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

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

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

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

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

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

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

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

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

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

Pressure Force/Area

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

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

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

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

STP P = 1 atm T = 0  C = 273 K

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

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

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

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

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

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

Boyle’s Law P 1 V 1 = P 2 V 2

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

Graph of Boyle’s Law, Pressure vs. Volume

Double the pressure Volume goes to ½ the original volume

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

Halve the pressure Volume goes to 2 X the original volume

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

What does the graph of a direct relationship look like?

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

Absolute Temperature Scale Kelvin: 0 K means 0 speed.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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

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

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

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

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