Unit 8 Kinetic Theory of Gases Chapter 13-14

This tutorial is designed to help students understand scientific measurements.

Objectives for this unit appear on the next slide.

◦ Each objective is linked to its description.

◦ Select the number at the front of the slide to go directly to its description.

Throughout the tutorial, key words will be defined.

◦ Select the word to see its definition.

Objectives

4 Define kinetic theory of gases including collisions

5 Define pressure, including atmospheric pressure, vapor pressure, pressure differentials, and how a barometer works

6 Describe boiling points, including normal boiling points, using vapor pressure graphs, explaining the difference between boiling and evaporation, and how intermolecular forces and molecular weight determine evaporation rates

7 Define and use data based on the triple point phase diagram

8 Define and know the variables of the Gas Laws, including Boyle’s Law, Charles’ Law, Gay-Lussac’s Law, and the combined gas law

9 State Avogadro’s Principle

10 Use the ideal gas law to solve problems and know the variables of the ideal gas law

11 State and use Dalton’s Law of Partial Pressures

12 State and use Graham’s Law of effusion and define diffusion

4 The Kinetic Theory

Particles at the molecular level have been

described previously.

It has been stated that these particles are

in a constant state of motion and are

attracted to each other through

intermolecular forces.

The kinetic theory as described on the

next slide is specific to gases.

Kinetic Theory of Gases

There are five parts to the kinetic theory

of gases.

1. Gases will fill the entire volume allowed.

• This means that is 10 oxygen molecules are

released in a classroom, they will arrange

themselves equally throughout that space. If

the same 10 were released in a gymnasium,

they will do the same.

Kinetic Theory of Gases

2. Gases can be compressed.

The volume a gas holds can be

increased or decreased.

3. The motion of gases is random.

Gas molecules will travel in straight

lines until they run into an object.

4. Gas molecules have elastic collision.

When gas molecules collide, there is

no loss in kinetic energy.

Kinetic Theory of Gases

5. The kinetic energy of a gas molecule is

measured by temperature.

As the temperature increases, gas

molecules move faster, and as the

temperature decreases, gas molecules

move slower.

Kinetic Theory of Gases

A quick recap:

1. Gases fill the entire volume allowed.

2. Gases can be compressed.

3. The motion of a gas is random.

4. Gases have elastic collisions.

5. The kinetic energy of gases is measured

with temperature.

The link below is for a simulator that demonstrates some of these ideas.

http://phet.colorado.edu/en/simulation/gas-properties

5 Pressure

Pressure is a measure of force per unit surface area.

◦ For instance, assume you are standing. You are exerting a force on the floor. The surface area is the size of both of your feet. If you stand on only one foot, the force would be the same but the surface area is halved so the pressure doubles.

When referring to gases, pressure is the measure of the force exerted when two gas particles collide.

Air Pressure and Vapor Pressure

The molecules that make of the air

around you are constantly colliding with

each other and the objects in the room

(including you).

These collisions make up air pressure.

Vapor pressure is the pressure exerted by

the air on a liquid.

Measuring pressure

Atmospheric pressure is determined using an instrument known as a barometer.

The barometer is filled with mercury because of its density.

As atmospheric pressure pushes down on the mercury, it forces the mercury up the column.

Atmospheric pressure is measured by the distance the mercury is displaced.

Mercury

760

mm

Atmospheric

Pressure

Pressure

The barometer was invented by a

scientist by the name of Torricelli.

◦ Pressure is often given with units of mm Hg

but the torr is used as well.

To make the numbers easier to work

with, atmospheric pressure was set equal

to 1 atm (atmosphere)

Units of Pressure

There are several units for pressure and all are used.

Therefore the following values are equal to atmospheric pressure:

1 atm = 101.325 kPa (kiloPascals)

101,325 Pa (Pascals)

760 mm Hg

760 torr

6 Temperature vs. Heat

The last part of the kinetic theory

mentioned temperature.

Temperature is often confused with heat but

the two are quite different.

Temperature is a measure of the average

kinetic energy of molecules.

Heat is the measure of the total kinetic energy

of molecules.

Temperature vs. Heat

All molecules are in a state of motion.

The motion is measured by kinetic energy.

However, not all molecules are moving at

the same speed and thus do not have the

same kinetic energy.

The average is taken to determine the

speed of the majority of the molecules.

The total is determined for a purpose

that will be discussed in Unit 9.

Temperature

The average kinetic energy is reported in

three different scales.

◦ Fahrenheit (°F)

◦ Celsius (°C)

◦ Kelvin (K)

Each scale is used by certain individuals

about the world.

The scientific community prefers Celsius

or Kelvin.

Temperature

The Celsius scale was designed to have the

boiling point of water be 100°C while the

freezing point of water would be 0°C.

The Kelvin scale was designed using the same

increments as Celsius but instead placed zero at

absolute zero.

Temperature

It is important to be able to convert from

one scale to another so the following

equations were determined:

◦ °F =°C9

5+ 32

◦ °C=(°F − 32) 𝑥 5

9

◦ K = 273.15 + °C

Boiling Points

Boiling is the process of taking a liquid to

the gaseous state.

This process occurs by adding heat to the

liquid.

However, there are additional factors that

can affect the boiling point.

◦ These include intermolecular forces and

vapor pressure.

Intermolecular Forces

When heat is added to a liquid, the particles in that liquid gain kinetic energy.

Gaining kinetic energy means that they are moving faster.

It is the intermolecular forces that hold the molecules close together.

With enough kinetic energy, a molecule can overcome the intermolecular forces and break free.

The stronger the intermolecular force, the more kinetic energy will be required to break free.

Boiling versus Evaporation

It also depends on where the heat is

added as to how easy it will be to

overcome the intermolecular force.

Both boiling and evaporation are ways to

bring a liquid to a gas but each can occur

at different temperatures.

Evaporation

When considering evaporation, the heat comes from a source above the liquid.

This means the particles on the top of the liquid gain kinetic energy (shown in red)

Once they gain enough energy, they can break free of the intermolecular forces.

Notice, it is only the top that increases kinetic energy while the rest of the molecules remain the same.

This is why the temperature of the liquid does not have to greatly increase during evaporation.

Heat

Boiling In comparison to evaporation, boiling adds heat to the bottom of the liquid.

Since the bottom particles have to work their way to the top, it is more difficult to overcome the intermolecular forces.

In order to overcome the intermolecular forces, all particles will need to gain kinetic energy.

Because all particles must gain energy, the temperature increases.

This is also why boiling proceeds faster than evaporation.

Vapor Pressure

The other factor effecting the boiling point is vapor pressure.

Vapor pressure is the pressure from the atmosphere above a liquid.

The gas particles above a liquid can prevent molecules that have enough energy to break free from the intermolecular forces from becoming a gas.

The image on the next slide illustrates this idea.

Vapor Pressure

Gas Particles

The particle escapes

but transfers its

energy to a gas

particle.

The particle falls

back to the liquid.

Vapor Pressure

If there were less particles above the

liquid, it would be easier to boil.

The boiling point at one atmosphere is

considered to be the normal boiling

point.

A vapor pressure diagram can help

determine the boiling point.

Vapor Pressure Diagrams

Vapor pressure diagrams show the relationship between vapor pressure and the boiling point.

The red line below represents the normal boiling point.

Notice, it is easier to boiling if there is a smaller vapor pressure. ◦ This liquid would boil at 62°C if the pressure of 0.18 atm. The

normal boiling point is 101°C at 1 atm.

0.00

0.20

0.40

0.60

0.80

1.00

0 20 40 60 80 100 120

Pre

ssu

re (

atm

)

Temperature (C)

Vapor Pressure Diagram

Standard Temperature and Pressure

(STP) For the purposes of scientific consistency,

a select temperature and pressure were

selected.

This way, all experiments could be

repeated at the same atmospheric

conditions.

STP is 1 atm of pressure and 0°C.

7 Triple Point Diagrams

The vapor pressure diagram shows a portion of a larger diagram known as the triple point diagram.

This diagram represents the three types of matter and their relationships to pressure and temperature.

The following slide shows a possible triple point diagram.

◦ There are six phase changes that occur as you cross each line form one phase to the next.

◦ The triple point is denoted with a blue dot.

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 20 40 60 80 100 120

Pre

ssu

re (

atm

)

Temperature (C)

Triple Point Diagram

Liquid

Gas

Solid

Freezing

Condensation

Vaporization

Triple Pt.

Critical Point

Melting

Sublimation

Deposition

Triple Point Diagrams

The triple point indicates a point where

all three phases are present at the same

time.

◦ It only occurs at one temperature and

pressure for each substance.

The critical point is also marked. The

critical point indicates where the kinetic

theory does not accurately describe the

properties of this chemical.

8 Gas Laws

Temperature, pressure, and volume have a

distinct affect on gases.

It was determined that these three

variables have distinct relationships.

These relationships are known as the gas

laws.

Boyle’s Law

Boyle’s Law describes the relationship

between pressure and volume.

The relationship is inverse which means as

one increases, the

other decreases.

The equation for

Boyle’s Law is:

P1V1=P2V2

0

0.5

1

0 2 4 6 8 10 12

Pre

ssu

re (

atm

)

Volume (L)

Boyle's Law

Charles’ Law

Charles’ Law describes the relationship

between temperature and volume.

The relationship is direct which means as

one increases, the

other increases.

The equation for

Charles’ Law is:

V1÷T1=V2÷T2

0

2

4

6

8

10

12

14

250 270 290 310 330 350

Vo

lum

e (

L)

Temperature (K)

Charles' Law

Gay-Lussac’s Law

Gay-Lussac’s Law describes the relationship

between pressure and temperature.

The relationship is direct which means as

one increases, the

other increases.

The equation for

Gay-Lussac’s Law is:

P1÷T1=P2÷T2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

250 270 290 310 330 350

Pre

ssu

re (

atm

)

Temperature (K)

Gay-Lussac's Law

Gas Laws

The three gas laws described require

certain units to be used.

◦ Volume = liters

◦ Temperature = Kelvin

◦ Pressure = kPa or atm

The three can also be combined.

Combined Gas Law

As that all three variables can be difficult

to hold constant, the three gas laws can

be combined to create the combined gas

law.

𝑃1𝑉1

𝑇1=

𝑃2𝑉2

𝑇2

Gas Law Recap

Gas Law Boyle’s Charles’ Gay-

Lussac’s Combined

Equation P1V1=P2V2 𝑉1

𝑇1=

𝑉2

𝑇2

𝑃1

𝑇1=

𝑃2

𝑇2

𝑃1𝑉1

𝑇1=

𝑃2𝑉2

𝑇2

Relationship Inverse Direct Direct

Constant Temperature Pressure Volume Nothing

9 Avogadro’s Principle

Up to this point, we have examined gases under the assumption that we always held the same number of moles in the container.

This is not always the case.

Just as a relationship was determined between pressure, volume, and temperature, a relationship was determined between the number of moles and volume.

Avogadro’s Principle

According to Avogradro’s Principle, if the

number of moles increase, the volume

also must increase assuming constant

temperature and pressure.

𝑉1

𝑛1=

𝑉2

𝑛2

n = moles

Avogadro’s Principle

Using this principle, it was determined

that at STP (standard temperature and

pressure), one mole of a gas would always

take up the same volume.

At 0°C and 1 atm, 1 mole will take up 22.4

liters.

10 Ideal Gas Law

With the inclusion of the mole into the

relationships of gases, it could be added

to the combined gas law as well.

𝑃𝑉

𝑇= 𝑘

𝑉

𝑛= 𝑘

𝑃𝑉

𝑛𝑇= 𝑘

K represents a constant

Ideal Gas Law

Upon further analysis, it was determined that the constant could be calculated and was the same for each container.

Assume STP conditions:

◦ 1 Mole 𝑃𝑉

𝑛𝑇= 𝑘

◦ 22.4 Liters

◦ 273.15 K 1 𝑎𝑡𝑚 𝑥 22.4 𝐿

1 𝑚𝑜𝑙𝑒 𝑥 273.15 𝐾= 𝑘

◦ 1 atm

k = 0.0821 𝑎𝑡𝑚 𝑥 𝐿

𝑚𝑜𝑙𝑒 𝑥 𝐾

Ideal Gas Law

The constant was changed to R and

requires specific units to be used.

There are two commonly used values for

R: 0.0821 𝑎𝑡𝑚 𝑥 𝐿

𝑚𝑜𝑙𝑒 𝑥 𝐾 or 8.314

𝑘𝑃𝑎 𝑥 𝐿

𝑚𝑜𝑙𝑒 𝑥 𝐾

Required Units:

Volume: Liters Amount: moles

Temperature: Kelvin Pressure: atm or kPa

Ideal Gas Law

The equation for the Ideal Gas Law is:

PV=nRT

The value of R is chosen based on the units

on the pressure.

11 Dalton’s Law of Partial Pressures

When gases were discussed in Unit 10, it

was mentioned that pressure was

measured with the collisions gas particles

underwent.

The total pressure is a sum of all of those

collisions.

Therefore, Dalton’s Law states that the

pressure of each gas can be added to

determine the total pressure.

Dalton’s Law of Partial Pressures

Though Dalton’s Law seems fairly basic, it

is extremely useful when collecting a gas.

When most experiments are performed,

the gases produced are allowed to

escape.

However, if it is the gas that needs to be

analyzed, the gas most be collected.

The collection of this gas is typically done

over water.

Collecting a Gas over Water

Collecting a gas over water requires a sealed container with a tube into a tank of water.

In the tank of water, an inverted tube is filled with water.

As the reaction progresses, the gas produced follows the tube into the water chamber and up the inverted tube.

Dalton’s Law

Dalton’s Law comes into play because a

small amount of water with change to a

gas in the container.

Therefore, the gas collected and water

vapor combine to give the pressure.

That pressure is equal to the atmospheric

pressure outside of the tube.

Therefore, the following equation applies:

Patmosphere = Pgas + Pwater

12 Effusion and Diffusion

Graham’s Law of Effusion states that at the same temperature, a heavier molecule will move slower than a lighter molecule.

◦ Recall that temperature is the average kinetic energy of a molecule.

◦ Kinetic energy is calculated by taking the mass times the velocity squared (KE=mv2)

◦ The relationship between speed and mass is inverse.

Diffusion is the dispersion of molecules from areas of high concentration to areas of low concentration.

This concludes the tutorial on

measurements.

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Definitions-Select the word to return to the tutorial

Absolute zero – the temperature at which

molecules no longer move.

Intermolecular Forces – forces that hold

molecules together. These

include hydrogen bonding,

dipole forces, and London

forces