CH301 Worksheet 8—Gases (Answer Key) 1. What do we assume about ideal gases? What is the ideal gas law? Give the units for each variable. Ideal gases are infinitely small, hard spheres that do not interact with each other. They are essentially "blind" to other gas molecules and will bounce off of each other just as they would bounce of a wall. The ideal gas law is PV = nRT. Coomon units for pressure, volume, n, and temperature are atmospheres, liters, moles, and Kelvin, respectively. R is a constant, which has a value of 0.08206 (l*atm)/(K*mol). 2. If you know the number of moles of an ideal gas, what is the minimum number of variables that you need to know in order to fully determine the system? If you know the number of moles of an ideal gas, you only need to know 2 more variables to recreate the system. Any two out of pressure, volume, and temperature is enough to define the final unknown term. 3. Assuming a constant molar quantity of gas, hoe could you produce the following effects? a. decrease pressure You could decrease the temperature or increase the volume. b. decrease volume You could decrease the temperature or increase the external pressure. c. increase pressure You could increase the temperature or decrease the volume. d. increase volume You could increase the temperature or decrease the external pressure. 4. You are scuba diving in a large fish tank. While you are at the bottom of the tank, you release a baloon full of air and watch it as it rises to the surface. What do you notice about the volume of the baloon? The pressure at the bottom of the tank is greater than the pressure at the top of the tank, so as it rises, you notice that its volume increases. 5. What is the temperature of .75 moles of argon in a 18 L container with a pressure of 790 Torr?n = .75 mole, V = 18 L, and P = 790 Torr (1 atm/760 Torr) = 1.04 atm T = PV / (nR) = (1.04 atm * 18 L) / (.75 mol * .082 Latm/molK) = 304.4 K 6. Rank the following in order of increasing density: 1 mole of CH4 at .1 atm and 273 K 2 moles O2 at 1 atm and 300 K 3 mol H2 3 atm and 290 K CH4 < H2 < O2 CH4: ρ = PMW / RT = (.1 atm)(16g/mol) / (0.082 Latm/Kmol)(273K) = 0.07147 g/L O2 ρ = PMW / RT = (1 atm)(32g/mol) / (0.082 Latm/Kmol)(300K) = 1.3 g/L H2 ρ = PMW / RT = (3 atm)(2g/mol) / (0.082 Latm/Kmol)(290K) = 0.2523 g/L 7. You are a little boy or girl and stole your parents' hot air balloon. You are also a thirsty kid and brought some cans of soda (each can holds 354 mL) with you. As you get higher in altitude you notice that your soda cans start to expand and then eventually explode. So now you are thirsty and desperate to figure out what happened. You find out that the pressure at sea level is 1 atm and where the cans exploded is .7 atm. You also note that at sea level the temperature is 30 °C and 25 °C where the cans exploded. Why did the cans explode? Without any calculations you should be able to do this problem. Note that the pressure dropped .3 atm. Pressure and volume are inversely related so volume must be increasing. Cans can only hold so much volume, hence why they exploded. Now to prove it with some math: PV = nRT at sea level:n = PV/RT n = (1 atm)(.354L) / (0.082 Latm/Kmol)(273 + 30) = 0.014 moles in the air: V = nRT/P = (.014 moles)(0.082 Latm/Kmol)(273 +25) / .7atm = .4887 L So that means the liquid expanded from 354 mL to 489 mL. 8. An adult's lungs can hold about 6L. How many grams of air can an adult hold at a pressure of 102 kPa? Normal body temperature is 37 °C and air is about 20% oxygen and 80% nitrogen. (101,325 Pa = 1 atm) Air is 20% O2 and 80% N2, oxygen and nitrogen are diatomic molecules Oxygen: 32 g/mol Nitrogen: 28 g/mol Oxygen contributes 6.4 g/mol of air and nitrogen contributes 22.4 g/mol of air. So, air has a total of 28.8 g/mol. (1 atm / 101,325 Pa)(102000 Pa) = 1.007 atm 37 °C + 273 = 310 K PV = nRT n = PV/RT n = (1.007 atm)(6L) / (0.082 Latm/Kmol)(310 K) n = 0.238 moles (0.238 moles)(28.8 grams / mole) = 6.85 grams of air 9. Is it possible for 1 mole of air in an adult's lungs to be at STP? Explain and prove by use the ideal gas law. No it's not possible, you would die. 1 mole of an ideal gas at STP has a volume of 22.4 L. This would be way too much for your lungs, which hold about 6L. PV = nRT At STP: 1 atm and 273K V = nRT/PV = (1 mole)(0.082 Latm/Kmol)(273K) / 1 atm V = 22.386 L 10. A gas exerts a pressure of 1.12 atm in a 4 L container at 19C. You know the density of the gas is 1.5 g/L. What is the molecule? PV = nRT (1.12 atm)(4L) = n (0.082 Latm/Kmol)(19+273) = .187 (0.187g/4L)(x g/mol) = 1.5 g/L x = 32g/mol O2 11. What assumptions do we make when using the ideal gas law? Which of these are pretty good and which are pretty bad? Gas molecules are infinitely small (i.e. euclidean points) - this is a very bad assumption, since all gases, even the smallest ones, have some volume. The energy contained in a gaseous system is determined only by the absolute temperature - this is a very good assumption and is true over a wide range of temperatures. All collisions (gas-gas or gas-container) are fully elastic - this is a very bad assumption. There are no attractive or repulsive forces between molecules - this is also a very bad assumption, if it were true everything would be in the gas phase at all temperatures. There are many more, but these are the ones we care about most. 12. What are the the two "fudge factors" (aka coefficients) in the van der Waals equation? Which terms in the ideal gas law do they correct/modify? These "fudge factors" are "a" which corrects the pressure term of the ideal gas law and "b" which corrects the volume term in the ideal gas law. 13. Rank the following gases from most to least ideal in terms of the van der Waals coefficient b: CO 2, SF6, O2, H2, He, CH4, Rn, H2 > He > CH4 > O2 > CO2 > SF6 > Rn Since coefficient b corrects for the volume occupied by the gas, larger gases will be less ideal. 14. At a given temperature, what will be the ratio of the rate of effusion of ozone to rate of effusion of molecular oxygen? (m1/m2) = (v2/v1)2 (moxygen/mozone)½ = (vozone/voxygen) (32/48)½ = (vozone/voxygen) 0.82:1 = vozone:voxygen 15. What is …
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