5 Postulates of Kinetic Theory

1) Spherical molecules in constant, random straight-line motion

2) “Elastic” collisions3) Point masses4) No interactions5) Avg. KE of gas molecules

Temperature

Random, straight-line motion?

The gas particles move in straight lines between

collisions.

Recall: straight-line motion implies that no forces are

acting on the particle.

Total KE is conserved.Total KE before collision

=Total KE after collision.

BUT KE may be TRANSFERRED!

Elastic Collisions

Elastic Collisions

Kinetic energy may be transferred between particles.

Inelastic Collision

Kinetic Energy is NOT conserved!

Point Mass

The volume of the gas molecule itself is tiny compared to the distance between

gas molecules. In other words, the distance between the molecules is more important than

their actual size. We say the volume of each molecule is

insignificant; but they need to be a point so we can locate them in space (give

them coordinates).

Temperature of a gas

Tgas KEavg

So all gases at the same T have the same average kinetic energy.

Recall that KE = ½ mv2.

At the same temperature, which of the following gases diffuses most

rapidly?

He Ne Ar Kr Xe

Lightest is fastest!

At the same temperature, which of the following gases diffuses most

slowly?

He Ne Ar Kr Xe

Heaviest is slowest!

For gases at the same Temperature

KE = ½ mv2

Lighter gas particles have higher average speeds than heavier gas

particles at the same temperature.

Ideal Gas

Gas that obeys all 5 assumptions of the kinetic theory all of the time. It doesn’t exist. It’s a model.

Real Gas

Most real gases obey the kinetic theory most of the time.

Which assumptions of the kinetic theory hold up?

1. Spherical molecules in random, straight-line motion

2. “Elastic” collisions

Which assumptions of the kinetic theory break

down?

1. Point masses2. No interactions

When do the assumptions of the kinetic theory

break down?

When the gas molecules are close to each other.

When are the gas molecules close to each

other?

At high pressure & low temperature.

When are the gas molecules far apart from

each other?

At low pressure & high temperature.

How do the gas molecules act when they are far apart from each

other?

Good!

Real Gases

Molecules are always attracted to one another, even if just weakly.

Molecules take up space.

What are the properties of gases?

1. Have mass2. Take the shape & volume of their

container3. Compressible4. Flow5. Diffuse6. Exert Pressure

Pressure

Force/Area

Pressure results from?

Collisions of the gas molecules with the walls of the

container.

With a Barometer!

P = DHggh

but since DHg & g don’t change, we just report h.

How do you measure air pressure?

How do you measure the pressure of a confined gas?

With a manometer!

Attach gas bulb here

To vacuumpump

Closed-ended manometer

A closed ended manometer:

h is directly proportional to the pressure of the confined gas.Pgas = DHggh but we just say h most of the time.

How do you measure the pressure of a confined gas?

With a manometer!An open ended manometer:

h tells you how far away the gas pressure is from the air pressure. So you also need a barometer to measure Patm.

AAAA

22222222

Pgas > Patm

Pgas = Patm + h

Pgas < Patm

Pgas = Patm - h

Pressure depends on?(microscopically)

# of impacts per unit time and force of each impact

Pressure depends on?(macroscopically)

# of gas molecules per unit volumeAnd

temperature

Pressure Units

• 1 atm = • 760 torr = • 760 mm Hg =• 101.3 kPa =• 101,325 Pa =• 14.7 lb / in2 or psi

Temperature

A measure of the avg. kinetic energy of the particles of a

substance.

4 variables needed to completely describe a

gas-phase system?

1.Temperature2.Pressure3.Volume4.# of moles

Can change size:

balloons orcylinders with pistons

Elastic containers

Walls are fixed.Size does not change.

Rigid Containers

STP

Standard Temperature & Pressure1 atm or 101.3 kPa or 760 torr

0C or 273K

Boyle’s Law

For a fixed mass and temperature, the pressure-

volume product is a constant.

Boyle’s Law

PV = k where k = a constant

Constant T, n

Boyle’s Law

P1V1 = P2V2

Graph of Boyle’s Law

Hyperbola – it’s an inverse relationship!

Graph of Boyle’s Law, Pressure vs. Volume

Double the pressure

Volume goes to ½ the original volume

Triple the pressure

Volume goes to 1/3 the original volume

Halve the pressure

Volume goes to 2 X the original volume

Quadruple the pressure

Volume goes to 1/4 of the original volume

What does the graph of a direct relationship look

like?

Which temperature scale has a direct

relationship to molecular velocity?

Kelvin: 0 K means 0 speed.

Which graph shows the relationship between average KE

and Kelvin temperature?

The top graph!

Graph of Volume vs. Kelvin Temperature

It’s a direct relationship.

Math expression of Volume & Kelvin

Temperature

V1/T1 = V2/T2

Charles’ Law

Constant P, n

What happens to the volume when the Kelvin temperature is doubled?

The volume doubles!

What happens to the volume when the Kelvin temperature is tripled?

The volume triples!

What happens to the volume when the Kelvin temperature is halved?

The volume is halved!

What happens to the Kelvin temperature when the

volume is halved?

It’s halved!

Graph of Pressure vs. Kelvin Temperature

It’s a direct relationship.

Constant V, n

Math expression for pressure &

temperature.

P1/T1 = P2/T2

Gay-Lussac’s Law

What happens to the pressure when the Kelvin temperature is doubled?

The pressure is doubled.

What happens to the pressure when the Kelvin temperature is halved?

The pressure is halved.

What happens to the pressure when the Kelvin temperature is tripled?

The pressure is tripled.

What happens to the Kelvin temperature when the pressure is doubled?

The Kelvin temperature is doubled.

Combined Gas Law

For constant n:

P1V1 = P2V2

T1 T2

If they do NOT mention a variable, it’s constant. Constant variables are the same on both sides, so you can neglect them.

V = knThe volume of a gas is directly proportional to the # of moles.

At STP, k = 22.4 liters/mole

Avogadro’s Law

Constant T, P

What is another way to state Avogadro’s Law?

Equal volumes of gases at the same temperature & pressure have equal numbers of molecules.

These 2 boxes have the same:

a) Mass c) # of molecules

b) Density d) # of atoms

He N2

Ideal Gas Law

Equation of state for a gas. Relates the macroscopic variables that describe the system.

PV = nRT

R = gas law constant. In US, we use R = 0.0821 Literatm

moleK

Ideal Gas Law units

Governed by R. If R = 0.0821 Latm then mole

KP in atmV in litersT in Kelvinsn in moles

PV = nRT

moles & mass

• From Table T:

# of moles = given massgram-formula mass

Ideal Gas Law Extension #1

Use it to find molar mass, M

PV = nRT = RTmass

M

Rearrange: M = massRTPV

Ideal Gas Law Extension #2

Use it to find the density of a gas:

PV = nRT = mRT where m = mass M

Density = m/V so MP = D or M = DRT RT P

Density of a gas at STP

Only at STP:

Density of a gas = Molar Mass (grams/mol)

22.4 (Liters/mol)

Vapor

Gas phase of a substance that is normally a liquid at room

temperature (298C).

How do you measure vapor pressure?

Closed container, at equilibrium (both liquid & gas phases

present)

http://www.chemteam.info/GasLaw/VaporPressureImage.GIF

Manometer!

Vapor pressure depends on?

Temperature of the liquid phase ONLY!

BOTH phases MUST be present for it to be a vapor. If no liquid is

present, it’s a gas.

Handy result: since vapor pressure only depends on the

temperature of the liquid phase …

It can be tabulated! You don’t have to

measure it every time you do an experiment!

What is Dalton’s Law of Partial Pressures?

Ptot = P1 + P2 + P3 + P4 + …

Gas Collection over Water

The test tube was full of water at the beginning. As the reaction proceeds, the gas displaces the water. There is

also some water vapor up there.

http://crescentok.com/staff/jaskew/isr/tigerchem/gas_laws/dalton2.gif

When the water levels inside and outside line up, then the gas pressure + the water vapor pressure is equal to the air pressure!

Gas Collection over Water

Pinside = Patm when levels align

http://abetterchemtext.com/gases/images/over_water.png

N2

N2(g) + H2O(g) = Pgas

Patm = PN2 + PH2O

But since it’s water vapor, we can look up PH2O in a table.

PN2 = Patm – PH2O

You need a barometer to measure Patm.

Dry volume of a gas at STP

450.0 mLs of a gas is collected over water at 23C. Patm = 748.0 torr. Find the

volume of the dry gas at STP.

1. Look up the vapor pressure of water at 23 C. It’s 21.1 torr.

2. Find the pressure of the gas alone. Pgas = Patm - PH2O = 748.0 - 21.1 = 726.9 torr

3. Use combined gas law to find volume of the gas at STP.

V2 = V1 X P X TP T

Correction ratios!

Diffusion

Spontaneous mixing of two substances caused by their random motion. The two gases move through each

other.

Effusion

Process by which gas particles pass through a tiny

opening.

http://chemwiki.ucdavis.edu/@api/deki/files/8671/e2.JPG?size=bestfit&width=350&height=209&revision=1

Graham’s Law of Effusion

The rates of effusion of gases at the same temperature and

pressure are inversely proportional to the square roots

of their molar masses.

Another way to find the molar mass of a substance!

Graham’s Law of Effusion

KE1 = ½ m1v12 and

KE2 = ½ m2v22

At the sa

me

temperature, these

two

gases h

ave the sa

me

average KE!

½ m1v12 = ½

m2v22

m1 / m2 = v2

2 / v12

Take the sq

uare

root o

f both

sides.

Graham’s Law of Effusion

Estimate the molar mass of a gas that effuses at 1.6 times the effusion rate of CO2.

= 1.6Squar

e bot

h sides

!

mCO2/munk = 2.56 or 44/x = 2.56X = 17

Graham’s Law – general. Stick in the labels for this problem