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<ul><li> Slide 1 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 1 Gases </li> <li> Slide 2 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 2 A Gas 4 Uniformly fills any container. 4 Can be compressed. 4 Mixes completely with any other gas 4 Exerts pressure on its surroundings. 4 Can diffuse into other gases. 4 Can be described in terms of its volume, temperature, pressure, and the amount present. </li> <li> Slide 3 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 3 Pressure 4 is equal to force/unit area 4 SI units = Newton/meter 2 = 1 Pascal (Pa) 4 1 standard atmosphere = 101,325 Pa 4 1 standard atmosphere = 1 atm = 760 mm Hg = 760 torr </li> <li> Slide 4 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 4 A Torricellian Barometer At sea level, latitude 45 o north (or south), the average atmospheric pressure supports a column of mercury 760 mm high in a simple mercury barometer at 0 o C This average pressure is called one atmosphere. </li> <li> Slide 5 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 5 The Effects of Decreasing the Volume of a Sample of Gas at Constant Temperature </li> <li> Slide 6 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 6 Boyles Law * Pressure Volume = Constant (T = constant) P 1 V 1 = P 2 V 2 (T = constant) V 1/P (T = constant) ( * Holds precisely only at very low pressures.) </li> <li> Slide 7 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 7 Plotting Boyles Data from Table 5.1 </li> <li> Slide 8 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 8 A Plot of PV versus P for Several Gases at Pressures Below 1 ATM </li> <li> Slide 9 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 9 A gas that strictly obeys Boyles Law is called an ideal gas. </li> <li> Slide 10 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 10 Example: Boyles Law At 25 o C, a sample of oxygen occupies 100. mL under a pressure of 380. torr. What volume would it occupy under a pressure of 1.00 atm at the same temperature? </li> <li> Slide 11 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 11 Answer 50.0 mL </li> <li> Slide 12 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 12 Example At 100. o C a sample of neon occupies 200. mL under a pressure of 4.00 atmospheres. What must the pressure be for it to occupy 800. mL at 100. o C? </li> <li> Slide 13 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 13 Answer 1.00 atm. </li> <li> Slide 14 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 14 The Effects of Increasing the Temperature of a Sample of Gas at Constant Pressure </li> <li> Slide 15 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 15 Charless Law The volume of a gas is directly proportional to temperature, and extrapolates to zero at zero Kelvin. V = bT (P = constant) b = a proportionality constant </li> <li> Slide 16 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 16 Charless Law </li> <li> Slide 17 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 17 Amazing Experiments have shown that when a 273 mL sample of gas at 0 o C is heated to 1 o C, its volume increases by 1 mL to 274 mL. Conversely each degree the gas is cooled its volume decreases 1 mL. What will the volume of the gas be at 273 o C? </li> <li> Slide 18 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 18 Plots of V Versus T (C) for Several Gases </li> <li> Slide 19 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 19 The Kelvin Temperature Scale The temperature at 273 o C, the lowest temperature possible is known as absolute zero. It is the basis of the Kelvin (absolute) temperature. K = o C + 273 </li> <li> Slide 20 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 20 Plots of V Versus T </li> <li> Slide 21 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 21 Example Charles Law A sample of hydrogen, H 2, occupies 100. mL at 25 o C and 740. torr. What volume would it occupy at 50.0 o C and 740. torr? </li> <li> Slide 22 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 22 Answer 108 mL </li> <li> Slide 23 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 23 Example A sample of oxygen, O 2, occupies 200. mL at 100. o C and 1.00 atm. At what temperature ( o C) will the oxygen occupy 400. mL if the pressure remains constant? </li> <li> Slide 24 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 24 Answer 746 K 473 o C </li> <li> Slide 25 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 25 The Effects of Increasing the Temperature of a Sample of Gas at Constant Volume: Whos Law? </li> <li> Slide 26 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 26 Gay-Lussacs Law P 1 P 2 T1T1 T2T2 = </li> <li> Slide 27 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 27 Combined Gas Law Boyles and Charles Laws can be combined together into the following mathematical expression: P 1 V 1 = P 2 V 2 T 1 T 2 </li> <li> Slide 28 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 28 A very convenient form: V 2 = V 1 P 1 T 2 P 2 T 1 The relationship has six variables. If any five are known, the sixth can be calculated. </li> <li> Slide 29 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 29 Example A sample of nitrogen, N 2, occupies 200. mL at 57 o C under a pressure of 840. torr. What volume would it occupy at 0 o C and 1.00 atm pressure? </li> <li> Slide 30 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 30 Answer 183 mL </li> <li> Slide 31 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 31 Example A sample of methane, CH 4, the main component of natural gas occupies 400. mL at 96 o C under a pressure of 0.500 atm. What volume would it occupy at 0 o C under a pressure of 1200 torr? </li> <li> Slide 32 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 32 Answer 93.7 mL </li> <li> Slide 33 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 33 Avogadros Law For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas (at low pressures). V = an a = proportionality constant V = volume of the gas n = number of moles of gas </li> <li> Slide 34 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 34 Standard Temperature and Pressure STP P = 1 atmosphere T = C The molar volume of an ideal gas is 22.42 liters at STP </li> <li> Slide 35 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 35 A Mole of Any Gas Occupies a Volume of Approximately 22.4 L at STP </li> <li> Slide 36 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 36 Example What volume does 36.3 g of oxygen, O 2, occupy at STP? </li> <li> Slide 37 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 37 Answer 25.4 L </li> <li> Slide 38 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 38 Molecular Weight Application of the gas laws provides a method of calculating the molecular weight of a gas. This plus elemental analysis provides mechanism for determining molecular formula </li> <li> Slide 39 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 39 Example If 2.00 g of a gas occupies 560.mL at STP, what is its molecular weight? </li> <li> Slide 40 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 40 Answer 80.0 g/mol </li> <li> Slide 41 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 41 Example A compound containing only carbon and hydrogen is 80.0% C and 20.0% H by mass. At STP 280. mL of the gas weighs 0.375 g. What is the molecular formula for the compound? </li> <li> Slide 42 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 42 Answer C2H6C2H6 </li> <li> Slide 43 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 43 Ideal Gas Law 4 An equation of state for a gas. 4 state is the condition of the gas at a given time. 4 Can be determined by combining Boyles Law, Charles Law, and Avogadros Law </li> <li> Slide 44 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 44 Ideal Gas Law PV = nRT R = proportionality constant = 0.0821 L atm mol P = pressure in atm V = volume in liters n = moles T = temperature in Kelvins Holds closely at P &lt; 1 atm </li> <li> Slide 45 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 45 Example What volume does 48.0 g of methane, CH 4, occupy at 140. o C under a pressure of 1280 torr? </li> <li> Slide 46 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 46 Answer 60.4 L </li> <li> Slide 47 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 47 Example A 250. mL flask contains a mixture of nitrogen, oxygen, and helium at a temperature of 27 o C and a pressure of 0.850 atm. How many moles of gas are present? </li> <li> Slide 48 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 48 Answer 8.63 x 10 -3 moles </li> <li> Slide 49 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 49 Example What pressure in kilopascals is exerted by 0.480 g of carbon dioxide in a 1.00 L flask at 100 o C? </li> <li> Slide 50 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 50 Answer 33.8 kPa </li> <li> Slide 51 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 51 Density Density has the units of mass per unit volume. We can arrange the ideal gas equation to obtain density D = P M RT Where M is the gram molar mass; D is in g/L </li> <li> Slide 52 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 52 Example What is the density of formaldehyde, CH 2 O, vapors at 95 o C and a pressure of 650. torr? </li> <li> Slide 53 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 53 Answer 0.849 g/L </li> <li> Slide 54 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 54 Gram Molecular Mass The Ideal Gas Equation can be rearranged to solve directly for gram molecular mass. mRT PV M =M = </li> <li> Slide 55 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 55 Example A 0.1842 g sample of phosphorus vapor in a 169 mL bulb exerts a pressure of 45.6 kPa at 350. o C. Calculate both the molecular mass and molecular formula of phosphorus vapor. (R = 8.31 kPa L/ mol K) </li> <li> Slide 56 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 56 Answer 124 g/mol P 4 </li> <li> Slide 57 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 57 Daltons Law of Partial Pressures For a mixture of gases in a container, P Total = P 1 + P 2 + P 3 +... </li> <li> Slide 58 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 58 Partial Pressure of Each Gas in a Mixture </li> <li> Slide 59 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 59 Example If 100 mL of hydrogen and 100. mL of oxygen, both measured at 25 o C and 1.00 atm pressure, were forced into one of the containers at 25 o C, what would be the total pressure of the two gases? </li> <li> Slide 60 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 60 Answer 2 atm </li> <li> Slide 61 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 61 Collecting Gas Over Water A gas can be collected by displacement of water This results in a mixture of gases: The gas you are collecting Water vapor </li> <li> Slide 62 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 62 Collecting Gas Over Water Vapor pressure is temperature dependent. P total = P gas + P water How do we correct for the water vapor? </li> <li> Slide 63 </li> <li> Example A sample of solid potassium chlorate (KClO 3 ) was heated in a test tube and decomposed by the following reaction: 2KClO 3 (s) 2KCl (s) + 3O 2 (g) The oxygen produced was collected by displacement of water at 22.0 C at a total pressure of 754 torr. The volume of the gas collected was 0.650 L, and the vapor pressure of the water at 22.0 is 21 torr. Calculate the partial pressure of O 2 in the gas collected and the mass of KClO 3 in the sample that was decomposed. </li> <li> Slide 64 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 64 Solution First, find the partial pressure of O 2 from Daltons Law of partial pressures Next, use the ideal gas law to find the number of moles of O 2 Calculate the moles of KClO 3 needed to produce this quantity of O 2 </li> <li> Slide 65 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 65 Answers P O 2 = 733 torr n O 2 = 2.59 x 10 -2 2.12 g KClO 3 </li> <li> Slide 66 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 66 Kinetic Molecular Theory 1.Gases consist of tiny discrete molecules that are relatively far apart. 2.Gases consist of molecules in continuous random motion. 3.Molecular collisions are elastic 4.The average kinetic energy of gaseous molecules is proportional to the absolute temperature. KE = mv 2 </li> <li> Slide 67 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 67 Examples Explain Gay Lussacs Law on the basis of the Kinetic Molecular Theory Explain Boyles Law on the basis of the Kinetic Molecular Theory Explain Charles Law on the basis of the Kinetic Molecular Theory </li> <li> Slide 68 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 68 Effusion: describes the passage of gas into an evacuated chamber. Diffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing. </li> <li> Slide 69 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 69 The Effusion of a Gas into an Evacuated Chamber </li> <li> Slide 70 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 70 Effusion: Diffusion: </li> <li> Slide 71 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 71 Example The average speed of oxygen molecules at 25 o C is 4.8 x 10 4 cm/s. What would be the average speed of sulfur dioxide molecules at the same temperature? </li> <li> Slide 72 </li> <li> Copyright2000 by Houghton Mifflin Company. All rights reserved. 72 Answer 3.39 x 10 4 cm/s </li> <li> Slide 73 </li> <li> Copyright2000 by Houghton Mifflin Company. All r...</li></ul>

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