Gas Law Practice Problems

IDEAL GAS LAW Use the Ideal Gas Law below to solve the following problems. PV = nRT where P = pressure in atmospheres V = volume in liters n = number of moles of gas R = Universal Gas Constant = 0.0821 L⋅atm/mol⋅K T = Kelvin temperature   How many moles of oxygen will occupy a volume of 2.5 liters at 1.2 atm and 25° C? 0.12 moles 1.2 x 2.5 = n x 0.0821 x 298 = 0.123 mol What volume will 2.0 moles of nitrogen occupy at 720 torr and 20° C? 51 L 720 torr = 0.95 atm 0.95 x V = 2.0 x 0.0821 x 293 = 51 L What pressure will be exerted by 25 g of CO₂ at a temperature of 25° C and a volume of 500 mL? 2.8 atm 25 g CO₂ = 0.568 mol P x 0.5 = 0.568 x 0.0821 x 298 = 2.8 atm At what temperature will 5.00 g of Cl₂ exert a pressure of 900 torr at a volume of 750 mL? 158 K = -119° C 5.00 g Cl₂ = 0.0707 mol 900 torr = 1.18 atm 1.18 x 0.75 = 0.0707 x 0.0821 x T = 158 K = -119° C What is the density of NH₃ at 800 torr and 25° C? 0.73 g/L 800 torr = 1.05 atm (1.05)(V) = n (0.0821)(298) n/V = 0.0429 mol/L 0.0429 mol/L x 17 g/mol = 0.73 g/L If the density of a gas is 1.2 g/L at 745 torr and 20° C, what is its molecular mass? 29 g/mol 745 torr = 0.98 atm 1.2 g/L = 0.98 x 0.0821 x 293 / M M = 29 g/mol How many moles of nitrogen gas will occupy a volume of 347 mL at 6680 torr and 27° C? 0.124 mol 6680 torr = 8.8 atm 8.8 x 0.347 = n x 0.0821 x 300 n = 0.124 mol What volume will 454 grams (1 lb) of hydrogen occupy at 1.05 atm and 25° C? 5290 L (1.05)(V) = (454/2)(0.0821)(298) V = 5290 L Find the number of grams of CO₂ that exert a pressure of 785 torr at a volume of 32.5 L and a temperature of 32° C. 59.0 g 785 torr = 1.03 atm 1.03 x 32.5 = n x 0.0821 x 305 n = 1.3 mol 1.3 mol x 44 g/mol = 59.0 g An elemental gas has a mass of 10.3 g. If the volume is 58.4 L and the pressure is 758 torr at a temperature of 2.5° C, what is the gas? Helium   (758/760)(58.4) = n(0.0821)(273 + 2.5) n = 2.06 mol 10.3 g / 2.06 mol = 5 g/mol (Helium) DALTON'S LAW OF PARTIAL PRESSURES Dalton's Law says that the sum of the individual pressures of all the gases that make up a mixture is equal to the total pressure or: Pₜ = P₁ + P₂ + P₃ + ... The partial pressure of each gas is equal to the mole fraction of each gas x total pressure.   Pₜ = P₁ + P₂ + P₃ + ... or (moles gas / total moles) x Pₜ = P Solve the following problems: A 250. mL sample of oxygen is collected over water at 25°C and 760.0 torr pressure. What is the pressure of the dry gas alone? (Vapor pressure of water at 25°C = 23.8 torr)   Pₜ = Pₒ₂ + Pₕ₂ₒ 760.0 torr = Pₒ₂ + 23.8 torr Pₒ₂ = 736.2 torr A 32.0 mL sample of hydrogen is collected over water at 20°C and 750.0 torr pressure. What is the volume of the dry gas at STP? (Vapor pressure of water at 20°C = 17.5 torr)   P₁V₁ / T₁ = P₂V₂ / T₂ (750 - 17.5) * 32.0 / (293) = (760) * V₂ / (273) V₂ = 28.7 mL A 54.0 mL sample of oxygen is collected over water at 23°C and 770.0 torr pressure. What is the volume of the dry gas at STP? (Vapor pressure of water at 23°C = 21.1 torr)   P₁V₁ / T₁ = P₂V₂ / T₂ (770 - 21.1) * 54.0 / (296) = (760) * V₂ / (273) V₂ = 49.1 mL A mixture of 2.00 moles of H₂, 3.00 moles of NH₃, 4.00 moles of CO₂, and 5.00 moles of N₂ exerts a total pressure of 800 torr. What is the partial pressure of each gas? Total moles = 2 + 3 + 4 + 5 = 14 P(H₂) = (2/14) * 800 = 114 torr P(NH₃) = (3/14) * 800 = 171 torr P(CO₂) = (4/14) * 800 = 229 torr P(N₂) = (5/14) * 800 = 286 torr The partial pressure of F₂ in a mixture of gases where the total pressure is 1.00 atm is 300. torr. What is the mole fraction of F₂? 300 torr / 760 torr = 0.395