Prentice Hall © 2003 Chapter 10

Prentice Hall © 2003 Chapter 10

Look here tomorrow after Period 5 for a link for your class work from the Gas Laws Packet. These problems are good practice, but spend more time looking at the problems listed in the notes as well as the problem set problems to prepare for your test

Prentice Hall © 2003 Chapter 10

Other information:• Solve the questions listed in today’s notes after notes are

completed.• DO THE PROBLEM SET WITHOUT LOOKING AT

THE ANSWERS 1st • There will be no board points for Chapter 10; There

will be a bonus on the exam.• Read the lab hand out by class time on Thursday.• There will be time to ask/answer questions on Thursday

while we are waiting for the lab to be completed.

Prentice Hall © 2003 Chapter 10

• Theory of moving molecules• Assumptions:

– Molecules in constant random motion– Volume of individual molecules is negligible– Intermolecular forces are negligible– Energy can be transferred between molecules, but total

KE is constant at constant T– Average KE of molecules is proportional to T

10.7: Kinetic Molecular Theory

Prentice Hall © 2003 Chapter 10

• Amount of pressure depends on frequency and magnitude of molecular collisions

• Gas molecules have an average kinetic energy– Each molecule has a different

energy

• Average KE increases with increasing T

Prentice Hall © 2003 Chapter 10

• As kinetic energy increases, the velocity of the gas molecules increases

• Root mean square speed, u, is the speed of a gas molecule having average kinetic energy

• Average kinetic energy, , is related to root mean square speed:

221mu

Prentice Hall © 2003 Chapter 10

• Kinetic Energy has a set value at a specified temperature

• Mathematically:

10.8: Molecular Effusion and Diffusion

MRT

u3

Molar mass in the denominator, so an increase in molar mass will decrease the u of the molecules

molKs

mkg

2

2

R = 8.314

This value of R

allows u to have velocity units

Prentice Hall © 2003 Chapter 10

Graham’s Law of Effusion

• Effusion is the escape of a gas through a tiny hole (a balloon will deflate over time due to effusion)

Prentice Hall © 2003 Chapter 10

• Consider two gases with molar masses M1 and M2.

The relative rate of effusion is given by:

• Only those molecules that hit the small hole will escape through it

• The higher the root mean square speed (rms), the more likely a gas molecule will hit the hole

1

2

2

1MM

r

rGraham’s Law

Prentice Hall © 2003 Chapter 10

Diffusion and Mean Free Path • Diffusion of a gas is the spread of the gas through space

• Diffusion is faster for light gas molecules

• Diffusion is significantly slower than rms speed• consider someone opening a perfume bottle: it takes

a while to detect the odor, but rms speed at 25C is about 1150 mi/hr

• Diffusion is slowed by gas molecules colliding with each other

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• Average distance traveled by a gas molecule between collisions is called mean free path• Varies with pressure

• At sea level, mean free path is about 6 10-6 cm

Prentice Hall © 2003 Chapter 10

• Sample Problems # 67, 69

Prentice Hall © 2003 Chapter 10

• From the ideal gas equation, we have

• For 1 mol of gas, PV/RT = 1 for all pressures• In a real gas, PV/RT varies from 1 significantly• The higher the pressure the greater the deviation from

ideal behavior

10.9: Real Gases: Deviations from Ideal

Behavior

nRTPV

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• As the gas molecules get closer together, the intermolecular distance decreases

• attractive forces take over (real gas)

Text, P. 394

Prentice Hall © 2003 Chapter 10

• As temperature increases, the gas molecules move faster and further apart• more energy is available to

break intermolecular forces

• Therefore, the higher the temperature, the more ideal the gas

Text, P. 394

Prentice Hall © 2003 Chapter 10

• The assumptions in kinetic molecular theory show where ideal gas behavior breaks down:– the molecules of a gas have finite volume– molecules of a gas do attract each other

Prentice Hall © 2003 Chapter 10

The van der Waals Equation• Two terms are added to the ideal gas equation:

• correct for volume of molecules• correct for intermolecular attractions

• The correction terms generate the van der Waals equation:

Prentice Hall © 2003 Chapter 10

• where a and b are empirical constants

• General form of the van der Waals equation:

2

2

V

annbV

nRTP

Corrects for molecular volume

Corrects for molecular attraction

nRTnbVV

anP

2

2

Prentice Hall © 2003 Chapter 10

Text, P. 395

Prentice Hall © 2003 Chapter 10

• Sample Problem # 77