Init 2/7/2012 by Daniel R. Barnes

WARNING: This presentation may contain images and other content that has been lifted from the world wide web without the permission of the owners of that intellectual property. Do not copy or distribute this presentation. Its very existence may be illegal.

SWBAT . . . . . . explain diffusion using kinetic theory.

Diffusion is . . . when a body of material starts out concentrated in a small, restricted area . . .

. . . and ends up spread out evenly throughout the available area due to . . . . . . random molecular motion

Diffusion happens in liquids and gases, but not in solids, since particles in a solid are stuck in place due to intermolecular forces.

Mr. Barnes, this would be a good time to do the hot beaker / cold beaker diffusion demonstration.

Cold water Hot water

5 oC 95 oC

What do you think will happen when Mr. Barnes puts a drop of food coloring into each beaker?

Do the demo and see what happens!

Click this red button if you don’t like to be confused and/or bored by complicated

stuff that you don’t really need to know to do well on the tests in here.

Click anywhere else on the screen if you do like the complicated stuff.

WARNING: Apparent differences in the rate of diffusion may not be entirely due to differences in random molecular speed

HYPOTHESIS: Mr. Barnes thinks that maybe there is more convection in the hot beaker than in the cold beaker and that this may mix the contents of the hot beaker. Convection is a mass movement of fluid that happens when the body of fluid is colder on the top and warmer on the bottom. The warmer fluid on the bottom, being puffy and less dense due to faster molecular motion, tends to float up, while the colder, calmer, more compact stuff on top tends to sink.

Since (1) evaporation cools off a liquid (it’s endothermic) and (2) evaporation happens only at the surface and (3) evaporation happens more quickly in hot water than in cold, Mr. Barnes thinks that evaporation causes a greater vertical temperature differential in the hot water beaker than in the cold water beaker, leading to greater convection, which, in turn, speeds up the homogenization process.

Whenever you’re thinking in terms of kinetic theory and temperature becomes part of your explanations and predictions for things, you have to make sure to think in terms of Kelvins, not degrees Celsius. Trust me for now on this one.

Cold water Hot water

5 oC 95 oC= (5 + 273) K = (95 + 273) K

= 278 K = 368 K

According to kinetic theory, the food coloring in the hot beaker should diffuse faster than the food coloring in the cold beaker . . . But by how much?

Since temperature (when measured in Kelvins) equals average molecular kinetic energy, the ratio of average molecular kinetic energy should equal the ratio of the Kelvin temperatures.

Temperature of hot water

Temperature of cold water

368 K

278 K= = 1.323741

This means that, on the average, water molecules in the hot beaker have 32% more kinetic energy than water molecules in the cold beaker.That’s a pretty significant difference, but you have to be a little careful interpreting this fact.

KE = ½mv2, so the ratio of molecular speeds is not the same as the ratio of molecular kinetic energies.

To get the ratio of typical molecular speed, you have to take the square root of the ratio of molecular energies.

(1.323741)^0.5 = 1.1505394. That’s not as big, is it?

Thus saith Mr. Barnes, but he has been known to be wrong.

According to this mathematical logic, the molecules in the hot water should be moving only about 15% faster than the molecules in the cold water. Somehow, the observed difference between the two beakers seems to be a little more dramatic than that to me.

Q1: What is diffusion?A: Diffusion is when molecules spread evenly throughout a fluid due to random molecular motion.

Q2: In what states of matter does diffusion happen?A: Diffusion can happen in a liquid or a gas, but not in a solid.

Q3: Why can’t diffusion happen in a solid?A: Particles in a solid may be able to vibrate, but because they are held in place by intermolecular forces, they can not wander.

Q4: What determines how fast diffusion happens?A: Random molecular motion gets faster with increasing temperature, so diffusion happens faster when it’s hotter.

SWBAT . . . . . . explain the properties of the states of matter using kinetic theory.

Here on Earth, the three main states of matter are . . .

solid

liquid

gas

If you put a one inch wide, plastic ball into a graduated cylinder . . . . . . it remains round and 1” wide.

If you put the ball into a bowl . . . . . . it remains round and 1” wide.

That’s because at room temperature, plastic is a solid.

Na+

Cl-

Na+Cl-

Na+

Cl- Na+

Cl-

Na+Cl-

Na+

Cl- Na+

Cl-

Na+Cl-

Na+

Cl- Na+

Cl-

Na+Cl-

Na+

Cl-

Na+Cl- Na+Cl- Na+Cl- Na+Cl-

Na+

Cl-

Na+Cl-

Na+

Cl- Na+

Cl-

Na+Cl-

Na+

Cl-

Na+Cl- Na+Cl-

Na+

Cl-

Na+Cl-

Na+

Cl- Na+

Cl-

Na+Cl-

Na+

Cl- Na+

Cl-

Na+Cl-

Na+

Cl- Na+

Cl-

Na+Cl-

Na+

Cl-

Na+Cl- Na+Cl- Na+Cl- Na+Cl-

Na+

Cl-

Na+Cl-

Na+

Cl- Na+

Cl-

Na+Cl-

Na+

Cl-

Na+Cl- Na+Cl-

Na+Cl- Na+Cl- Na+Cl- Na+Cl- Na+Cl- Na+Cl-

This is a close-up of a sodium chloride crystal lattice.

The orderly, repeating pattern of ionsseems to go on and on without end.

This would be a single . . . . . . salt crystal.

Solids* Retain their shape

* Retain their volume

* Often have an orderly, crystalline structure

EXPLANATIONSPROPERTIES

* Do not experience diffusion

* Particles “fall” into positions where attractive forces are maximized and repulsive forces are minimized.

* Although particles in a solid can vibrate, they are stuck in place due to intermolecular forces, so they are not free to wander.

This is a water molecule.

This is another water molecule.

They like each other.

They’re attracted to each other by intermolecular forces.

Liquids* Take the shape of their container.

* Have a constant volume, regardless of container.

EXPLANATIONSPROPERTIES

* Particles in a liquid are free to wander.

* Particles in a liquid remain huddled together.

* Experience diffusion * Particles in a liquid wander randomly.

Gases* Take the shape of their container.

* Expand to fill their containers

EXPLANATIONSPROPERTIES

* Particles in a gas wander freely, flying through space.

* Particles in a gas move quick enough and attract each other weakly enough that they don’t stay stuck together. They just fly apart.

* Experience diffusion * Particles in a gas wander randomly.

* Experience effusion * Particles in a gas fly randomly in all directions, eventually wandering out of holes in containers by chance.

Q1: What are the particles in a solid doing?A: Particles in a solid are stuck in place, but can vibrate.

SWBAT . . . . . . explain the cause of gas pressure using kinetic theory.

The process is pretty random, so gas molecules tend to zig-zag around.

Air is a gas.

Air is made of a mixture of gases, but it’s mostly nitrogen (78%) and oxygen (21%).

Gas molecules fly in straight lines . . .

. . . until they hit something.

When gas molecules collide with each other, they change speed and direction.

[state of matter?]

[element?] [element?]

If you were to watch a single gas molecule in the air, you would see it wander around in an unpredictable, disorderly way.

Every time you see it change direction, that’s because it just collided with another gas molecule.

Every so often, a gas molecule will collide with an object . . . . . . like you, perhaps.

SMACK!

Whenever something hits you, it pushes on you a little.

Therefore, all the billions of tiny air molecules that hit you every second exert pressure on your skin.

Collisions cause pressure.

Air molecules are crashing into you from all directions, so the result is that the pressure of the atmosphere crushes you.

Just how hard does the air crush you? You don’t really feel like you’re being crushed, do you? It must not be very hard. Well . . .

Imagine one square inch of area on your skin.

All the molecules that collide with that one square inch of skin . . .

. . . exert a force of about 14.7 pounds.

Since pressure equals force divided by area . . .

We say that the atmosphere exerts a pressure of 14.7 pounds per square inch.

(assuming that you’re at sea level)

How many square inches of area do you think there are on your body?

Probably hundreds. Now multiply one hundred times 14.7 pounds.

Even if there’s only 100 square inches of surface area on the human body, that’s still 1470 pounds of force.

That’s almost a ton of force . . . And you don’t even feel it!

However, if you get tossed into outer space without a space suit, it’ll hurt a lot when there’s no air crushing you any more.

It turns out that it’s good for you to get smacked around . . .

. . . by air molecules.

If you ever stop getting smacked around by air molecules, you will swell up painfully and die.

You NEED to be squeezed.There. That’s MUCH better.

SWBAT . . . . . . describe the relationship between molecular motion and temperature

Usually, in Mr. Barnes’ class, to get an “A” on a test, you have to score . . . 90% or better. (and 80% for a “B”, 70% for “C”, etc…)

What if a test is so hard that nobody, even the smartest, hardest-working, most obedient students gets 90%? Don’t they deserve an “A”?

Maybe. If a teacher decides to, he can decide to grade on a “curve”. This ensures that at least somebody gets an “A”.

Grading “on a curve” pretty much means that there’s at least one “A”, and that would at least be the person with the highest score on the test.

F D C B A

It would then be typical to give a few of the people who almost scored that high “B’s” on the test.

The largest group would be the people with more or less average scores, who would be given “C’s” on the test, regardless of what % they got correct.

F D C B A

Then, a few people with below-average scores would be given “D’s”.

Finally, at least one person would have to get an “F”. If you’re grading on a curve, that often happens. Even if the worst person in the class is amazing, they might still get an “F” for coming in last. Yeah, that’s pretty mean, but some teachers do that.

F D C B A

This distribution of grades, if graphed, ends up being a “bell curve”.

Num

ber

of p

eopl

e

Let’s shift from people to particles.

Num

ber

of p

artic

les

Kinetic energy

Let’s imagine that this graph shows the speeds of the atoms in a paperclip sitting on a table. It’s a solid, so the atoms are vibrating.

Lots and lots of atoms in the paperclip are jiggling

at medium speedsSeveral of the atoms are vibrating at faster-than-

average speedsVery few atoms

are vibrating extremely quickly.

Several atoms are vibrating slower than

averageA very small number of atoms are

barely moving at all.

Num

ber

of p

artic

les

Kinetic energy

Although it’s a fact that atoms and molecules move faster at higher temperatures, keep in mind that at any given temperature, the particles in an object are NOT all moving at the same speed.

Num

ber

of p

artic

les

Kinetic energy

Now, imagine that we put the paperclip in the refrigerator. What happens to the KE distribution graph?The blue line represents the KE distribution for the atoms in the paperclip when it’s cold. Notice how the hump moved to the left.

Slower speeds Faster speedsMedium speeds

Medium speeds

Num

ber

of p

artic

les

The hump moving to the left makes sense because the average speed of the molecules got slower when the paperclip got colder.

Temperature = average molecular kinetic energy

Slower speeds Faster speeds

KE = ½ mv2 m = mass v = speed

Num

ber

of p

artic

les

It may seem odd that the hump got taller, but you’re just going to have to trust me that when the hill gets narrower, it has to get taller so that it represents the same number of molecules.

Less kinetic energy More kinetic energy

Num

ber

of p

artic

les

Now, imagine that you put the paperclip into an oven.

Kinetic energy

As the paperclip gets hotter, the atoms vibrate faster and faster.

Therefore, the graph should shift . . . to the right

cold paperclip

room temperature

paperclip

hot paperclip