55 L) ( L atm/k/mol)(290 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)(290 K) (28 g/mol) (kg/m 2 /s 2 ) ( ) 1000 g J kg m/s.
4 Version 001 HW04Ideal Gas Laws, Gas Mixtures and KMT sparks (52100) 4 Mlib points Which of the following statements about the KineticMolecular Theory of gases is false? 1. Gases consist of molecules in continuous, random motion. 2. Collisions between molecules are elastic. 3. The average kinetic energy of a gas molecule is independent of the temperature. correct 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. as the temperature increases, a high proportion of molecules have very slow speeds. 2. at low temperatures, most molecules have speeds close to their average speed. correct 3. as the temperature decreases, the spread of speeds widens. 4. at high temperatures, most molecules have speeds close to their average speed. 5. as the temperature decreases, a high proportion of molecules have very high 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. 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 He gas because it is less massive and moving with a higher average velocity correct 2. They are the same since the pressure is the same 3. The O 2 since it has a higher average momentum since it is more massive 4. The O 2 since it has a higher average kinetic energy because it is more massive 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.
5 Version 001 HW04Ideal Gas Laws, Gas Mixtures and KMT sparks (52100) 5 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 atm atm atm 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 correct Cannot be determined Applying the ideal gas law P V n P V (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 343 mg of methane, 176 mg of argon, and 202 mg of nitrogen. The partial pressure of nitrogen at 321 K is 19 kpa. Calculate the total pressure of the mixture.
6 Version 001 HW04Ideal Gas Laws, Gas Mixtures and KMT sparks (52100) 6 Correct answer: kpa. m N2 202 mg g m CH4 343 mg g m Ar 176 mg g P N2 19 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 V n V nt R P ( mol)(321 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. P N2 19 kpa P CH4 n CH 4 P N2 n N mol 19 kpa mol kpa P Ar n Ar P N2 n N mol 19 kpa mol kpa P total kpa kpa +19 kpa kpa. 015 (part 2 of 2) 10.0 points Calculate the volume. Correct answer: L. R L atm T 321 K K mol Using the total moles and pressure, n total mol mol mol mol.
= 1.038 atm. 760 mm Hg. = 0.989 atm. d. 767 torr = 767 mm Hg. = 1.01 atm
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