# Chapter 8 - Chapter 8 Gases The Gas Laws of Boyle, Charles...

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Chapter 8 Gases The Gas Laws of Boyle, Charles and Avogadro The Ideal Gas Law Gas Stoichiometry Dalton’s Laws of Partial Pressure The Kinetic Molecular Theory of Gases Effusion and Diffusion Collisions of Gas Particles with the Container Walls Intermolecular Collisions Real Gases Chemistry in the Atmosphere

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09/08/10 2 States of Matter Solid Liquid Gas We start with gases because they are simpler than the others.

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V 1 / V 2 = T 1 / T 2 (fixed P,n) P 1 V 1 = P 2 V 2 (fixed T,n) Boyle’s Law Charles’ Law V x P   = const V / T   = const V /  n   = const (fixed P,T) Avogadro 1662 1787 1811 n = number of moles
Boyle’s Law: Pressure and Volume The product of the pressure and volume, PV , of a sample of gas is a constant at a constant temperature: PV = k = Constant (fixed T,n)

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Boyle’s Law: The Effect of Pressure on Gas Volume Example The cylinder of a bicycle pump has a volume of 1131 cm 3 and is filled with air at a pressure of 1.02 atm. The outlet valve is sealed shut, and the pump handle is pushed down until the volume of the air is 517 cm 3 . The temperature of the air trapped inside does not change. Compute the pressure inside the pump.
Charles’ Law: T vs V At constant pressure, the volume of a sample of gas is a linear function of its temperature. V = bT T(°C) =273°C[(V/V o )] When V=0, T=-273°C

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Charles’ Law: T vs V The Absolute Temperature Scale Kelvin temperature scale T (Kelvin) = 273.15 + t (Celsius) Gas volume is proportional to Temp V = V o ( 1 + ) t 273.15 o C
Charles’ Law: The Effect of Temperature on Gas Volume V 1 / V 2 = T 1 / T 2 (at a fixed pressure and for a fixed amount of gas) V vs T

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Avogadro’s law (1811) V = a n n= number of moles of gas a = proportionality constant For a gas at constant temperature and pressure the volume is directly proportional to the number of moles of gas.
V 1 / V 2 = T 1 / T 2 (at a fixed pressure) P 1 V 1 = P 2 V 2 (at a fixed temperature) Boyle’s Law Charles’ Law V =  k -1 V =  b T V =  an (at a fixed pressure and temperature) Avogadro V =  n RTP - 1 n = number of moles PV =  n RT ideal gas law an empirical law

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Example At some point during its ascent, a sealed weather balloon initially filled with helium at a fixed volume of 1.0 x 10 4 L at 1.00 atm and 30 o C reaches an altitude at which the temperature is -10 o C yet the volume is unchanged. Calculate the pressure at that altitude . n 1 = n 2 V 1 = V 2 2 2 2 2 1 1 1 1 T n V P T n V P = 2 2 1 1 T P T P = P 2 = P 1 T 2 /T 1 = (1 atm)(263K)/(303K)
STP (Standard Temperature and Pressure) For 1 mole of a perfect gas at O°C (273K) (i.e., 32.0 g of O 2 ; 28.0 g N 2 ; 2.02 g H 2 ) nRT = 22.4 L atm = PV At 1 atm, V = 22.4 L STP = standard temperature and pressure = 273 K (0 o C) and 1 atm

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