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PROFESSOR: So we will have weekly quiz tomorrow.
There's been a lot of coverage, and so to focus you
a bit, I'm going to confine the weekly quiz to glasses and
chemical kinetics.
So you don't have to worry about diffusion.
We'll catch up on that, but I know there's so
much material there.
Let's keep it confined to glasses and chemical kinetics.
And I'll be available today 4:30 to 5:30.
If you can't be at that time, send me a note, and I'm sure
we can figure out a time to get together.
So what I want to do today is to start a new unit.
We're going to start talking today about solutions, and do
some solution chemistry, OK?
Today we talk about solutions.
And you might initially say, why are we
talking about solutions?
This is solid-state chemistry.
I think up until now, you've seen that it's pretty rare
that we use solids in their pure form.
We usually have mixtures.
So for example, when we studied glasses, we modified
the glasses with an alkaline earth oxide.
Well we, in fact, were making a solution of
more than one component.
So it's to get certain properties
that we study solutions.
Secondly, coming out of liquid phase is a way to make solids.
So in terms of processing, we need to understand something
about solutions.
And then lastly, we're going to be studying, towards the
end of the semester, a big unit on biochemistry.
And biochemistry, why, you say, biochemistry?
Why is he doing biochemistry?
I thought this was solid-state chemistry.
We are solid-state devices, but we're made of soft matter.
At least the exoskeleton is soft matter.
The endoskeleton is ceramic, right?
Our bone structure is ceramic.
Hydroxyapatite, calcium hydroxyapatite, and the
outside is a polymer.
So look at this.
Confirmational changes in polymer.
But the chemistry, the biochemistry, so much of it
takes place in aqueous solution.
So hence, we better know something
about aqueous solution.
So to this, we go almost right back to the first day.
You remember, was the second lecture, and we showed this
figure, and all the different categories of matter.
And we started over here with elements, and we moved into
some pure substance compounds, et cetera, et cetera.
Now we're going to move over to here.
So homogeneous mixture containing uniform composition
and properties, as opposed to a heterogeneous mix.
So we're now over here.
We're working our way through the diagram.
All right.
So let's get a couple of basic definitions up.
So the solution is really a mix of at least two
constituents.
One, the majority constituent is called the solvent, and
then we can have one or more solutes.
So the solvent, this is the majority constituent, and then
the solutes are the minority constituents.
And in some instances, it's pretty hard to
tell which is which.
And as far as types of solutions, I
want to broaden this.
You know, when I say solution, you're probably thinking about
aqueous solution.
But I want to take a minute and work through this chart.
And this is all posted, so you don't have to
write it all down.
Just follow with me.
So most of the general chemistry subjects will just
stop at the end of the first line.
They'll treat solutions as aqueous solutions.
But in material science, we think of things broadly.
So a good example of a simple aqueous solution is sodium
chloride and water.
Sodium chloride is the solute and water is the solvent.
But you can have a liquid solute.
So wine--
in case you've ever encountered this beverage,
it's primarily water, but it can contain up to about 14%
ethyl alcohol, and there are other constituents that give
the color and the flavor and so on.
And you can have a gas in a liquid, and that would be
seltzer, where CO2 is dissolved.
It's actually dissolved.
If you take a look at a bottle of bubbly water on the shelf,
you don't see the bubbles.
The carbon dioxide is actually dissolved.
You can have a gas as a solvent, and air would be an
example of that, where the solvent is nitrogen.
And then we have as solutes oxygen, argon, carbon dioxide,
if you live next to a power plant, it's sulfur dioxide, if
you live next to an aluminum smelter, it's
tetrafluoromethane, and so on.
So we have all kinds of solutes in the air.
And then we can have solid solutions.
And OK, as soon as you see the word solid, you know, that
means you're 3.091.
So what do we see for solids?
Metal alloys.
We saw carbon dissolved in iron.
Well, that's a solution.
It's homogeneous, single phase, just as the definition
on that chart 1.11 said.
Semiconductor, boron doping into silicon, the boron sits
on a silicon lattice site.
So this is a true solution.
The boron is the solute, and silicon is the solvent.
We can have the ceramic.
We talked about the oxygen sensor.
The oxygen sensor is zirconia, which has been stabilized with
the addition of calcium oxide.
As one example.
In contemporary work, they might use another oxide.
But what's the purpose of the calcium oxide?
Well, I told you that it's to increase the vacancy
population, give you a rapid response
on your oxygen sensor.
And as we're going to learn later, that's true, and
there's a second value in putting in the calcium oxide.
And it stabilizes, that's why they use the term stabilize,
it stabilizes the cubic form of zirconia.
Zirconia has a different crystallographic
modifications.
The cubic one is the one that gives us the best ability to
transfer oxygen, and the addition of calcium oxide as a
solute, the calcium ions actually sit on the zirconium
lattice, that's a true solid solution.
It also makes the cubic zirconia stable, and with
Christmas coming, you know, it's the poor man's diamond,
and that's the same material there.
And to modify a glass, as I mentioned earlier, adding a
alkaline earth oxide breaks the silicate network.
That's a solution.
Now here's an inverse one, where the solid is the
solvent, and the liquid is the solute.
So this was dentist's office practice going back to the
time when I was your age.
If you had a feeling, the dentist had silver and mercury
in the dentist's office, and would add liquid mercury to
silver and make up this amalgam, and then jam that
into the tooth.
Actually, that was the B part of the operation.
There was this dentist here in the United States, and if I
could find him, I would like to have a word with him.
But he had this theory.
You see, the amalgam is a metallic alloy.
And so obviously, it has metallic bonding.
And the tooth is--
it's a ceramic.
So what kind of bonds are going to form between a metal
and a ceramic?
They're not very good.
So this dentist had the theory that the way to increase the
bonding capability of the amalgam to the tooth was to
maximize contact areas.
So when you went in with a tiny, tiny little cavity, the
dentist would drill the tooth out, removing about 75% of the
volume of the tooth, and then they would make this amalgam
and shove that in.
And you'd wear that for about 20 years, until one day you
bite into a muffin that's got a little piece of walnut shell
in it, and the amalgam flexes, and your
thin-walled tooth goes bang!
Like that.
And now you get to go back to the dentist's office for yet
some more medieval treatment.
Actually, things have improved somewhat.
Thanks to material science.
But they're not using this amalgam anymore.
But there are a number of us who are still walking around
with silver and mercury in our mouths, and--
yeah.
Enough about my dental problems.
Now let's go on to intercalation.
You can put a gas into a solid.
And I told you about this one, where if you want to store
hydrogen, and this is a big problem, if we're going to
talk about hydrogen-powered vehicles.
A problem as big as, how to get the fuel cell cheap
enough, is where are you going to store the hydrogen on the
car, and one of the materials that's been proposed is this
alloy of lanthanum and nickel that can intercalate huge
amounts of hydrogen.
So that forms a solid solution.
So those are examples of solutions, and we're going to
go back and make sure that we cover the basic Gen Chem at
the top here.
But I want you know that solution
chemistry is very broad.
Now when you dissolve something, you actually have
things down at the atomic level.
So for example, in brine, you actually have below two
nanometers as particle size.
You actually have sodium ions and chloride ions dissolved
completely, which means that the solution is clear,
colorless, and transparent to visible light.
Water is clear, colorless, transparent to visible light.
If you had sodium chloride, it remains clear, colorless,
transparent to visible light.
You can't filter, and you can't wait for the sodium
chloride to settle out, because it's bonded within the
structure of the liquid water.
And this has implications.
There's so much water on the planet, but there's not so
much fresh water on the planet.
And desalination can't be accomplished by filtration.
A filter that had a pore size small enough to trap sodium
ions, the pore size would be so small, water molecules
couldn't go through.
So this is the concept.
At the other end, you can get something called a suspension,
where the particle size is greater than about 1,000
nanometers, and blood is a good example of that, where
it's opaque.
Visible light doesn't go through, but you can filter
out some of the matter in blood.
And if you let it sit for a while, it'll settle in it
gravitational field.
And in between, you have this whole zone of colloids.
And so between colloids and suspensions, the only
difference is particle size.
And this whole thing we would just call a dispersion of
another phase, either another solid phase, or
another liquid phase.
And it's kind of an interesting physical chemistry
about the dispersion, what makes it work.
For example, in milk, milk is a good example of a
dispersion.
You have a fatty phase, and you have an aqueous phase.
The aqueous phase, where all the minerals are.
Why?
Because the minerals are--
what kind of compound?
They're not metallic, they're not covalent.
They're ionic.
The ionic compounds dissolve in the aqueous phase, and then
in the fatty phase, that's where you have the
protein and so on.
But the fatty phase is clear and colorless, and the aqueous
phase is clear and colorless.
And yet milk is white.
It's, as the term implies, it's milky.
Why?
What's going on?
You have a second phase here.
This could be the fatty phase, and this is the aqueous phase.
They're both clear and colorless, but they have
different indices of refraction.
And since this has n fatty phase, and this has n aqueous
phase, this interface scatters the light.
So if you want to start a business, if you want to try
to tailor the index so that the index of the aqueous phase
matches the index of refraction of the fatty phase,
you'd have the two dissolve, one and the other, and it
would be transparent, divisible light.
So you would have milk that isn't milky.
I mean, the public would be very confused.
But anyways.
So that's what you do.
So why does this thing not settle?
Because they do have a density difference, and again, going
back to the days when I was not a college student but a
youngster, there was still this form of milk called
pasteurized milk.
Well, all milk is pasteurized, but this milk was not
homogenized.
And what would happen is, there was this person that
would deliver milk.
This was a borosilicate glass bottle.
And here would be the cream.
The cream would rise to the top.
We have all these expressions in our language.
And then this would be the milk here, and you could skim
this off for coffee or sugar, and then this would be a
low-fat milk.
But people wanted this all mixed, so then they went to
homogenized milk.
So what is homogenized milk?
This is your red cap, now.
All the milk is homogenized.
This was a big thing.
This was simply called pasteurized.
I'm going to get to the physical chemistry here.
It's very interesting.
Because this is lower density, and yet in homogenized milk it
doesn't rise.
So let's take a look at what goes on in the physical
chemistry of homogenized milk, because it's all about these
various systems. So I'm going to take this particle here,
and its sum insoluble cluster.
And I'm not specifying the cluster size.
It's probably greater than about two nanometers.
So there are two forces acting on this.
There's a settling force and there's a buoyancy force.
Obviously, otherwise it wouldn't float.
So there's some kind of a buoyancy force.
Settling force and a buoyancy force.
Well, the settling force, this is just the gravity.
Right?
This is the force of gravity.
And we know the force of gravity.
That goes with the mass.
Come on, get that cell phone out of here.
This force of gravity goes as the mass, and the mass, we
know, goes as the volume.
And the volume goes as the cube of the radius.
I'm assuming this is a spherical particle, all right?
Now, the buoyancy force.
The buoyancy force is the interfacial
force between the two.
There's some binding across here.
Maybe weak van der Waals, or if this fatty phase has
molecules in it that are polar, then there could be
dipole-dipole interaction.
But in any case, there's some kind of an
interfacial force here.
And this is all chemical bonding
between solute and solvent.
But you see, the force is a weak force.
If it were a really strong force, it would
dissolve this thing.
It won't quite dissolve it, but there is some kind of
dipole-dipole weak force.
And this one here is operating across the surface area.
That's the contact.
So this force goes as the area, and area goes as the
square of the radius, whereas mass goes as
the cube of the radius.
So you know, from your math, that r cubed dominates r
squared, but only at large r.
It's not always the case, is it?
Maybe before you got here, you thought that.
But now that you've been at MIT a few months, you know
that r squared can dominate r cubed at small r.
Interfacial forces dominate.
And that's exactly what happens in these dispersions,
and that's why they don't settle out.
Now, homogenized milk is simply milk that has been
agitated in such a way as to reduce the fat globule size
below a critical value so that these interfacial forces hold
the fat globules in suspension.
If you waited long enough, they would agglomerate and
settle, but that time is probably longer than the shelf
life of the milk.
So the milk probably spoils before stuff settles out.
So this is all very important to understand.
The range that exists between insolubility and this sort of
clustering, and suspension, and so on.
By the way, a lot of pharmaceuticals are like this.
A lot of pharmaceuticals.
So when it says, shake well before
using, they're not kidding.
Because the active ingredient will settle.
And you're drinking just the solvent, just the vehicle.
And all of the potency is on the bottom of the bottle.
Shake that thing up!
I can't say what it does to the taste, but
that's another problem.
Actually, I threw in this slide here.
We're not going to spend any time on it, but you can look
at it at some point.
This is a whole taxonomy of colloids.
Solid-liquid emulsions, aerosols, they're all part of
this magic zone between solubility and
just brick, all right?
There's this whole fine, pardon the pun,
the whole fine structure.
OK, So let's get to the chemistry.
Obviously there's something to do with bonding here, right?
So here's a simple experiment, and this is taken right from
the reading.
So I've just taken this episode that is written up in
the reading.
So we've got two beakers here, and in each
beaker, we have a bilayer.
We've poured in some carbon tetrachloride, liquid, and
we've poured in some water.
And these two are immiscible, because carbon tetrachloride
is obviously a non-polar liquid, and water is a polar
liquid with hydrogen bonding capability.
And in one beaker, we introduce crystals of iodine.
In the other beaker, we introduce crystals of
potassium permanganate.
And then we shake them up, and we wait.
And eventually we see that on the left, the iodine dissolves
in the carbon tetrachloride.
And we're using the purple color as an indicator.
And this is kind of cute, because both potassium
permanganate and iodine will render things purple.
So you're comparing purple to purple.
They could have chosen something else, but this is
kind of cute.
All right.
So here you end up with a solution of iodine and carbon
tetrachloride, whereas on the right side, you end up with a
solution of potassium permanganate and water, and
nothing in the carbon tetrachloride.
So what can we infer from this?
Well, let's take a look at the possible interactions.
So first of all let's categorize H2O.
This is polar, it's a polar liquid, with hydrogen bonding
capability.
Carbon tetrachloride is non-polar.
It's very toxic.
When I was a child, we had this in the medicine cabinet.
It's a non-polar solvent.
It's fantastic for getting grease stains off.
Every man had this.
With a little handkerchief, you'd take a little grease
stain off your tie.
You can't buy this stuff.
You can't even guy it for research anymore.
It's too bad.
It's great stuff.
Highly toxic, though.
But you know, there's a time and a place.
All right.
So then here's iodine.
Iodine, we know, is non-polar.
It's a homonuclear molecule, it has to be non-polar.
And so what holds iodine together in the crystal?
There's only one bond, and that's van der Waals, right?
It's a van der Waals solid, whereas potassium permanganate
is an ionic solid.
Potassium permanganate is ionic, and it consists of
potassium cations and permanganate anions.
And what we find is that the non-polar solute dissolves in
the non-polar solvent, and the ionic solute dissolves in the
polar solvent with hydrogen bonding capability.
So from this, we can infer the general rule, which is
encapsulated in the language used in chemistry textbooks.
Like dissolves like.
And what they're really saying here, is that like solutes
dissolve in like solvents.
Solute-solvent is like dissolves like.
OK.
It's a good place to start, but it's
an incomplete picture.
So I want to show you that there's some
sophistication here.
This is taken from one of the other books.
And it shows just the rules for ionic compounds in water.
And I just showed you, from this example, that the ionic
compound dissolved in water.
And what you see here is that some ionic compounds dissolve
in water, but there's a whole set or
insoluble ionic compounds.
So it's not straightforward.
But we know from 3.091, we know that we can make sense of
this on the basis of competition.
Competition between what holds the compound in the solid
state versus what will pull it into the liquid state.
So for example, we can compare sodium chloride, which we know
dissolves in water.
So sodium chloride, as a crystalline solid, will
dissolve to form sodium chloride aqueous solution.
Whereas if you look at magnesium oxide, which is also
an ionic crystal, it does not, to any standard imaginable,
dissolve to form an aqueous solution of magnesium oxide.
And what's the difference here?
The difference here is, compare solvation energy, in
other words, the energy that you got by pulling this into
solution, and forming bonds between sodium and chlorine in
water, with the crystallization energy.
And what's that all about?
Well, that's the Madelung constant, remember?
Madelung constant.
q1 q2 over 4 pi epsilon 0 r, where this
is the cation anion.
And you can see here that sodium chloride has sodium
cations and chloride anions, and there's a certain binding
energy in the crystal.
Magnesium has 2 plus.
Oxide is 2 minus.
The binding energy between magnesium and oxygen is so
great that there's no driving force to dissolve.
Now, I don't expect you to be able to look at this and tell
me whether something's going to dissolve or not.
But if I were to say to you, explain why sodium chloride
forms solutions with water, and magnesium oxide doesn't,
that you could go through this rationalization.
And here's a cartoon from the textbook that tries to
illustrate this solvation.
Here you can see a crystal of sodium chloride, in the
inimitable fashion, as drawn by chemistry books, where the
chloride ion is green, and the sodium ion is blue.
And that's OK.
I can live with the color-coding, as long as we
agree amongst ourselves, these ions are clear and colorless,
because they have octet stability in
their electronic shell.
And here's water, with the hydrogen shown in white, and
the oxygen shown in red.
And you can see that the oxide end, the oxygen end, the delta
negative end of the water, is trying to wrest sodium cation
out of the lattice, and ultimately
surround it by a cage.
And the same thing here.
You see the hydrogen ends of the water trying to pull
chloride out, and ultimately surround it with
a water-like cage.
So this is the competition I was talking about.
In the case of sodium chloride, water wins.
In the case of magnesium oxide, water loses.
The binding energy between magnesium and oxygen and the
crystal dominate.
So you don't see that solvation.
OK.
Let's talk about metrics now.
Let's look at some metrics of solubility.
It's quantifiable.
So we can express a measure of solubility in terms of a
quantity known as molarity.
So we can express moles of solute per liter of solvent.
And this is called molarity, and the symbol is capital M.
So we can say, for example, a 1 molar solution of sodium
chloride in water, we'll write 1 molar NaCl, and then we'll
write subscript aq, meaning aqueous.
So it's an aqueous solution at a concentration of 1 mole of
NaCl per liter.
And the liter is named after a person, so that's capital L,
per liter of solution.
And remember, the solution is the sum of
the water plus solute.
For dilute solutions, there's very little difference between
the total amount of water and the total amount of solution.
But in certain instances, the presence of the solute
actually has a volumetric change on here.
So strictly speaking, it's per liter of solution
And as I've shown you, there are degrees of solubility.
So people represent the threshold of solubility as c
of the solute.
When c of the solute is less than about a million molar,
0.001 molar, we call this insoluble.
So something is vanishingly soluble, we
say that's the value.
So we'll call this the threshold.
And then, something that's quite soluble, we'd say that
the concentration of the solute starts to exceed at
about 0.1 molar.
And then we would say, that qualifies as soluble.
So now let's look at two extremes in solubility,
operating off of this.
So in the one case, we can have complete solubility.
So examples of that, where things are completely miscible
in one another.
Complete solubility.
By the way, some people will use the term miscibility.
When something is miscible it means it's soluble.
Same idea.
If something is insoluble, some people might say it's
immiscible.
Same thing.
OK?
So complete solubility is ethyl alcohol and water.
You can mix them in all proportions.
Continuously variable.
On the solid alloy is silver and gold.
Silver and gold, you can make alloys of any composition
between 100% gold and 100% silver.
Now, that's the exception.
Most cases are situations of limited solubility.
So they go up to a maximum, which we can denote C-star or
C saturation.
This is the maximum solubility.
So an example of something that's sparingly soluble in
water is silver chloride.
Let's look at silver chloride.
So silver chloride, I'm going to start here, silver chloride
as a crystal, and I'm going to dissolve that in water.
So that gives me AgCl aq.
So that's just simply the formation of an aqueous
solution of silver chloride.
And when the reaction moves from left to right, we call
that dissolution.
The silver chloride is dissolving, and when the
system moves from right to left, we call that--
now here I'm going to nitpick with the book.
The book calls the left reaction crystallization.
And that's correct.
It is crystallization in this case, because silver chloride
is a crystal.
But it is possible, in other systems, to have the solute
come out of solution, and make a solid that is
noncrystalline.
And you know that all crystals are solids, but not all solids
are crystals.
You can have an amorphous solid.
So what would happen if you were to bring out of solution
an amorphous solid?
It would be silly to call it crystallization.
So I prefer to use the term precipitation.
And there's another term that you can use, and I learned
this one from reading the literature of geochemistry.
What the geochemists call the reaction going from solution
to make a solid, they say the system exsolves.
This is dissolve, this is exsolve.
So this is called exsolution.
It's amazing what you can do when you know a
little bit of Latin.
So this exsolves.
So that's the exsolution, or the crystallization reaction.
Now I'm going to show you what won Arrhenius his Nobel prize.
Arrhenius did not get the Nobel prize for his brilliant
work on activation energy.
He got his Nobel prize on the theory of electrolytic
dissociation, which was, people knew that you could
dissolve salts and water, but they didn't know how.
And it was Arrhenius who said that the salts go into
solution by dissociating and forming ions.
So goes in as Ag plus Ag plus aq plus chloride ion--
thank you.
And that, ladies and gentleman, was a Nobel prize
for Arrhenius.
And you can see that there's a relationship between the
amount of silver chloride and the amount of ions.
So there's a mass balance there, that the concentration
of silver chloride dissolved, in fact, equals, in this case,
by stoichiometry, the concentration of Ag plus,
because of the nature of the dissociation reaction on a
mass balance basis.
And that also equals the concentration of the
chloride ion, OK?
So that's the way we can look at the system.
And how do we know that this thing has limited solubility?
Well, there's various ways of measuring it, and one of them
involves conductivity.
Here's the conductivity of pure water.
And you know that water has very, very poor conductivity,
and in fact, what's happening here, when we add silver
chloride is, we're adding charge carriers, because the
audience are charged species.
So they can carry charge.
And you can see that this is a measure of conductivity as a
function of silver chloride concentration.
And as you add silver chloride to higher and higher values,
the conductivity goes up.
And look at even the tiniest amount of silver chloride has
a conductivity that's about, what, half an order of
magnitude higher than the conductivity
of pure water itself.
So I would say that this is akin to doping, isn't it?
So up here, when you've got 10 to the minus 6 Siemens per
centimeter conductivity, that aqueous solution is
demonstrating the extrinsic behavior.
This is very similar to doping.
And at some point, we get to this value here, around 10 to
the minus 5 moles of silver chloride per liter, and then
adding more silver chloride has no impact on conductivity.
Which tells you that you've hit saturation.
This is akin to adding more and more sugar to the cup of
tea, until finally the sugar just falls to the bottom.
You can stir all you want, but you won't get it to dissolve,
because you've hit saturation.
So that indicates the presence of a saturated solution.
And so we can talk about that value, and we can say that for
silver chloride, the concentration at saturation is
equal to 1.3 times 10 to the minus 5 moles per liter.
Moles of silver chloride per liter.
And obviously, that's equal to, according to that, it's
equal to the silver ion concentration.
I'm going to use square brackets to indicate moles of
silver, ion per liter of solution, which
is also equal to--
pardon me-- it's also equal to the chloride ion concentration
at saturation.
Now I'm going to ask you a simple question.
Suppose I've got a beaker here, and I know the maximum I
can get here, the maximum is 1.3 times 10 to the minus 5.
Now this is a really simple question.
Suppose I am about to add silver chloride--
let's say this is 1 liter already.
All right?
I've got one liter.
And you'd tell me, well, you can put in 1.3 times 10 to the
minus 5 moles to get the saturation.
Suppose instead of 1 liter of pure water, I had 1 liter of
water already containing, say, 1 times 10 to the minus 5
molar silver chloride.
Well, that's kind of obvious, isn't it?
I'm only going to be able to put 0.3 moles in, because 0.3
times 10 to the minus 5, because I've already got
silver chloride in there.
That's easy.
Now let's make the question a little more interesting.
Suppose instead of a certain amount of silver chloride in
there, I have no silver chloride in there.
But I've got, say, 0.1 molar sodium chloride.
It's a salt.
It's a difference salt.
So the question is, does the presence of a different salt
have an impact on how much silver chloride I can put into
this solution?
And the answer is, yes.
The answer is yes.
So what we find is that the presence of the other salt, in
this case, has an impact, because sodium chloride goes
in as sodium plus, and chloride minus.
So there's already a boatload of chloride ion in there, and
that has an impact on this relationship.
So how do we answer the question, what is the
solubility of silver chloride in the presence of other
chloride ions?
And for that, we define something called the
solubility product.
And you need it in order to answer the question, how do
you determine the solubility of a solute when there are
other solutes present already?
And it's denoted capital K, lowercase sp, subscript.
Solubility product.
And it's equal to simply the ion products of the
constituents.
So the solubility product of silver chloride is the product
of the silver ion concentration, and the
chloride ion concentration.
And you know that in a solution of silver chloride
alone, if nothing else, that the concentration of silver
ion equals the concentration of chloride ion.
That's the whole business of dissolving by itself.
And so I can then just say that Ksp.
will then equal the concentration of silver ion
squared, which we also know is equal to the concentration of
silver chloride aqueous.
See, all of these are the same.
So this solubility is the same.
I can just put that in, which is just concentration of
silver chloride.
Square that.
So if I square 1.3 times 10 to the minus 5, I end up with a
solubility product of 1.8 times 10 to the minus 10.
So now I can use this in order to determine how much
solubility I get in the presence of another salt.
So in this case, I'm going to put 0.1 molar sodium chloride.
And these are strong salts, so we're going to get complete
dissociation.
Gives me 0.1 molar sodium ion, and 0.1 molar chloride ion,
when it dissociates.
Now you see the difference.
Because the silver chloride, by itself, gives me 10 to the
minus 5 molar chloride ions.
When I add sodium chloride, I get 4 as a
magnitude more chloride.
So let's go back to the Ksp.
So Ksp, this is for silver chloride.
Ksp for silver chloride is going to be equal to the
silver concentration and the chloride concentration.
And in this case, the silver concentration is just equal to
whatever that solubility is.
Because there's only source of silver ion,
and it's silver chloride.
So I can write that as
concentration of silver chloride.
That's good.
And now this one here is what?
I've got two sources.
I've got silver chloride, I I've got sodium chloride.
So it's going to equal this thing here.
0.1 plus whatever I get from silver chloride.
And it's vanishingly small, isn't it?
The concentration of silver chloride, whatever it is.
This is nothing, so I'm just going to neglect it.
It's dominated now.
The chlorine is flooded by the silver chloride.
And this product is a constant.
That's still equal to 10 to the minus 10.
So I can turn this around and solve for the concentration of
silver chloride, which is equal to the
concentration of silver io.
And that's equal to, what is it, 10 to of the minus 10
divided by 0.1, which then gives me--
what's the number here?
Plug that in.
And I end up with 10 to the 1.8 times 10
to the minus 9 molar.
Right?
So look.
Look at what's happened by having the chloride present
from sodium chloride in such a large amount.
It's repressed.
It has repressed the dissolution.
The presence of chloride then has a negative impact on
solubility, and instead of having 10 to the minus 5
molar, it's down to 10 to the the minus 9 molar.
And this effect of repressing solubility by adding a second
solute is called the common ion effect, OK?
Solubility repression by second solute is known as the
common ion effect.
And this is used in processing.
If I want to trigger the precipitation--
see, if I started with a solution containing 10 to the
minus 5 molar of silver chloride, and I throw in some
sodium chloride, it'll start
precipitating out silver chloride.
So if I wanted to make a fine precipitate of silver
chloride, I make a pregnant solution.
And I could drop the temperature, because you can
imagine that solubility is a function of temperature, or I
could keep it isothermal, throw in some sodium chloride,
and out comes silver chloride.
So since the common ion effect on it and its value in
processing.
OK.
Good.
Well, I think I'm going to hold it there.
I"ll show you just one more thing.
If you've got stoichiometry like this--
this is a difluoride of magnesium.
If it goes into solution, you get magnesium cation plus 2
fluoride anions.
And so if I wrote the Ksp for this reaction, it would be the
product of the magnesium concentration and the fluoride
ion concentration.
Because there's the two here, this is squared.
So this, too, will transfer up there, and then throw in some
sodium fluoride, and cause the other thing to exsolve, and
away we go.
All right.
I've got a couple of things to show you.
We're talking a lot about Arrhenius.
This is a book I have. It's an English translation of a book
written by Arrhenius in the late 1800s, and it was printed
in English around 1908.
And Arrhenius was a genius.
He wrote on all sorts of topics here.
Biology, physics, you name it.
And one of the things and he was interested in was the
origins of the earth.
So this chapter is called, Celestial Bodies as Abodes of
Organisms. Already speculating on whether you could have life
as we know it exist elsewhere in the universe.
And one of the things he talks about is global warming.
So this is Arrhenius on global warming.
I'll read you the last paragraph of this chapter.
There had been some major volcanic eruptions that had
caused cooling when Krakatoa in 1883 and
Martinique in 1902.
Major plumes of soot that caused dramatic decreases in
temperature.
So now here comes the last paragraph.
We often hear lamentations that the coal stored up in the
earth is wasted by the present generation--
remember, this is written 100 years ago--
without any thought of the future.
And we are terrified by the awful destruction of life and
property which is followed the volcanic eruptions of our day.
We may find a kind of consolation in the
consideration that adheres in every other case.
There is good mixed with the evil.
By the influence of the increasing percentage of
carbonic acid in the atmosphere-- that's CO2--
we may hope to enjoy ages with more equitable and better
climates.--
Remember, he's a Swede; it's cold--
especially as regards the colder regions of the earth,
ages when the earth will bring forth much more abundant crops
than at present for the benefit of
rapidly propagating mankind.
So it's interesting to see the world--
it's a great book to read.
And you can see people in the 1830s were already calculating
heat transfer coefficients to how much
the earth was changing.
We're going to post these to the website.
This was, last year, in the New York Times.
Every Tuesday they have a science section.
And this was about glass.
And very, actually, with your 3.091 knowledge, you'll read
this like a newspaper, and it'll be very easy.
And they go through the structure.
Here's the structure of a window glass.
You can see the network, former network
modifier, and so on.
And they talk about how difficult it is from a first
principle's standpoint to model the structure of glass.
These oxide glasses are complex and not easy to model.
So when you're trying to engineer the glasses, instead
of trial and error, it's hard to do so by theory.
And it talks about some efforts at theory, and so on.
And the last thing I want to talk about is
bulk metallic glasses.
You recall that I showed you metallic glass that was made
by melting gold silicon, and dripping it onto a
water-cooled copper wheel that was zooming around to give us
a cooling rate of about a million degrees a second.
And those strips had to be very, very
thin, the metal strips.
Because you've got liquid dripping down, and we're
pulling the solid away, and there's a
finite thickness here.
Let's use a Greek letter, xi.
There's a finite thickness xi.
Because what's happening is that this is the water-cooled
copper wheel, and you're extracting heat here.
But eventually, the thermal conductivity of the metal is
the limiter.
In other words, I don't care how cold.
You can put this in liquid helium if you want.
You can't get the heat through the metal fast enough.
And what happens is, when you look down here, the lower part
is amorphous and the upper part is crystalline.
So you don't end up with metallic glass.
You end up with some metallic glass, and the upper part is
crystalline.
So what happens when you end up with the limitation being
the thermal conductivity of the metal?
At that point, you're finished.
And this was typically on the order of microns.
And then they got up to, sort of, submillimeter.
And that was it.
So the glass that I showed you was foil.
Now what happened was, with more research--
so here we are.
This is Pol Duwez at Caltech, gold silicon.
And this is the thickness in centimeters.
So you were down here at some tens of microns, all right?
Now, in the '60s, research at Harvard uncovered a set of
palladium alloys that had better thermal conductivity
and, remember the first day, about the analogy to the
musical chairs?
These things have slightly more complicated crystal
structures.
So for a given cooling rate, the metal has more difficulty
finding the proper lattice site.
And they were able to make metallic glasses that were on
the order of 0.1 centimeters.
That's still fairly thin.
And then back to Caltech in the late '80s, early '90s, and
a man by name of Bill Johnson was able to develop a set of
alloys that can be made in bulk form.
Totally amorphous metal.
And these are known as bulk metallic glasses.
And look at the complexity of the alloy designation.
So now you see, well, why are they doing this?
Because look, this is strength versus elastic limit.
So you can either have things like polymers, that you can
stretch very, very far, but they don't have much strength.
Or you can have things like certain steels, that are very,
very strong, but you can't bend them very far.
And bulk metallic glass has put you right up here.
You have strong alloys that have very, very
high elastic limits.
So they make great golf clubs and tennis rackets and so on,
because they can flex way back, store enormous energy,
and then spring.
So here are some bulk metallic glasses, and
here's a classic one.
This is zirconium, titanium, copper, nickel, beryllium.
All right, now how do we get that?
Well, zirconium and titanium are body-centered cubic, we've
got copper and nickel are face-centered cubic, and
beryllium is hexagonal close-packed.
So the idea here is the principle of confusion.
So the alloy is fighting with itself.
You know, am I face-centered cubic, am I body-centered
cubic, am I hexagonal?
And this confusion about what the crystal structure is to be
leads to quenching and the disorder of a liquid state,
and preventing the formation of grain boundaries,
dislocations and so on.
So I want to show you one example besides golf clubs.
Dave, could we cut to the document camera here?
Get this thing down.
So this is a--
I'm not endorsing the product at all, but you know, this is
one of the companies that makes, this
is SanDisk, I think.
And they make these flash memories.
This just looks like a another piece of metal, and in fact,
it's very disarming, because they call
this model the Titanium.
Well, it has about 13% titanium.
The interesting thing here, what's so cool about this,
this is bulk metallic glass.
And what's attractive about the fact that it's bulk
metallic glass is, that it can be shaped by casting, from the
liquid state to very, very fine precision.
So you see all of these slots and everything, and on the
side, all of this kind of stuff, and on the end.
All of this is done by casting from the liquid
state, in one operation.
And this is a clam shell.
There's two pieces here.
I don't know if you can see, but there's two pieces that
have been sandwiched together.
You can see on the edge there.
And the impact that has on manufacturing costs is
phenomenal, because normally you make the basic shells,
then you have to drill, and you've got to
auger out, and so on.
This thing, one step operation,
including the labeling.
There's no subsequent processing.
And this is done by a company out in Michigan
called Liquid Metal.
And they've licensed the technology and so on.
And again, I'm not trying to make a commercial thing, but
I'm just trying to show you that these ideas of changing
properties for engineered materials, you know, are
around us everywhere.
And this is relatively recent.
Bulk metallic glass.
Fantastic example of structure property relations.
OK.