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Chapter 14Gases

Pioneer High School

Ms. Julia V. Bermudez

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OBJECTIVES:

• Explain pressure and volume are related

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OBJECTIVES:

• To calculate the volume and pressure of a sample of gas before and after a change.

Boyle’s Law In 1662, Robert Boyle

first confirmed the relationship between the pressure and the volume of a gas using a vacuum pump.

Boyle’s Law The gas

particles in the cylinder apply pressure on the balloon.

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Boyle’s Law As the gas

particles in the cylinder are removed the pressure on the balloon decreases.

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Boyle’s Law ….And thus

the volume of the balloon Increases!

Boyle’s Law Boyle’s Law can be considered an

inverse law. Why?

• As one variable increases the other variable will decrease

• And vice versa

Boyle’s Law As the volume gets

smaller the molecules have less room to move.

The molecules will hit the sides more often, causing more pressure

As Volume goes Pressure goes

Boyle’s Law In a larger container, molecules have

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

often.

As Volume goes Pressure goes

Boyle’s LawIn order for this law to work:

Must be @ a constant temperature

This means the temperature of the gas does not change!

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ExamplesUsing Boyle’s Law we can predict the change in pressure or volume of a gas at constant temperature.

Formula to use:

P1 V1 = P2 V2

P1 = Pressure (start) V1 = Volume (start)

P2 = Pressure (end) V2 = Volume (end)

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?

Example #1

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Example #2 A sample of He gas in a balloon is

compressed from 4.0 L to 2.5 L at a constant T. If the pressure of the gas at 4.0 L is 210 kPa, what will the pressure be at 2.5 L?

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Practice Problems

Pg. 422 # 1-4

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Gases

OBJECTIVES:

• Understand the Kelvin scale of temperature

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Gases

OBJECTIVES:

• Convert values of temperature between Celsius and Kelvin.

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Kelvin Scale What causes tires to

appear low on air on a cold day?

The relationship between temperature and volume can help explain this anomaly.

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Kelvin Scale

In 1787 Jacques Charles studied the relationship between volume and temperature.

He noticed as temperature increases for a gas so does the volume when pressure was held constant.

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Kelvin Scale

• Gas particles move inside a balloon and collide with the sides creating the volume of the balloon.

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Kelvin Scale• As the temperature increases the kinetic energy of the gas also increase.

•The gas molecules collide with the sides more frequently and with greater force.

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Kelvin Scale

• …..Thus the volume of the balloon will also increase.

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Kelvin Scale The graph of Volume vs. Temp. is a

straight line. Charles predicted the temp. at which

volume is 0 L.

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Kelvin Scale He extrapolated (continued) the line and

described the theoretical temperature at which matter stops moving.

This is called Absolute Zero…

(- 273 oC or 0 K)

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Kelvin Scale You can convert between different

temperatures by using a simple equation:

K = 273 + oCoC = K - 273

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Kelvin ScaleConvert the following temperatures:

1. 25 oC = ______ K

2. 310 K = ______oC

3. 457 K = ______oC

4. 100 oC = ______ K

5. 212 oC = ______ K

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HOMEWORK

Pg 448 # 88 a&c, 90, 107 a&c

CLASSWORK Prelab for Absolute Zero

• Title• Purpose• Procedure (in your own words)• Data Table

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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

Examples What is the temperature of a gas

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

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

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

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?

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

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.

Examples 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?

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?

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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Section 12.4Ideal Gas

OBJECTIVES:

• Calculate the amount of gas at any specific conditions of: a) pressure, b) volume, and c) temperature.

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Section 12.4Ideal 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 #1 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)

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 =

Examples How many moles of air are there

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

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

Samples 12-5, 12-6 on pages 342 and 343

6. Ideal Gas Law #2 P x V = m x R x T

M Allows LOTS of calculations! m = mass, in grams M = molar mass, in g/mol

Molar mass = m R T P V

Density Density is mass divided by volume

m

V

so,

m M P

V R T

D =

D = =

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 12.5Gas Molecules:

Mixtures and Movements

OBJECTIVES:

• State a) Avogadro’s hypothesis, b) Dalton’s law, and c) Graham’s law.

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Section 12.5Gas Molecules:

Mixtures and Movements

OBJECTIVES:

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

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Section 12.5Gas Molecules:

Mixtures and Movements

OBJECTIVES:

• Calculate a) partial pressures, and b) rates of effusion.

Avogadro’s Hypothesis Avogadro’s Hypothesis: Equal

volumes of gases at the same temp. and pressure contain equal numbers of particles.

• Saying that two rooms of the same size could be filled with the same number of objects, whether they were marbles or baseballs.

7. 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

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?

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?

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.

8. Graham’s Law

The rate of effusion and diffusion is inversely proportional to the square root of the molar mass of the molecules.

Kinetic energy = 1/2 mv2

m is the mass v is the velocity.

RateA MassB

RateB MassA

=

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