Unit 13

Section 1 – Properties of Gases

Section 2 – Gas Laws, and Gas Stoichiometry

Section 3 – Kinetic Molecular Theory

1. To learn about atmospheric pressure and how barometers work 2. To learn the units of pressure 3. To understand how the pressure and volume of a gas are related 4. To do calculations involving Boyle’s Law 5. To learn about absolute zero 6. To understand how the volume and temperature of a gas are

related 7. To do calculations involving Charles’s Law 8. To understand how the volume and number of moles of a gas

are related 9. To do calculations involving Avogadro’s Law

Objectives Section 1 – Properties of Gases

Properties of Gases

• In organized soccer, a ball that is properly inflated will rebound faster and travel farther than a ball that is under-inflated. If the pressure is too high, the ball may burst when it is kicked. You will study variables that affect the pressure of a gas.

Compressibility

• Compressibility– Why are gases easier to compress than solids or

liquids are?

Compressibility• Compressibility is a measure of how much the volume of

matter decreases under pressure. When a person collides with an inflated airbag, the compression of the gas absorbs the energy of the impact.

Compressibility• Gases are easily compressed because of the space

between the particles in a gas.»The distance between particles in a gas is

much greater than the distance between particles in a liquid or solid.

»Under pressure, the particles in a gas are forced closer together.

Factors Affecting Gas Pressure

• Factors Affecting Gas Pressure– What are the three factors that affect gas

pressure?

Factors Affecting Gas Pressure

– The amount of gas, volume, and temperature are factors that affect gas pressure.

Factors Affecting Gas Pressure• Four variables are generally used to describe a gas. The

variables and their common units are– pressure (P) in kilopascals– volume (V) in liters– temperature (T) in kelvins– the number of moles (n).

Factors Affecting Gas Pressure

– Amount of Gas• You can use kinetic theory to predict and explain how

gases will respond to a change of conditions. If you inflate an air raft, for example, the pressure inside the raft will increase.

Factors Affecting Gas Pressure

• Collisions of particles with the inside walls of the raft result in the pressure that is exerted by the enclosed gas. Increasing the number of particles increases the number of collisions, which is why the gas pressure increases.

Factors Affecting Gas Pressure• If the gas pressure increases until it exceeds the

strength of an enclosed, rigid container, the container will burst.

Factors Affecting Gas Pressure

• Aerosol Spray Paint

Factors Affecting Gas Pressure

– Volume• You can raise the pressure exerted by a contained gas

by reducing its volume. The more a gas is compressed, the greater is the pressure that the gas exerts inside the container.

Factors Affecting Gas Pressure• When the volume of the container is halved, the

pressure the gas exerts is doubled.

Factors Affecting Gas Pressure

– Temperature• An increase in the temperature of an enclosed gas

causes an increase in its pressure. • As a gas is heated, the average kinetic energy of the

particles in the gas increases. Faster-moving particles strike the walls of their container with more energy.

Factors Affecting Gas Pressure• When the Kelvin temperature of the enclosed gas

doubles, the pressure of the enclosed gas doubles.

Pressure

• Barometer – device that measures atmospheric pressure– Invented by Evangelista Torricelli

in 1643

Measuring Pressure

Pressure

– Changing weather conditions

Atmospheric Pressure

Pressure

– Changing altitude

Atmospheric Pressure

Pressure

1 standard atmosphere = 1.000 atm = 760.0 mm Hg = 760.0 torr = 101,325 Pa

Units of Pressure

Pressure

• A manometer measures the pressure of a gas in a container.

Units of Pressure

Pressure and Volume: Boyle’s Law • Robert Boyle’s experiment

Pressure and Volume: Boyle’s Law

Pressure and Volume: Boyle’s Law • Graphing Boyle’s results

Pressure and Volume: Boyle’s Law

• This graph has the shape of half of a hyperbola with an equation PV = k

• Volume and pressure are inversely proportional. – If one increases the other decreases.

Boyle’s Law: Pressure and Volume

Pressure and Volume: Boyle’s Law

Another way of stating Boyle’s Law isP1V1 = P2V2

(constant temperature and amount of gas)

• As the temperature of the water increases, the volume of the balloon increases.

Volume and Temperature: Charles’s Law

Volume and Temperature: Charles’s Law

• Graphing data for several gases

Volume and Temperature: Charles’s Law

• It is easier to write an equation for the relationship if the lines intersect the origin of the graph. – Use absolute zero for the temperature

Volume and Temperature: Charles’s Law

• These graphs are lines with an equation V = bT (where T is in kelvins)

• Volume and temperature are directly proportional. – If one increases the other increases.

• Another way of stating Charles’s Law is V1 = V2

T1 T2

(constant pressure and amount of gas)

Volume and Moles: Avogadro’s Law

Volume and Moles: Avogadro’s Law • Volume and moles are directly proportional.

– If one increases the other increases. – V = an – constant temperature and pressure

• Another way of stating Avogadro’s Law is V1 = V2

n1 n2

(constant temperature and pressure)

1. To understand the ideal gas law and use it in calculations 2. To understand the relationship between the partial and total

pressure of a gas mixture 3. To do calculations involving Dalton’s law of partial pressures 4. To understand the molar volume of an ideal gas 5. To learn the definition of STP 6. To do stoichiometry calculations using the ideal gas law

Objectives Section 2 – Gas Laws, and Gas Stoichiometry

The Ideal Gas Law

• Boyle’s Law V = k (at constant T and n) P

• Charles’s Law V = bT (at constant P and n) • Avogadro’s Law V = an (at constant T and P)

We can combine these equations to get

The Ideal Gas Law Rearranging the equation gives the ideal gas law

PV = nRTR = 0.08206 L atm

mol K

Dalton’s Law of Partial Pressures • What happens to the pressure of a gas as we mix different gases in

the container?

Dalton’s Law of Partial Pressures

Dalton’s law of partial pressures • For a mixtures of gases in a container, the total pressure exerted is the sum of

the partial pressures of the gases present. • Ptotal = P1 + P2 + P3

• The partial pressure of oxygen must be 10.67 kPa or higher to support respiration in humans. The climber below needs an oxygen mask and a cylinder of compressed oxygen to survive.

Dalton’s Law of Partial Pressures

Dalton’s Law of Partial Pressures

• The pressure of the gas is affected by the number of particles.

• The pressure is independent of the nature of the particles.

Dalton’s Law of Partial Pressures

Two crucial things we learn from this are: • The volume of the individual particles is not very important. • The forces among the particles must not be very important.

Dalton’s Law of Partial Pressures

Collecting a gas over water

• Total pressure is the pressure of the gas + the vapor pressure of the water.

Dalton’s Law of Partial Pressures

Collecting a gas over water • How can we find the pressure of the gas

collected alone?

C. Gas Stoichiometry

Molar Volume

• Molar volume of an ideal gas at STP 22.4 L

• Standard temperature and pressure (STP)– 0oC and 1 atm

• For one mole of a gas at STP

Graham’s Law• Diffusion is the tendency of molecules to move toward

areas of lower concentration until the concentration is uniform throughout.

Graham’s Law

• Bromine vapor is diffusing upward through the air in a graduated cylinder.

Graham’s Law

• After several hours, the bromine has diffused almost to the top of the cylinder.

Graham’s Law

• During effusion, a gas escapes through a tiny hole in its container.

– Gases of lower molar mass diffuse and effuse faster than gases of higher molar mass.

Graham’s Law

– Thomas Graham’s Contribution• Graham’s law of effusion states that the rate of

effusion of a gas is inversely proportional to the square root of the gas’s molar mass. This law can also be applied to the diffusion of gases.

Graham’s Law

– Comparing Effusion Rates• A helium filled balloon will deflate sooner than an air-

filled balloon.

Graham’s Law• Helium atoms are less massive than oxygen or nitrogen

molecules. So the molecules in air move more slowly than helium atoms with the same kinetic energy.

Graham’s Law• Because the rate of effusion is related only to a

particle’s speed, Graham’s law can be written as follows for two gases, A and B.

Graham’s Law• Helium effuses (and diffuses) nearly three times faster

than nitrogen at the same temperature.

1. To understand the relationship between laws and models (theories)

2. To understand the postulates of the kinetic molecular theory 3. To understand temperature 4. To learn how the kinetic molecular theory explains the gas

laws 5. To describe the properties of real gases

Objectives Section 3 – Kinetic Molecular Theory

Laws and Models: A Review

Laws and Models: A Review • A model can never be proved absolutely true. • A model is an approximation and is destined to be modified.

The Kinetic Molecular Theory of Gases

The Implications of the Kinetic Molecular Theory

• Meaning of temperature – Kelvin temperature is directly proportional to the average kinetic energy of the gas particles

• Relationship between Pressure and Temperature – gas pressure increases as the temperature increases because the particles speed up

• Relationship between Volume and Temperature – volume of a gas increases with temperature because the particles speed up

Real Gases • Gases do not behave ideally under conditions of high pressure

and low temperature. • Why?

Real Gases

• At high pressure the volume is decreased – Molecule volumes become important – Attractions become important