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Additional Gas Laws Slide 2 Grahams Law b Diffusion Spreading of gas molecules throughout a container until evenly distributed. b Effusion Passing of gas molecules through a tiny opening in a container Slide 3 C. Johannesson Grahams Law KE = mv 2 b Speed of diffusion/effusion Kinetic energy is determined by the temperature of the gas. At the same temp & KE, heavier molecules move more slowly. Larger m smaller v Slide 4 C. Johannesson Grahams Law b Grahams Law Rate of diffusion of a gas is inversely related to the square root of its molar mass. The equation shows the ratio of Gas As speed to Gas Bs speed. Slide 5 C. Johannesson b Determine the relative rate of diffusion for krypton and bromine. Kr diffuses 1.381 times faster than Br 2. Grahams Law The first gas is Gas A and the second gas is Gas B. Relative rate mean find the ratio v A /v B . Slide 6 C. Johannesson b A molecule of oxygen gas has an average speed of 12.3 m/s at a given temp and pressure. What is the average speed of hydrogen molecules at the same conditions? Grahams Law Put the gas with the unknown speed as Gas A. Slide 7 C. Johannesson b An unknown gas diffuses 4.0 times faster than O 2. Find its molar mass. Grahams Law The first gas is Gas A and the second gas is Gas B. The ratio v A /v B is 4.0. Square both sides to get rid of the square root sign. Slide 8 Slide 9 Daltons Law b The total pressure of a mixture of gases equals the sum of the partial pressures of the individual gases. P total = P 1 + P 2 +... Slide 10 When a H 2 gas is collected by water displacement, the gas in the collection bottle is actually a mixture of H 2 and water vapor. Slide 11 Daltons law of partial pressures and a table of known vapor pressures of water can be used to determine the pressure of dry gas that has been collected. Slide 12 C. Johannesson GIVEN: P H2 = ? P total = 94.4 kPa P H2O = 2.72 kPa WORK: P total = P H2 + P H2O 94.4 kPa = P H2 + 2.72 kPa P H2 = 91.7 kPa Daltons Law b Hydrogen gas is collected over water at 22.5C. Find the pressure of the dry gas if the atmospheric pressure is 94.4 kPa. Look up water-vapor pressure on chart for 22.5C. Sig Figs: Round to least number of decimal places. The total pressure in the collection bottle is equal to atmospheric pressure and is a mixture of H 2 and water vapor. Slide 13 C. Johannesson GIVEN: P gas = ? P total = 742.0 torr P H2O = 42.2 torr WORK: P total = P gas + P H2O 742.0 torr = P H2 + 42.2 torr P gas = 699.8 torr b A gas is collected over water at a temp of 35.0C when the barometric pressure is 742.0 torr. What is the partial pressure of the dry gas? Look up water-vapor pressure on table for 35.0C and convert to torr. Sig Figs: Round to least number of decimal places. Daltons Law The total pressure in the collection bottle is equal to barometric pressure and is a mixture of the gas and water vapor. Slide 14 Sample Problem #1 Mixtures of helium and oxygen are used in the air tanks of underwater divers for deep dives. For a particular dive, 12 L of O 2 at 25 o C and 1.0 atm and 46 L of He at 25 o C and 1.0 atm were both pumped into a 5.0-L tank. A)Calculate the partial pressure of each gas B)Calculate the total pressure in the tank at 25 o C (298 K). 14 *Because the partial pressure of each gas depends on the total moles present, we must first calculate n for each gas using the ideal gas law. PV = nRT n = PV RT n O 2 = (1.0 x 12) (0.08206 x 298) = 0.49 mol n He = (1.0 x 46) (0.08206 x 298) = 1.9 mol P = nRT V P O 2 = (0.49 x 0.08206 x 298) 5.0 = 2.4 atm P He = (1.9 x 0.08206 x 298) 5.0 = 9.3 atm *The tank has a volume of 5.0-L and temperature of 298 K, so we can figure out the partial pressure of each gas Determine the total pressure: P total = P O 2 + P He = 2.4 atm + 9.3 atm = 11.7 atm Slide 15 Sample Problem #2 A sample of solid potassium chlorate, KClO 3, was heated in a test tube and decomposed according to the reaction: 2KClO 3 (s) 2KCl (s) + 3O 2 (g) The oxygen produced was collected by displacement of water at 22 o C. The resulting mixture of O 2 and H 2 O vapor had a pressure of 754 torr and a volume of 0.650-L. Calculate the partial pressure of O 2 in the gas collected and the number of moles of O 2 present. The vapor pressure of water (P H 2 O ) at 22 o C is 21 torr. 15 Slide 16 Sample Problem #2 Solution We know: P total = 754 torr P H 2 O = 21 torr Next, we solve the ideal gas law for n O 2 n O 2 = (P O 2 V) (RT) Then solve: P = 0.964 atm V = 0.650 L T = 22 o C = 22 + 273 = 295 K R = 0.08206 L atm/K mol 16 So we can determine: P total = P H 2 O + P O 2 OR P total - P H 2 O = P O 2 SO 754 torr 21 torr = 733 torr P O 2 = 733 torr Convert pressure from torr to atm: 733 torr x (1 atm/760 torr) = 0.964 atm n O 2 = (0.964 x 0.650) (0.0821 x 295) n O 2 = 0.0259 mol O 2 Slide 17 Daltons Law Practice Problems 1.If a gaseous mixture is made of 2.41 g of He and 2.79 g of Ne in 1.04-L container at 25 o C, what will be the partial pressure of each gas and the total pressure in the container? 2.How many moles of helium gas would be required to fill a 2.41-L container to a pressure of 759 mm Hg at 25 o C? 3.A sample of oxygen gas (O 2 ) is saturated with water vapor (H 2 O) at 27 o C. The total pressure of the mixture is 772 torr, and the vapor pressure of water is 26.7 torr at 27 o C. What is the partial pressure of the oxygen gas? 4.Suppose a gaseous mixture of 1.15 g helium and 2.91 g argon is placed in a 5.25-L container at 273 o C. What pressure would exist in the container? 5.A tank contains a mixture of 3.0 mol of N2, 2.0 mol of O2, and 1.0 mol of CO2 at 25 o C and a total pressure of 10.0 atm. Calculate the partial pressure (in torr) of each gas in the mixture. 17