Chapter 12Chapter 12

Actual NEW information!Actual NEW information!

Kinetic Molecular TheoryKinetic Molecular Theory(Ok… Maybe not new)(Ok… Maybe not new)

The average kinetic energy of the gas The average kinetic energy of the gas molecules is proportional to the gases molecules is proportional to the gases temperature. temperature.

If two gases have the same temp, they If two gases have the same temp, they have the same average KEhave the same average KE

KE= ½ muKE= ½ mu22

Other KMT pointsOther KMT points

The space between gas molecules is SO The space between gas molecules is SO BIG compared to the sizes of the actual BIG compared to the sizes of the actual molecules themselvesmolecules themselves

The molecules are in continuous random The molecules are in continuous random motionmotion

When gas molecules collide, it is a When gas molecules collide, it is a perfect elastic collision with no loss of perfect elastic collision with no loss of energyenergy

Average KE does not Average KE does not paint the complete paint the complete picture!picture!

Although the temp tells you the average, Although the temp tells you the average, there are some molecules going faster and there are some molecules going faster and slower at any given point. At higher slower at any given point. At higher temperatures, the molecules move faster. temperatures, the molecules move faster.

Pretty graph!Pretty graph! Furthermore since KE is mass and velocity, Furthermore since KE is mass and velocity,

heavier gases have a slower speedheavier gases have a slower speed

How do we figure out the How do we figure out the speed?speed?

Well Billy, we use the root-mean-square Well Billy, we use the root-mean-square speed a.k.a rms speed… This is also called speed a.k.a rms speed… This is also called “Maxwell’s expression”“Maxwell’s expression”

2 3RTu

M

Molar mass

TinK!!!

So when the move, what So when the move, what happens?happens?

Well… Thanks for asking… When Well… Thanks for asking… When someone does not shower and you can someone does not shower and you can smell them across the room (yes I am smell them across the room (yes I am talking to you)… That is called diffusiontalking to you)… That is called diffusion

DiffusionDiffusion is the mixing of two or more is the mixing of two or more gases due to their molecular motiongases due to their molecular motion

Given time, the molecules of two gases Given time, the molecules of two gases will completely mixwill completely mix

Well give me the math!Well give me the math!

Related to diffusion is effusion Related to diffusion is effusion It is the movement of gas through a tiny It is the movement of gas through a tiny

opening in a container into another container opening in a container into another container where the pressure is low..where the pressure is low..

Where is the math… Well if you want to Where is the math… Well if you want to compare effusion rates you can use Graham’s compare effusion rates you can use Graham’s Law (got a cracker and a law named after Law (got a cracker and a law named after him… he is special... Like you)him… he is special... Like you)

Umm.. Where is my mathUmm.. Where is my math

Rate of effusion is inversely proportional Rate of effusion is inversely proportional to the square root of its molar mass.to the square root of its molar mass.

Or

2

2

1 1

2 2

Rate of effusion of gas u of gas

Rate of effusion of gas u of gas

1 3 /( 1)

2 3 /( 2)

Rate of effusion of gas RT M of gas

Rate of effusion of gas RT M of gas

One moreOne more

1 2

2 1

Rate of effusion of gas molar mass of gas

Rate of effusion of gas molar mass of gas

Demo time! Demo time!

If we use 6M HCl and 6M NHIf we use 6M HCl and 6M NH33 (NH (NH44Cl) Cl)

and put them on opposite side of a tube, and put them on opposite side of a tube, simultaneously and at the same time, simultaneously and at the same time, where will they meet?where will they meet?

Applications?Applications?

Helium Balloons?Helium Balloons?

Non-Ideal GasesNon-Ideal Gases

Gases are attractive and actually have a Gases are attractive and actually have a volumevolume

How could you think it doesn’t?How could you think it doesn’t? We need correction factors for We need correction factors for

intermolecular attractions and molecular intermolecular attractions and molecular volume.volume.

This is the van der Waals equation which This is the van der Waals equation which comes from the ideal gas law.comes from the ideal gas law.

2

nP a V bn nRT

V

atm L2/mol2

Correction for intermolecular forces

L/mol

Correction for molecular volume

Vapor PressureVapor Pressure

Liquids will reach a dynamic equilibrium Liquids will reach a dynamic equilibrium between the liquid and vapor phase as between the liquid and vapor phase as molecules evaporate. molecules evaporate.

If it is a closed container, there is no net If it is a closed container, there is no net change in molecules once equilibrium is change in molecules once equilibrium is reached.reached.

In an open container, the molecules will In an open container, the molecules will escape and leave. escape and leave.

The gas molecules from the liquid will then The gas molecules from the liquid will then exert a pressure on the surroundings. This is exert a pressure on the surroundings. This is called the VAPOR PRESSUREcalled the VAPOR PRESSURE

How does this effect the How does this effect the gas problems.gas problems.