ChE102_Notes_-_Chap_3

# ChE102_Notes_-_Chap_3 - ChE102 Div 9 10 Fall 2009 CHAPTER 2...

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Fall 2009 CHAPTER 2 – Gases Petrucci: 6.1-6.9 Definition of Pressure When talking about gases, four properties are often used: amount (moles), temperature, Pressure is the force per unit area = force/area Force resulting from the collision of the gas molecules against the walls of the container Area of the walls of the container holding the gas Understanding Pressure Gas pressure is usually measured indirectly, by comparing it with liquid pressure Liquid pressure is directly proportional to the liquid density and the height of the liquid column P Hg = P air Understanding Pressure (2) Open-ended Manometer Course Notes 3 1 A g m A F P air air air . = = g h A g A h A g V A g m A F P Hg Hg Hg Hg Hg Hg Hg . . . . . . . . ρ = = = = = m Hg = m air

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Fall 2009 The Simple Gas Laws Boyle’s Law (1662): “For a fixed amount of gas at a constant temperature, the gas volume is inversely proportional to the gas pressure” PV = constant for a given temperature and given amount of substance The Simple Gas Laws (2) Charles’ Law (1787): “The volume of a fixed amount of gas at constant pressure is directly proportional to the Kelvin (absolute) temperature” For all gases at small pressures, c = 273.15 Aside – Definition of Temperature from Charles’s Law Temperature is measured using the ratio of the volume of a gas at the measured temperature to the volume of the same gas at 0ºC (freezing point of water) If T = –273.15°C (absolute zero), then V = 0. Lowest temperature possible before V < 0, which has no physical meaning Kelvin temperature scale is based on this concept: T (K) = T (°C) + 273.15 Substituting this definition into Charles’ law gives: Course Notes 3 2 + = c C T V V o ) ( 1 0 V 0 : volume of the gas at 0ºC t : temperature in ºC c : a constant + = 15 . 273 ) ( 1 0 C T V V o ( 29 c K T V K T V V 0 0 15 . 273 15 . 273 ) ( 1 = - + =
Fall 2009 The Simple Gas Laws (3) Avogadro’s Law (1808): “At a fixed temperature and pressure, the volume of a gas is directly proportional to the amount of gas” STP: Standard Temperature and Pressure Temperature = 0ºC = 273.15 K Pressure = 1 atm = 760 mm Hg 1 mol = 22.4 L The Ideal Gas Equation Combining all three gas relationships… Avogadro: Charles: Boyle: Combines to: Or the Ideal Gas Equation: PV = nRT Where R = C/c Ideal Gas Constant At STP 1 mol of most gases occupies 22.4 L: R can also be given in units of J/(mol·K), since: General Gas Equation (setting R = R): Course Notes 3 3 n V c T V V 0 = P nC V = P nC V = 0 c T P nC V = K mol atm L K mol L atm nT PV R = = = 082 . 0

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ChE102_Notes_-_Chap_3 - ChE102 Div 9 10 Fall 2009 CHAPTER 2...

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