Chapter 14

The Behavior of Gases

Did you hear about the chemist who was reading a book about Helium?  He just couldn't put it down.

14.1 Properties of Gases

OBJECTIVES:Explain why gases are easier to compress than solids or liquids are

Describe the three factors that affect gas pressure

CompressibilityGases can expand to fill its

container, unlike solids or liquidsThe reverse is also true:

They are easily compressed, or squeezed into a smaller volume

Compressibility is a measure of how much the volume of matter decreases under pressure

Compressibility

This is the idea behind placing air bags in automobiles In an accident, the air compresses

more than the steering wheel or dash when you strike it

The impact forces gas particles closer together, which is possible because there is a lot of empty space between them

Compressibility At 25oC, the distance between particles is

about 10x the diameter of the particle Fig. 14.2Shows spacing betweenO2 and N2 moleculesin air

This empty space makes gases good insulators down & fur keep animals warm because the air trapped in

them prevents heat from escaping the animal’s body) How does the volume of the particles in a gas

compare to the overall volume of the gas (kinetic theory)?

Variables that describe a Gas The four variables and their common

units:

1. pressure (P) in kilopascals

2. volume (V) in Liters

3. temperature (T) in Kelvin

4. amount (n) in moles

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

1. Amount of GasWhen we inflate a balloon, we are

adding gas molecules. Increasing the number of gas

particles increases the number of collisionsthus, pressure increases

If temperature is constant, then doubling the number of particles doubles the pressure

Pressure and the number of molecules are directly related

More molecules means more collisions, and…

Fewer molecules means fewer collisions.

Gases naturally move from areas of high pressure to low pressure, because there is empty space to move into

Using Gas Pressure A practical application is

aerosol (spray) cansgas moves from higher

pressure to lower pressure

a propellant forces the product out

whipped cream, hair spray, paint

Fig. 14.5, page 416 Is the can really ever

“empty”?

2. Volume of Gas In a smaller container, the

molecules have less room to move.

The particles hit the sides of the container more often.

As volume decreases, pressure increases. (syringe example)Thus, volume and pressure are

inversely related to each other

3. Temperature of Gas Raising the temperature of a gas increases the pressure, if

the volume is held constant. (T and P are directly related) The faster moving molecules hit the walls harder, and

more frequently! Should you throw an aerosol can into a fire? When should your automobile tire pressure be checked?

14.2 The Gas Laws

OBJECTIVES:OBJECTIVES:Describe the relationships among the temperature, pressure, and volume of a gas

Use the combined gas law to solve problems

The Gas Laws are mathematicalThe gas laws will describe HOW

gases behavebehavior can be predicted by

theoryThe amount of change can be

calculated with mathematical equations (laws)

You need to know both of these: the theory, and the math

Robert Boyle(1627-1691)

• Boyle was born into an aristocratic Irish family

• Became interested in medicine and the new science of Galileo and studied chemistry. 

• A founder and an influential member of the Royal Society of London

• Wrote extensively on science, philosophy, and theology.

• Wore really cool clothes

Don’t you love my

swell scarf??

#1. Boyle’s Law - 1662Gas pressure is inversely proportional to volume, at a constant temperature (Check out this cool animation)

Pressure x Volume = a constant Equation: P1V1 = P2V2 (at a constant T)

As volume increases, pressure decreasesAn inverse relationship!

- Page 419

Jacques Charles (1746-1823)

• French Physicist• Part of a scientific

balloon flight in 1783 – one of three passengers in the second balloon ascension that carried humans

• This is how his interest in gases started

• It was a hydrogen filled balloon – good thing they were careful!

#2. Charles’ Law - 1787For a fixed mass (moles), gas volume is directly proportional to the Kelvin temperature, when pressure is constant.This extrapolates to zero volume at a temperature of zero Kelvin.

Charles’ Law Animation

VT

VT

P1

1

2

2 ( constant)

Converting Celsius to Kelvin

•Gas law problems involving temperature always require Kelvin temperature.

Kelvin = C + 273 °C = Kelvin - 273and

- Page 421

Practice Problems 9-10Practice Problems 9-10

9.9. If a sample of gas occupies 6.80 L at If a sample of gas occupies 6.80 L at 325325ooC, what will its volume be at 25C, what will its volume be at 25ooC C if the pressure does not change?if the pressure does not change?

10.10. Exactly 5.00 L of air at –50.0Exactly 5.00 L of air at –50.0ooC is C is warmed to 100.0warmed to 100.0ooC. What is the new C. What is the new volume if the pressure remains volume if the pressure remains constant?constant?

Joseph Louis Gay-Lussac (1778 – 1850)

French chemist and physicist Known for his studies on the physical properties of gases. In 1804 he made balloon ascensions to study magnetic forces and to observe the composition and temperature of the air at different altitudes.

#3. Gay-Lussac’s Law - 1802•The pressure and Kelvin temperature of a gas are directly proportional, provided that the volume remains constant.

2

2

1

1

T

P

T

P

•How does a pressure cooker affect the time needed to cook food? (Note page 422)

Practice Problems 11-12Practice Problems 11-12

11.11. A sample of nitrogen gas has a pressure of 6.58 A sample of nitrogen gas has a pressure of 6.58 kPa at 539 K. If the volume does not change, kPa at 539 K. If the volume does not change, what will the pressure be at 211 K?what will the pressure be at 211 K?

12.12. The pressure in a car tire is 198 kPa at 27The pressure in a car tire is 198 kPa at 27ooC. C. After a long drive, the pressure is 225 kPa. What After a long drive, the pressure is 225 kPa. What is the temperature of the air in the tire (assume is the temperature of the air in the tire (assume the volume is constant).the volume is constant).

#4. The Combined Gas LawThe combined gas law expresses the relationship between pressure, volume and temperature of a fixed amount of gas.

2

22

1

11

T

VP

T

VP

Practice Problems 13-14Practice Problems 13-14

13.13. A gas at 155 kPa and 25A gas at 155 kPa and 25ooC has an initial volume C has an initial volume of 1.00 L. The pressure of the gas increases to of 1.00 L. The pressure of the gas increases to 605 kPa as the temperature is raised to 125605 kPa as the temperature is raised to 125ooC. C. What is the new volume?What is the new volume?

14.14. A 5.00 L air sample has a pressure of 107 kPa at A 5.00 L air sample has a pressure of 107 kPa at – 50– 50ooC. If the temperature is raised to 102C. If the temperature is raised to 102ooC and C and the volume expands to 7.00 L, what will the new the volume expands to 7.00 L, what will the new pressure be?pressure be?

See Sample Problem 14.4, page 424 if needed

The combined gas law contains all the other gas laws!

If the temperature remains constant...

P1 V1

T1

x=

P2 V2

T2

x

Boyle’s Law

The combined gas law contains all the other gas laws!

If the pressure remains constant...

P1 V1

T1

x=

P2 V2

T2

x

Charles’s Law

The combined gas law contains all the other gas laws!

If the volume remains constant...

P1 V1

T1

x=

P2 V2

T2

x

Gay-Lussac’s Law

14.3 Ideal Gases

OBJECTIVES:OBJECTIVES:Compute the value of an

unknown using the ideal gas law

Compare and contrast real an ideal gases

5. The Ideal Gas Law #1 Equation: P x V = n x R x T Pressure times Volume equals the number

of moles (n) times the Ideal Gas Constant (R) times the Temperature in Kelvin.

R = 8.31 (L x kPa) / (mol x K) The other units must match the value of the

constant, in order to cancel out. The value of R could change, if other units of

measurement are used for the other values (namely pressure changes)

Units and the Ideal Gas Units and the Ideal Gas LawLaw

R = R = 8.318.31 L· L·kPakPa//KK·mol (when P in ·mol (when P in kPakPa)) R = R = 0.08210.0821 L· L·atmatm//KK·mol (when P in ·mol (when P in atmatm)) R = R = 62.462.4 L· L·mmHgmmHg//KK·mol (when P in ·mol (when P in mmHgmmHg))

Temperature always in Temperature always in KelvinsKelvins!!!!

We now have a new way to count moles (the amount of matter), by measuring T, P, and V. We aren’t restricted to only STP conditions:

P x V R x T

The Ideal Gas Law

n =

Practice ProblemsPractice Problems A rigid container holds 685 L of HeA rigid container holds 685 L of He(g).(g). At a At a

temperature of 621 K, the pressure of the temperature of 621 K, the pressure of the gas is 1.89 x 103 kPa. How many grams of gas is 1.89 x 103 kPa. How many grams of gas does the container hold?gas does the container hold?

A child’s lungs hold 2.20 L. How many moles A child’s lungs hold 2.20 L. How many moles of air (mostly Nof air (mostly N22 and O and O22) do the lungs hold at ) do the lungs hold at

3737ooC and a pressure of 102 kPa.C and a pressure of 102 kPa.

Ideal Gases We are going to assume the gases

behave “ideally”- in other words, they obey the Gas Laws under all conditions of temperature and pressure

Ideal gases do not really exist, but it makes the math easier and is a very close approximation.

Particles have no volume? Wrong! No attractive forces? Wrong!

Ideal Gases

There are no gases that are absolutely “ideal” however…

Real gases do behave “ideally” athigh temperature, and low pressure

Because under these conditions, the gas particles themselves are so far apart they take up a very small proportion of the gas’s volume and the IM forces are so weak that they can be ignored

Ideal Gas Law: Useful Variations

PV = nRT Replace n with mass/molar mass

1. P x V = m x R x T M

m = mass, in grams M = molar mass, in g/mol

Rearrange equation 1 Molar mass = M = m R T

P V

n (moles) = mass (g) molar mass (g/mol)

Using Density in Gas Calculations

Density is mass divided by volume

m

V so, we can use a density value to give

us two values needed in PV = nRT Volume (usually 1 L) and… n, if we know the molar mass, because we

can calculate itgrams (from D) x 1 mole

grams

D =

Using Density in Gas Calculations

What is the pressure of a sample of COWhat is the pressure of a sample of CO22

at 25at 25ooC, with a density of 2.0 g/L?C, with a density of 2.0 g/L?

PV = nRT PV = nRT P = P = V = 1 L, R = 8.31 V = 1 L, R = 8.31 LL··kPakPa//molmol··KK n = 2.0 g x 1 mole/44.0 g = 0.045 molen = 2.0 g x 1 mole/44.0 g = 0.045 mole

P = P = 0.045 mole x 8.31 x 298 K0.045 mole x 8.31 x 298 K = 113 kPa = 113 kPa1 L1 L

nRTV

Ideal Gases don’t exist, because:

1. Molecules do take up space

2. There are attractive forces between particles

- otherwise there would be no liquids

Real Gases behave like Ideal Gases...

When the molecules are far apart.

The molecules take up a very small percentage of the space We can ignore the particle

volume. True at low pressures

and/or high temperatures

Real Gases behave like Ideal Gases…

When molecules are moving fast = high temperature

Collisions are harder and faster. Molecules are not next to each other

very long. Attractive forces can’t play a role.

Real Gases do NOT Behave Real Gases do NOT Behave Ideally…Ideally…

When temperature is very lowWhen temperature is very low Because the low KE means particles Because the low KE means particles

may interact with one another for may interact with one another for longer periods of time, allowing longer periods of time, allowing weaker IM forces to have an effectweaker IM forces to have an effect

When the pressure are highWhen the pressure are high Because the particles are smashed Because the particles are smashed

together more closely and thus together more closely and thus occupy a much greater percentage of occupy a much greater percentage of the volumethe volume

14.4 Gas Mixtures & Movements

OBJECTIVES:Relate the total pressure of a

mixture of gases to the partial pressures of its component gases

Explain how the molar mass of a gas affects the rate at which it diffuses and effuses

#7 Dalton’s Law of Partial Pressures

For a mixture of gases in a container,

PTotal = P1 + P2 + P3 + . . .

•P1 represents the “partial pressure”, or the contribution by that gas.•Dalton’s Law is useful in calculating the pressure of gases collected over water – a common lab technique

Collecting a Gas over Collecting a Gas over WaterWater

A common lab technique for A common lab technique for collecting and measuring a gas collecting and measuring a gas produced by a chemical reactionproduced by a chemical reaction

The bottle is filled with water and The bottle is filled with water and inverted in a pan of waterinverted in a pan of water

As the gas is produced in a As the gas is produced in a separate container, tubing is used separate container, tubing is used to carry it to the bottle where it to carry it to the bottle where it displaces the water in the bottledisplaces the water in the bottle

When the level of the gas in the When the level of the gas in the bottle is even with the water in the bottle is even with the water in the pan, the pressure in the bottle = pan, the pressure in the bottle = atmospheric pressureatmospheric pressure

A graduated cylinder is often used A graduated cylinder is often used to collect the gas (for ease of to collect the gas (for ease of measuring the gas volume)measuring the gas volume)

Atmosphericpressure

Gas beingproduced

Dalton’s Law of Partial Pressures If the gas in containers 1, 2 & 3 are all put into the

fourth, the pressure in container 4 = the sum of the pressures in the first 3

2 atm + 1 atm + 3 atm = 6 atm

1 2 3 4

Practice ProblemsPractice Problems

Determine the total pressure of a gas Determine the total pressure of a gas mixture containing oxygen, nitrogen and mixture containing oxygen, nitrogen and helium: Phelium: POO22

= 20.0 kPa, P= 20.0 kPa, PNN22 = 46.7 kPa, P= 46.7 kPa, PHeHe

= 20.0 kPa.= 20.0 kPa.

A gas mixture containing oxygen, nitrogen A gas mixture containing oxygen, nitrogen and carbon dioxide has a total pressure of and carbon dioxide has a total pressure of 32.9 kPa. If P32.9 kPa. If POO22

= 6.6 kPa and P= 6.6 kPa and PNN22 = 23.0 = 23.0

kPa, what is the PkPa, what is the PCOCO22 ??

Diffusion and Effusion

Effusion = gas particles escaping through a tiny hole in a container

Both diffusion and effusion depend on the molar mass of the particle, which determines the speed at a given temperature (= average KE)

Diffusion = molecules moving from areas of high to areas of low concentrationIs mathematical phenomenon caused by random movements of gas particles

Diffusion

• describes the mixing of gases

• Molecules move from areas of high concentration to low concentration

• A function of probability

•Fig. 14.18, p. 435Two gases mix after the wall separating them is removed.

Effusion: a gas escapes through a tiny hole in its container

- balloons slowly lose air over time

Diffusion and effusion are explained by the next gas law: Graham’s

8. Graham’s Law

The rate of effusion and diffusion is inversely proportional to the square root of the molar masses (M) of the gases.

Relationship based on: KE = ½ mv2

At a given temperature (avg KE) larger molecules will have lower velocities

RateA MB

RateB MA

=

Graham’s Law ExplainedGraham’s Law Explained Temperature is a measure of the average KE of Temperature is a measure of the average KE of

the particles in a sample of matterthe particles in a sample of matter At a given temperature (say 25At a given temperature (say 25ooC), the molecules C), the molecules

of a lighter gas will be moving faster than of a lighter gas will be moving faster than molecules of a heavier one, so…molecules of a heavier one, so…

Faster-moving particles spread out faster!Faster-moving particles spread out faster!

Light Gas = NLight Gas = N22

(mw = 28 g/mol)(mw = 28 g/mol)Heavy Gas = COHeavy Gas = CO22

(mw = 44 g/mol)(mw = 44 g/mol)

KE = ½ mKE = ½ mvv22 KE = ½ KE = ½ mmvv22

Sample: compare rates of effusion of Helium (He) with Nitrogen (N2) – p. 436

With effusion and diffusion, the type of particle is important: Gases of lower molar mass diffuse and

effuse faster than gases of higher molar mass.

Helium effuses and diffuses 2.7 times faster than nitrogen – thus, helium escapes from a balloon quicker than air, which is ~79% N2!

Graham’s Law