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Chapter 14 The Behavior of Gases

Chemistry Honors

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Beans beans the royal fruit the more you eat the more you toot

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Section 14.1The Properties of Gases

OBJECTIVES:

• Describe the properties of gas particles.

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Section 14.1The Properties of Gases

OBJECTIVES:

• Explain how the kinetic energy of gas particles relates to Kelvin temperature.

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THREE STATES OF THREE STATES OF MATTERMATTER

THREE STATES OF THREE STATES OF MATTERMATTER

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Kinetic Theory Revisited1. Gases consist of hard, spherical

particles (usually molecules or atoms)

2. Small- so the individual volume is considered to be insignificant

3. Large empty space between them

4. Easily compressed and expanded

5. No attractive or repulsive forces

6. Move rapidly in constant motion

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Kinetic Theory Revisited Recall: that the average kinetic

energy of a collection of gas particles is directly proportional to the Kelvin temperature of the gas.

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We can measure gases in 4 ways:

Measurement UnitAmount of gas (n) Moles

Volume (V) Liters (L)

Temperature (T) K

Pressure (P) atm, kPa, Torr, mm Hg,

1. Amount of Gas When we inflate a balloon, we are

adding gas molecules. Increasing the number of gas

particles increases the number of collisions

• thus, the pressure increases If temp. is constant- doubling the

number of particles doubles pressure

Pressure and the number of molecules are directly related

More molecules means more collisions.

Fewer molecules means fewer collisions.

Gases naturally move from areas of high pressure to low pressure because there is empty space to move in too- spray can is example.

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Common use? Aerosol (spray) cans

• gas moves from higher pressure to lower pressure

• a propellant forces the product out

• whipped cream, hair spray, paint Fig. 14.5, p. 416

2. Volume of Gas In a smaller container, molecules

have less room to move. Hit the sides of the container

more often. As volume decreases, pressure

increases. (think of a syringe)

3. Temperature of Gas Raising the temperature of a gas

increases the pressure, if the volume is held constant.

The molecules hit the walls harder, and more frequently!

The only way to increase the volume at constant pressure is to increase the temperature.

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Result? Figure 14.7, p. 417 Think of tire pressure

• measured when “cold”

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Pressure (P)

The force per unit area on a

surface

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Pressure is caused by gas particles

slamming into the container’s walls.

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Section 14.2The Gas Laws

OBJECTIVES:

• State: a) Boyle’s Law, b) Charles’s Law, c) Gay-Lussac’s Law, and d) the Combined Gas Law.

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Robert Boyle (1627-1691)"From a knowledge of His work, we shall know Him"One of the founders of the Royal Society in 1660, Robert

Boyle was sometimes called 'the son of the Earl of Cork and the father of chemistry.' Although he spent most of his life in Britain, Robert was born at Lismore Castle in Co. Waterford

Ireland, the youngest of fourteen children.Robert was born into a world in which the theories of

Aristotle and the beliefs of alchemy were paramount. He made many great contributions in both physics and

chemistry, and we particularly remember him when we learn Boyle's Law, which state that at constant temperature, the volume of a gas is inversely proportional to the pressure

applied to it.

(V x p = constant)

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Section 14.2The Gas Laws

OBJECTIVES:

• Apply the gas laws to problems involving: a) the temperature, b) the volume, and c) the pressure of a contained gas.

The Gas Laws These will describe HOW gases

behave. Can be predicted by the theory. Amount of change can be

calculated with mathematical equations.

1. Boyle’s Law

At a constant temperature, gas pressure and volume are inversely related.

• As one goes up the other goes down

Formula to use: P1 x V1= P2 x V2

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Boyle’s LawBoyle’s LawBoyle’s LawBoyle’s LawA bicycle pump is a A bicycle pump is a

good example of good example of Boyle’s law. Boyle’s law.

As the volume of the As the volume of the air trapped in the air trapped in the pump is reduced, pump is reduced, its pressure goes its pressure goes up, and air is up, and air is forced into the tire.forced into the tire.

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A gas occupies a volume of 0.458 L at a pressure of 1.01 kPa and

temperature of 295 Kelvin. Although the temperature stays the same, the volume is increased to 0.477 L. What is the new

pressure?

0.970 kPa

A balloon is filled with 25 L of air at 1.0 atm pressure. If the pressure is changed to 1.5 atm what is the new volume?

Examples

P1V1 = P2V2

1.0 atm x 25 L = 1.5 atm x V2

1 atm x 25 L = 16.7 L 1.5 atm

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A balloon is filled with 73 L of air at 1.3 atm pressure. What pressure is needed to change the volume to 43 L?

P1V1 = P2V2

1.3 atm x 73 L = P2 x 43 L

1.3 atm x 73 L = 2.21 atm 43 L

2. Charles’s Law

The volume of a gas is directly proportional to the Kelvin temperature, if the pressure is held constant.

Formula to use: V1/T1 = V2/T2 If one temperature goes up, the If one temperature goes up, the

volume goes up!volume goes up!

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Charles’s original balloonCharles’s original balloon

Modern long-distance balloonModern long-distance balloon

Warm air is less dense than cooler air

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What will be the volume of a gas sample at 309 K if its volume at 215 K is 3.42 L?

Assume that pressure is constant.

4.92 L

Examples What is the temperature of a gas expanded

from 2.5 L at 25 ºC to 4.1L at constant pressure?

V1 = V2 2.5 L = 4.1 L

T1 T2 298 K T2

Temperature must be in K

T2 = 488.7 K or 215.7 °C

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What is the final volume of a gas that starts at 8.3 L and 17 ºC, and is heated to 96 ºC?

V2 = 10.6 L

3. Gay-Lussac’s Law

The temperature and the pressure of a gas are directly related, at constant volume.

Formula to use: P1/T1 = P2/T2

If one temperature goes up, If one temperature goes up, the pressure goes up!the pressure goes up!

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Gay-Lussac’s Law: Pressure and TemperatureGay-Lussac’s Law: Pressure and Temperature When a gas is heated at constant volume, the When a gas is heated at constant volume, the

pressure increases.pressure increases.

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A balloon with a pressure of 0.900 atm is heated from

105 K to 155 K. If volume is held constant, what is the new pressure?

1.33 atm

Examples What is the pressure inside a 0.250 L can

of deodorant that starts at 25 ºC and 1.2 atm if the temperature is raised to 100 ºC?

P2 = 1.5 atm

At what temperature will the can be above have a pressure of 2.2 atm?

T2 = 546.3 K

4. Combined Gas Law The Combined Gas Law deals with

the situation where only the number of molecules stays constant.

Formula: (P1 x V1)/T1= (P2 x V2)/T2

This lets us figure out one thing when two of the others change.

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Combined Gas Law The good news is that you

don’t have to remember all three gas laws! Since they are all related to each other, we can combine them into a single equation. BE SURE YOU KNOW THIS EQUATION!

No, it’s not related to R2D2

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Combined Gas Law

If you should only need one of the other gas laws, you can cover up the item that is constant and you will get that gas law!

=

P1 V1

T1

P2 V2

T2

Boyle’s Law

Charles’ Law

Gay-Lussac’s Law

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Combined Gas Law ProblemCombined Gas Law Problem

A sample of helium gas has a volume of 0.180 L, a pressure of 0.800 atm and a temperature of 29°C. What is the new temperature(K) of the gas at a volume of .090 L and a pressure of 3.20 atm?

Set up Data Table

P1 = 0.800 atm V1 = .180 L T1 = 302 K

P2 = 3.20 atm V2= .090 L T2 = ??

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CalculationCalculationP1 = 0.800 atm V1 = .180 L T1 = 302 KP2 = 3.20 atm V2= .090 L T2 = ??

P1 V1 P2 V2

= P1 V1 T2 = P2 V2 T1

T1 T2

T2 = P2 V2 T1

P1 V1

T2 = 3.20 atm x .090 L x 302 K

0.800 atm x .180 L

= 604 K

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The gas in a 0.010 L container has a pressure of 1.39 atmospheres. When the gas is transferred to a 0.017 L container

at the same temperature, what is the pressure of the gas?

0.818 atm

Example A 15 L cylinder of gas at 4.8 atm

pressure and 25 ºC is heated to 75 ºC and compressed to 17 atm. What is the new volume?

V2 = 4.9 L

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If 6.2 L of gas at 723 mm Hg and 21 ºC is compressed to 2.2 L at 4117 mm Hg, what is the final temperature of the gas?

T2 = 594 K or 321 °C

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

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Tips for Gas Law ProblemsTips for Gas Law Problems 1) Determine which gas law you need1) Determine which gas law you need

• Pressure and volume = Boyle’sPressure and volume = Boyle’s• Temperature and volume = Charles’Temperature and volume = Charles’• Temperature and Pressure = Gay-Lussac’sTemperature and Pressure = Gay-Lussac’s• Temperature, pressure, and volume = CombinedTemperature, pressure, and volume = Combined

2) Identify your variables. Be sure you put the proper numbers 2) Identify your variables. Be sure you put the proper numbers togethertogether

3) Change all variables into the correct units3) Change all variables into the correct units• Temperature must be KTemperature must be K• Pressure units must matchPressure units must match• Volume units must matchVolume units must match

4) Put numbers into the gas law equation and solve4) Put numbers into the gas law equation and solve

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And now, we pause for this commercial message from STP

OK, so it’s really not THIS kind of STP…

STP in chemistry stands for Standard Temperature and

Pressure

Standard Pressure = 1 atm (or an equivalent)

Standard Temperature = 0 deg

C (273 K)

STP allows us to compare amounts of

gases between different pressures and temperatures

STP allows us to compare amounts of

gases between different pressures and temperatures

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STPStandard

Temperature and Pressure:

00C and 1 atmC and 1 atm

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Section 14.3Ideal Gases

OBJECTIVES:

• Distinguish between ideal and real gases.

Ideal Gases We are going to assume the gases

behave “ideally”- obeys the Gas Laws under all temp. and pres.

An ideal gas does not really exist, but it makes the math easier and is a close approximation.

Particles have no volume. No attractive forces.

Ideal Gases There are no gases for which

this is true; however, Real gases behave this way at

high temperature and low pressure.

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

number of moles times the Ideal Gas Constant (R) times the temperature in Kelvin.

This time R does not depend on anything, it is really constant

R = 8.31 (L x kPa) / (mol x K) or 0.0821 (L x atm) / (mol x K)

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Ideal Gas LawThe mother of all gas

laws. It includes everything!

PV = nRT

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P = pressure (atm)V = volume (L)n = moles (mol)

R = Gas ConstantT = Temperature

(Kelvin)

PV = nRT

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Using PV = nRTUsing PV = nRTP = Pressure V = VolumeP = Pressure V = Volume

T = Temperature N = number of molesT = Temperature N = number of moles

R is a constant, called theR is a constant, called the Ideal Gas Ideal Gas Constant. Depending what your pressure Constant. Depending what your pressure unit is determines which of the 3 gas unit is determines which of the 3 gas constants you need to use.constants you need to use.

R = 8.314 R = .0821R = 8.314 R = .0821

R = 62.4 R = 62.4

L • kPa Mol • K

L • kPa Mol • K

L • mm Hg

Mol • K

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

P x V

R x T

The Ideal Gas Law

n =

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If the pressure exerted by a gas at 0.00°C in a volume of 0.0010 L is

5.00 atm, how many moles of gas are present?

2.2 x 10-4 moles

Examples How many moles of air are there in

a 2.0 L bottle at 19 ºC and 747 mm Hg?

n = P x V

R x T

n = 747 mmHg x 2 L = .0820 moles air 62.4 L mmHg x 292 K mole K

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What is the pressure exerted by 1.8 g of H2 gas in a 4.3 L balloon at 27 ºC?

P = 5.10

You have to get moles from the 1.8 g of H2 by multiplying by the molar mass of H2

Ideal Gases don’t exist Molecules do take up space There are attractive forces otherwise there would be no

liquids formed

Real Gases behave like Ideal Gases...

When the molecules are far apart

The molecules do not take up as big a percentage of the space

We can ignore their volume.

This is at low pressure

Real Gases behave like Ideal gases when...

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.

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Section 14.4Gas Molecules:

Mixtures and Movements

OBJECTIVES:

• Calculate: a) moles, b) masses, and c) volumes of gases at STP.

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Avagadro’s Hypothesis

Equal volumes of gas (at same T and P) contain the same

amount of particles

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1 mole = 6.02 x 1023 particles

Only works at same T and P

1 mole = 22.4 L

6. Dalton’s Law of Partial Pressures

The total pressure inside a container is equal to the partial pressure due to each gas.

The partial pressure is the contribution by that gas.

PTotal = P1 + P2 + P3

We can find out the pressure in the fourth container.

By adding up the pressure in the first 3.2 atm

+ 1 atm

+ 3 atm

= 6 atm

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A balloon contains O2 and N2 gas. If the partial pressure of the O2 is 0.75 atm and the partial pressure of the

N2 is 0.55 atm, what is the total pressure of the balloon?

1.30 atm

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Table of Vapor Pressures for Water

1.40 kPa

3.56 kPa

5.65 kPa

31.2 kPa

Examples What is the total pressure in a balloon filled

with air if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg?

Ptotal = 170 mm Hg + 620 mm Hg

Ptotal = 790 mm Hg

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In a second balloon the total pressure is 1.3 atm. What is the pressure of oxygen if the pressure of nitrogen is 720 mm Hg?

First: Convert 720 mm Hg to atm

720 mm Hg x 1 atm = .95 atm 760 mm Hg

PTotal = 1.3 - .95

PTotal = .35 atm

Diffusion

Effusion: Gas escaping through a tiny hole in a container.

Depends on the speed of the molecule.

Molecules moving from areas of high concentration to low concentration.

Example: perfume molecules spreading across the room.

Heavier molecules move slower at the same temp. (by Square root)

Heavier molecules effuse and diffuse slower

Helium effuses and diffuses faster than air - escapes from balloon.

Graham’s Law

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Graham’s Law

Gases with smaller masses move faster than gases with large masses

(like a kid in Walmart)

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H2 moves faster than N2. Which of the following gases

moves the fastest?O2

CO2

NH3

Cl2

I2

H2O

Ar

N2

Br2