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4 Postulates of Kinetic Theory 1) Spherical molecules in constant, random straight-line motion 2) “Elastic” collisions 3) Point masses 4) No interactions

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Ideal Gas Gas that obeys all 4 assumptions of the kinetic theory all of the time. It doesn’t exist. It’s a model.

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Real Gas Most real gases obey the kinetic theory most of the time.

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Which assumptions of the kinetic theory hold up? 1. Spherical molecules in random, straight-line motion 2. “Elastic” collisions

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Which assumptions of the kinetic theory break down? 1. Point masses 2. No interactions

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When do the assumptions of the kinetic theory break down? When the gas molecules are close to each other.

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When are the gas molecules close to each other? At high pressure & low temperature.

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When are the gas molecules far apart from each other? At low pressure & high temperature.

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How do the gas molecules act when they are far apart from each other? Good!

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What are the properties of gases? 1. Have mass 2. Take the shape & volume of their container 3. Compressible 4. Diffuse (spread spontaneously) 5. Exert Pressure

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Pressure Force/Area

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Pressure results from? Collisions of the gas molecules with the walls of the container.

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Pressure depends on? (microscopically) # of impacts per unit time and force of each impact

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Pressure depends on? (macroscopically) # of gas molecules per unit volume And temperature

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Units of Pressure? 1 atm = 760 mm Hg = 760 torr = 101.3 kPa

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STP P = 1 atm T = 0 C = 273 K

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Molar Volume at STP The volume of 1 mole of any gas at STP = 22.4 Liters

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Temperature A measure of the avg. kinetic energy of the particles of a substance.

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4 variables needed to completely describe a gas- phase system? 1.Temperature 2.Pressure 3.Volume 4.# of moles

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Boyle’s Law For a fixed mass and temperature, the pressure-volume product is a constant.

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Boyle’s Law Volume of a gas varies inversely with the pressure.

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Boyle’s Law PV = k where k = a constant

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Boyle’s Law P 1 V 1 = P 2 V 2

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Graph of Boyle’s Law Hyperbola – it’s an inverse relationship!

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Graph of Boyle’s Law, Pressure vs. Volume

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Double the pressure Volume goes to ½ the original volume

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Triple the pressure Volume goes to 1/3 the original volume

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Halve the pressure Volume goes to 2 X the original volume

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Quadruple the pressure Volume goes to 1/4 of the original volume

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What does the graph of a direct relationship look like?

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Which temperature scale has a direct relationship to molecular velocity? Kelvin: 0 K means 0 speed.

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Absolute Temperature Scale Kelvin: 0 K means 0 speed.

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Graph of Volume vs. Kelvin Temperature It’s a direct relationship.

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Math expression of relationship between volume & Kelvin temperature V 1 /T 1 = V 2 /T 2 Charles’ Law

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Verbal expression of Charles’ Law Volume of a gas varies directly with the Kelvin temperature.

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What happens to the volume when the Kelvin temperature is doubled? The volume doubles!

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What happens to the volume when the Kelvin temperature is tripled? The volume triples!

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What happens to the volume when the Kelvin temperature is halved? The volume is halved!

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What happens to the Kelvin temperature when the volume is halved? It’s halved!

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Graph of Pressure vs. Kelvin Temperature It’s a direct relationship.

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Math expression for relationship between pressure & Kelvin temperature. P 1 /T 1 = P 2 /T 2 Gay-Lussac’s Law

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Verbal expression of relationship between pressure & Kelvin temperature. The pressure of a gas varies directly with the Kelvin temperature.

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What happens to the pressure when the Kelvin temperature is doubled? The pressure is doubled.

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What happens to the pressure when the Kelvin temperature is halved? The pressure is halved.

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What happens to the pressure when the Kelvin temperature is tripled? The pressure is tripled.

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What happens to the Kelvin temperature when the pressure is doubled? The Kelvin temperature is doubled.

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Combined Gas Law P 1 V 1 = P 2 V 2 T 1 T 2 Same pressure & volume units on both sides. Temperature must be in Kelvins.

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What is Avogadro’s Principle? Equal volumes of gases at the same temperature & pressure have equal numbers of molecules.

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These 2 boxes have the same: a)Massc) # of molecules b)Densityd) # of atoms HeN2N2

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What is Dalton’s Law of Partial Pressures? P tot = P 1 + P 2 + P 3 + P 4 + …

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At the same temperature, which of the following gases diffuses most rapidly? He Ne Ar Kr Xe Lightest is fastest!

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At the same temperature, which of the following gases diffuses most slowly? He Ne Ar Kr Xe Heaviest is slowest!

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The Gas Laws 1. A gas is composed of particles molecules or atoms – hard spheres far enough apart- ignore volume Empty space The Kinetic Theory of Gases.

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