Unformatted text preview: Chem 3615 Answer Key for Problem Set # 1: Ideal or Perfect Gas Behavior Due September 2, 2008
Read Chapter 1, the Handout on the Barometric Distribution Law & Chapter 6 (Sections 6.1 and 6.2) regarding the phase rule. Problems 1 through 6 are due at the start of class and will be graded. You may assume all gases behave ideally. You should show all unit conversions and express all answers with the correct number of significant figures. 1. A standard gas cylinder has a volume of about 30.0 L. If the gas is stored under a pressure of about 1.610 x 104 kPa at 25.00 C, how many moles of gas are contained in the cylinder assuming ideal gas behavior? What would be the mass in kilograms of the nitrogen gas in its standard state of aggregation in such a cylinder? Use the appropriate number of significant figures. Solution: . . . . . . . . / . . . . . . . . . 2. A spherical balloon containing 5.035 mg of hydrogen gas in its standard state of aggregation behaving ideally is attached to one end of an open tube cylindrical mercury manometer (see figure) where atmospheric pressure is 101325 Pa and the temperature is 293.15K? If the tube has a radius of 1.000 mm, there is 50.00 cm between the balloon and the mercury, and a difference in height between the mercury levels of 45.00 cm. What is the volume of the balloon in m3? What is the corresponding diameter in cm of the balloon assuming it is a sphere? You may assume that the density of the mercury is 13.5462 x 103 kg/m3 and that g = 9.807 m/s2. Hint: Determine the pressure and use this information to deduce the total volume of the system. Then use the total volume and the dimensions of the tube filled with H2, to determine the volume of the balloon. R = ? patm 50.00 cm 45.00 cm r = 1.000 mm Page 1 of 8 Solution: The pressure of the H2 in the tube and in the balloon can be obtained from . . . . . . . . . . . . . . . . . . . . ~ . ~ . Put another way, a bulb with a diameter of about 1.6 inches and a pressure close to atmospheric pressure and close to room temperature will have ~ 1 mmol of an ideal gas. Furthermore, note that the volume of the U-tube, was nearly negligible. While it is unlikely that I would not give you such a complicated problem on an exam, I could give you one where I told you the volume of the capillary was negligible. Page 2 of 8 3. A sample of air is collected over water at 30.00C. At equilibrium, the total pressure of the moist air is 0.9970 atm. The equilibrium vapor pressure of water at 30.00 C is 31.824 Torr. The composition of dry air is 78.08 mol% N2, 20.95 mol% O2, 0.93 mol% Ar and 0.04 mol% CO2. a) Calculate the partial pressures in atm of N2, O2, Ar and CO2 in the wet mixture assuming ideal gas behavior. b) Calculate the mole fractions of H2O, N2, O2, Ar and CO2 in the wet mixture, again assuming ideal gas behavior. Use the appropriate number of significant figures. Solution: The approach for solving this problem is to use Dalton's Law of partial pressures for ideal gases: , Alternatively, it can also be expressed as pi = xiptotal In this problem, you know ptotal, pH2O, and xi for the remaining species. In principle, ptotal = pwet + pdry. If we subtract pH2O from ptotal, we will be left with pdry and can write that pi,dry = xi,drypdry: . . . . . . As a test, note that . . . . . . Now we can calculate the mole fraction of each component in the total (wet) mixture using Dalton's law where . . . . . . . . Test: . . . . . . . . . . . . . . . . . . Page 3 of 8 . . . . . Notice how CO2 is not very important. Frequently we ignore all gases except nitrogen, oxygen, and argon. As you can see in this problem, if the system is wet we cannot ignore water as it is the amount of argon and will become even more significant at higher temperatures (i.e. higher humidity).
4. Given air is 78.08 mol% N2, 20.95 mol% O2, 0.93 mol% Ar and 0.04 mol% CO2, calculate the average molecular weight of dry air in units of g/mol. Use the appropriate number of significant figures. Solution: . . . . . . . . . Slightly different from previous years where CO2 was neglected (M = 29.0 g/mol)
5. A gas sample is known to be a mixture of methane and butane. A bulb of 200.0 cm3 capacity is filled with gas to a pressure of 100.0 kPa at 20.0C. If the weight of the gas in the bulb is 0.3846 g, what is the mole fraction of butane in the mixture? You may assume ideal gas behavior. Solution: Start by determining the number of moles from pV = nRT. . . . . . . . . . . . . Because we know the number of moles and the mass, we can calculate the average molar mass: . . . Page 4 of 8 Hence, Or . . . . . 6. What is the ratio of / for a perfect gas (express this answer in the simplest form in terms of n, R, and V)? Is / an extensive or intensive property? Note that Solution: For a perfect gas, pV = nRT or that V = nRT/p, whereby
, , Page 5 of 8 Practice Problems (These will not be graded). Please note that these problems were taken from various PCHEM textbooks. As a result some of the answers may make reference to equations that do not correspond to equations in your textbook!!! A. A perfect gas undergoes isothermal compression, which reduces its volume by 2.20 L. The final pressure and volume of the gas are 3.78 x 103 Torr and 4.65 L, respectively. Calculate the original pressure of the gas in (a) Torr, and (b) atm. (2.57 x 103 Torr, 3.38 atm) B. A sample of 255 mg of neon occupies 3.00 L at 122K. Us the perfect gas law to calculate the pressure of the gas. (4.27 x 103 Pa) (4.20 x 10-2 atm)x(101325 Pa/atm) = 4.27 x 103 Pa C. At 500 C and 699 Torr, the mass density of sulfur vapor is 3.71 g/L. What is the molecular formula of sulfur under these conditions? (S8) Page 6 of 8 D. Given that the density of air at 740 Torr and 27 C is 1.146 g/L, calculate the mole fraction and partial pressure of nitrogen and oxygen assuming that (a) air consists only of these two gases, and (b) air also contains 1.0 mol percent Ar. (nitrogen mole fractions, partial pressures) (a) (0.7583, 561 Torr) (b) (0.7507, 555.5 Torr) Page 7 of 8 E. The density of a gaseous compound was found to be 1.23 g/L at 330 K and 150 Torr. What is the molar mass of the compound? (169 g/mol) F. A 1.0 L bulb contains 1.0 x 1023 hydrogen molecules. If the pressure exerted by the gas is 100 kPa, what is the temperature of the gas? (72K) Page 8 of 8 ...
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