the first scheduled quiz will be given next tuesday during lecture. it will last 15 minutes

The first scheduled quizwill be given next Tuesday

during Lecture.

It will last 15 minutes. Bring pencil, calculator,

and your book.

The coverage will be pp 364-424,

i.e. Sections 10.0 through 11.4.

• Theory developed to explain gas behavior.• Theory based on properties at the molecular level.• Kinetic molecular theory gives us a model for

understanding pressure and temperature at the molecular level.

• Pressure of a gas results from the number of collisions per unit time on the walls of container.

10.7 Kinetic Molecular Theory10.7 Kinetic Molecular Theory

• There is a spread of individual energies of gas molecules in any sample of gas.

• As the temperature increases, the average kinetic energy of the gas molecules increases.

Kinetic Molecular TheoryKinetic Molecular Theory

• Assumptions:– Gases consist of a large number of molecules in constant

random motion.

– Volume of individual molecules negligible compared to volume of container.

– Intermolecular forces (forces between gas molecules) negligible.

– Energy can be transferred between molecules, but total kinetic energy is constant at constant temperature.

– Average kinetic energy of molecules is proportional to temperature.

10.7 Kinetic Molecular Theory10.7 Kinetic Molecular Theory


• Magnitude of pressure given by how often and how hard the molecules strike.

• Gas molecules have an average kinetic energy.

• Each molecule may have a different energy.

• 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:


221 mu

Do you remember how to calculatevxy from vx and vy ?

21

22yxxy vvv

And how about v from all threecomponents?

21

222zyx vvvv

Remember these equations!! They’ll popup again in Chap. 11.

21

21

21

3Speedrms

8SpeedAverage

2SpeedProbaleMost

M

RTv

M

RTv

M

RTv

rms

mp

225.1:128.1:13:8

:2::, 212

1

21

rmsmp vvvAnd

ump<u>

urms

1. Be careful of speed versus velocity. The former is the magnitudeof the latter.

2. The momentum of a molecule is p = mv. During a collision, thechange of momentum is Δpwall = pfinal – pinitial = (-mvx) – (mvx) = 2mvx .

3. Δt = 2ℓ / vx Δpx / Δt = . . . = mvx2 / ℓ, where ℓ is length of the box

4. force = f = ma = m(Δv / Δt) = Δp / Δt = mvx2 / ℓ = force along x

5. And for N molecules, F = N(m(vx2 )avg / ℓ )

6. But

7. And

( ) . . .v vN

v v v vx a vg x x x x xN2 2

12

22

32 21

PF

A

N m

Av a n d A V so th a t P V N m vx x

2 2

u v v v v so th a t P V N m ux y z x2 2 2 2 2 1

323

N o w w e h a ve P V N m u a n d P V n R T 13

2

But N = nN0 , so we can divide both sides by n to obtain

13 0

20

13

2N m u R T b u t N m M so M u R T , ,

Application to Gas Laws• As volume increases at constant temperature, the average

kinetic of the gas remains constant. Therefore, u is constant. However, volume increases so the gas molecules have to travel further to hit the walls of the container. Therefore, pressure decreases.

• If temperature increases at constant volume, the average kinetic energy of the gas molecules increases. Therefore, there are more collisions with the container walls and the pressure increases.


Molecular Effusion and Diffusion• As kinetic energy increases, the velocity of the gas

molecules increases.• Average kinetic energy of a gas is related to its mass:

• Consider two gases at the same temperature: the lighter gas has a higher rms than the heavier gas.

• Mathematically:


221 mu

M

RTu

3

Molecular Effusion and Diffusion• The lower the molar mass, M, the higher the rms.



Graham’s Law of Effusion• As kinetic energy increases,

the velocity of the gas molecules increases.

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

• The rate of effusion can be quantified.

Graham’s Law of Effusion

• 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.

• Therefore, the higher the rms the more likelihood of a gas molecule hitting the hole.


1

2

2

1MM

rr

Graham’s Law of Effusion

• 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.

• Therefore, the higher the rms the more likelihood of a gas molecule hitting the hole.


1

2

2

1

2

1

2

13

3

MM

M

M RT

RT

uu

rr

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 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.


Diffusion and Mean Free Path • Average distance of a gas molecule between collisions is

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


• From the ideal gas equation, we have

• For 1 mol of gas, PV/nRT = 1 for all pressures.• In a real gas, PV/nRT varies from 1 significantly and is

called Z.

• The higher the pressure the more the deviation from ideal behavior.

Real Gases: Deviations Real Gases: Deviations from Ideal Behaviorfrom Ideal Behavior

1nRT

PVorn

RT

PV

nRT

PVZ

• From the ideal gas equation, we have

• For 1 mol of gas, PV/RT = 1 for all temperatures.• As temperature increases, the gases behave more ideally.• 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.


nRTPV

• As the pressure on a gas increases, the molecules are forced closer together.

• As the molecules get closer together, the volume of the container gets smaller.

• The smaller the container, the more space the gas molecules begin to occupy.

• Therefore, the higher the pressure, the less the gas resembles an ideal gas.


• As the gas molecules get closer together, the smaller the intermolecular distance.


• The smaller the distance between gas molecules, the more likely attractive forces will develop between the molecules.

• Therefore, the less the gas resembles and ideal gas.• As temperature increases, the gas molecules move faster

and further apart.• Also, higher temperatures mean more energy available to

break intermolecular forces.


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


The first scheduled quizwill be given next Tuesday

during Lecture.

It will last 15 minutes. Bring pencil, calculator,

and your book.

The coverage will be pp 364-424,

i.e. Sections 10.0 through 11.4.

The van der Waals Equation• We add two terms to the ideal gas equation one to correct

for volume of molecules and the other to correct for intermolecular attractions

• The correction terms generate the van der Waals equation:

where a and b are empirical constants characteristic of each gas.


2

2

V

annbV

nRTP

The van der Waals Equation

• General form of the van der Waals equation:


2

2

V

annbV

nRTP

nRTnbVV

anP

2

2

Corrects for molecular volume

Corrects for molecular attraction

Chapter 11 -- Chapter 11 -- Intermolecular Forces, Intermolecular Forces,

Liquids, and SolidsLiquids, and Solids

In many ways, this chapter is simply acontinuation of our earlier discussion of‘real’ gases.

Remember this nice, regular behavior described by the ideal gas equation.

This plot for SO2 is a morerepresentativeone of real systems!!!

And this is a plot for an ideal gas of the dependence of Volume on Temperature.

Now this one includes a realistic one for Volume as a function of Temperature!

Why do the boiling points vary? Is there anything systematic?

London Dispersion Forces

Hydrogen Bonding

Dipole-Dipole Forces

Intermolecular Forces -- forces between molecules --are now going to be considered.

Note that earlier chapters concentrated on Intramolecular Forces, those within the molecule.

Important ones:

ion-ion similar to atomic systems

ion-dipole (review definition of dipoles)

dipole-dipole

dipole-induced dipole

London Dispersion Forces:induced dipole-induced dipole polarizability

Hydrogen Bonding

How do you know the relative strengthsof each? Virtually impossible experimentally!!!

Most important though: Establish which are present. London Dispersion Forces: Always All others depend on defining property such as existing dipole for d-d.

It has been possible to calculate therelative strengths in a few cases.

Relative Energies of Various Interactions

d-d d-id disp

Ar 0 0 50

N2 0 0 58

C6H6 0 0 1086

C3H8 0.0008 0.09 528

HCl 22 6 106

CH2Cl2 106 33 570

SO2 114 20 205

H2O 190 11 38

HCN 1277 46 111

Ion-dipole interaction

Let’s take a closer look at these interactions:

Let’s take a closer look at dipole-dipole interactions.This is the simple one.

But we also have to consider other shapes.Review hybridization and molecular shapes.

Recall the discussion of sp, sp2, and sp3

hybridization?

London dispersion forces (interactions)

A Polarized He atomwith an induced dipole

molecule F2 Cl2 Br2 I2 CH4

polarizability 1.3 4.6 6.7 10.2 2.6

molecular wt. 37 71 160 254 16

Molecular Weight predicts the trends in the boiling points of atoms or molecules without dipole moments because polarizability tends to increase with increasing mass.

But polarizability also depends on shape, as well as MW.

Water provides our best example of Hydrogen Bonding.

But hydrogen bonding is not limited to water:

These boiling points demonstrate the enormouscontribution of hydrogen bonding.

Water is alsounusual in the relative densities of the liquid and solid phases.

The crystal structure suggests a reason for the unusual

high density of ice.

But water isn’t the only substance to show hydrogen bonding!

Viscosity—the resistance to flow of a liquid, such asoil, water, gasoline, molasses, (glass !!!)

Surface Tension – tendency to minimize the surface areacompare water, mercury

Cohesive forces—bind similar molecules together

Adhesive forces – bind a substance to a surface

Capillary action results when these two are not equal

Soap reduces the surface tension, permitting onematerial to ‘wet’ another more easily

11.3 Some Properties of Liquids11.3 Some Properties of Liquids

Examples of Viscosity

The unit of viscosity is poise, which is 1 g/cm-s, buttypical values are much smaller and are usuallylisted as cP = 0.01 P.

RationaleforSurfaceTension

Surface Tension• Surface molecules are only attracted inwards towards the

bulk molecules.– Therefore, surface molecules are packed more closely than bulk

molecules.

• Surface tension is the amount of energy required to increase the surface area of a liquid, in J/m2.

• Cohesive forces bind molecules to each other.• Adhesive forces bind molecules to a surface.

Surface Tension• Meniscus is the shape of the liquid surface.

– If adhesive forces are greater than cohesive forces, the liquid surface is attracted to its container more than the bulk molecules. Therefore, the meniscus is U-shaped (e.g. water in glass).

– If cohesive forces are greater than adhesive forces, the meniscus is curved downwards.

• Capillary Action: When a narrow glass tube is placed in water, the meniscus pulls the water up the tube.

• Remember that surface molecules are only attracted inwards towards the bulk molecules.

also called

FUSION

• Sublimation: solid gas.• Vaporization: liquid gas.• Melting or fusion: solid liquid.• Deposition: gas solid.• Condensation: gas liquid.• Freezing: liquid solid.

Phase ChangesPhase Changes

Cp(s):37.62

J/mol-K

ΔHfus:6,010 J/mol

Cp(l):72.24

J/mol-K

ΔHvap:40,670 J/mol

Cp(g):33.12

J/mol-K

the first scheduled quiz will be given next tuesday during lecture. it will last 15 minutes

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