PS 22 2022 key~

Problem Set 22 – Mixtures of Gases Chem 105 STP 1. (a) What is meant by standard temperature and pressure (STP)? standard temperature and pressure (informally abbreviated as STP) as a temperature of 273.15 K (0 °C, 32 °F) and an absolute pressure of exactly 100,000 Pa (1 bar, 14.5 psi, 0.9869 atm). (b) What is the volume of 1 mole of an ideal gas at STP? Does it matter what gas? PV=nRT, V = 22.4L no matter what gas it is. Density of gases 2. (a) Birds and sailplanes take advantage of thermals (rising columns of warm air) to gain altitude with less effort than usual. Why does warm air rise? Warm air is lighter, that is, less dense than cold air, because the molecules of gases occupy a larger volume since they have more kinetic energy. (b) Radon is a naturally occurring radioactive gas found in the ground and in building materials. It is easily inhaled and emits α particles when it decays. Cumulative radon exposure is a significant risk factor for lung cancer. a. Calculate the density of radon at 298 K and 1 atm of pressure. D = 222 g mol × 1 atm 0.0821 L∙atm mol∙ K × 298 K = 9.08 g / L b. Are radon concentrations likely to be greater in the basement or on the top floor of a building? The density of radon is greater than the density of air. So radon is more likely to be concentrated in the basement. 3. (a) What is the density (in g/L) of sulfur hexafluoride at 227 ºC and 2.00 atm of pressure? ρ = m V = nM nRT P = MP RT = ( 146 g mol ) ( 2.00 atm ) ( 0.08206 Latm mol K ) ( 500. K ) = 7.12 g / L (b) The density of air at 25 ºC and 642 torr is 1.00 g/L. What is the molar mass of air? Use 1.00 L of gas (for convenience, we could choose any volume). The density tells us the mass of this volume of gas: m = ρV = 1.00 g L 1.00 L = 1.00 g Next, use this volume (1.00 L) to calculate the moles: n = PV RT = ( 642 torr ) ( 1 atm 760 torr ) ( 1.00 L ) ( 0.08206 Latm mol K ) ( 298 K ) = 0.035 moles

Finally, calculate the molar mass: M = m n = 1.00 g 0.035 mol = 29 g / mol 4. 26.2 g of an unknown gas occupies 5.3 L at 40.ºC and 742 torr. What is the molar mass of this gas? Further studies indicate that this gas is monoatomic – which element do you suspect this gas is? Use the gas laws to determine the number of moles in the sample: n = PV RT = ( 742 torr× 1 atm 760 torr ) ( 5.3 L ) 0.0821 L∙atm mol∙K × 313 K = 0.20 mol Use the mass and the moles to calculate the molar mass: (26.2 g)/(0.20 mol)=130 g/mol This looks like xenon (131 g/mol) Partial Pressures 5. (a) What is meant by the partial pressure of a gas? The pressure that a particular gas contributes to the total pressure (b) A gas mixture contains 7.0 g N 2 , 2.0 g H 2 , and 16.0 g CH 4 . What is the mole fraction of H 2 in the mixture? Moles of N 2 = 7g x 1mol/28.01g = 0.25mol Moles of H 2 = 1mole Moles of CH 4 = 1mol Total moles in gas mixture = 2.25mol X H2 = 1mol/2.25 = 0.44 X N2 = 0.11 X CH4 = 0.44 (c) Calculate the pressure of the gas mixture and the partial pressure of each constituent gas if the mixture is in a 5.0 L vessel at 20°C. P total = 2.25 x 0.08206 x 293/5 = 10.8atm P H2 = 0.44 x 10.8 = 4.80 atm P N2 = 0.11 x 10.8 = 1.20 atm P CH4 = 0.44 x 10.8 = 4.80 atm 6. (a) A glass container with a volume of 5.00 L holds 0.120 g of Cl 2 gas and 0.145 g of F 2 gas at a total pressure of 1.80 atm. Determine the partial pressure of each of the gases. We use Dalton's Law ( P total = P 1 + P 2 + P 3 + …), solving for the partial pressure of each gas. To do this, we need the mole fraction of each gas. The mole fraction of a gas is defined as the moles of the gas divided by the total moles of all gases present. Since we are given the mass of each gas, we first need to convert to moles using the molecular weight.