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Lecture Comments (4)

1 answer

Last reply by: Professor Hovasapian
Fri Mar 25, 2016 10:34 PM

Post by Tania Bore on March 21, 2016

How did you get the conversion factor from IPr to liters?

1 answer

Last reply by: Professor Hovasapian
Sat Jan 11, 2014 5:32 PM

Post by Angela Patrick on January 11, 2014

Does the phase diagram for water say that at any temperature past the triple point (say 10 degrees celsius) water is incapable of becoming a solid?

Phase Diagrams & Solutions

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Phase Diagrams and Solutions 0:22
    • Definition of a Phase Diagram
    • Phase Diagram Part 1: H₂O
    • Phase Diagram Part 2: CO₂
    • Solutions: Solute & Solvent
    • Ways of Discussing Solution Composition: Mass Percent or Weight Percent
    • Ways of Discussing Solution Composition: Molarity
    • Ways of Discussing Solution Composition: Mole Fraction
    • Ways of Discussing Solution Composition: Molality
    • Example 1: Question
    • Example 1: Mass Percent
    • Example 1: Molarity
    • Example 1: Mole Fraction
    • Example 1: Molality

Transcription: Phase Diagrams & Solutions

Hello, and welcome back to, and welcome back to AP Chemistry.0000

Last time, we talked about heating curves and changes of state.0004

Today, we are going to introduce something called a phase diagram--a very, very important diagram in chemistry.0009

And we are going to also continue our discussion of solutions.0016

Let's just jump right on in with the notion of a phase diagram: we are going to do two phase diagrams today--we are going to give you the one for H2O, and we're going to give you the one for CO2.0019

As it turns out, each one of these is actually unusual in its own way; but because carbon dioxide and water are such ubiquitous substances--things that we use all the time--these are the ones that we want to concentrate on.0030

OK, so let's go ahead and...well, let me actually write down what a phase diagram is, and then I'll start out with the one for water.0045

Let's see: A phase diagram shows which state (in other words, solid, liquid, or gas) exists (not at which--I should say "at a given"--you know what, I really think I had better stop abbreviating things and just write my words out; OK) at a given temperature and pressure.0061

So, we have temperature on the x-axis, and we have pressure on the y-axis, and the different values tell you what state the particular substance is in.0106

Here is what it looks like; so we are going to do the one for H2O now--so let's go ahead and do that.0114

Actually, you know what, I'm going to need a little bit more room on the left, so let me go over here; so that is that...and something like that.0123

Once again, we have temperature (which is in degrees Celsius), and here we have pressure (it could be in torr; it could be in atmosphere; I'm going to go ahead and do atmospheres here, if I'm not mistaken; there we go).0134

OK, so now, here is what happens--what you get is something that looks like this.0153

Put this a little bit higher here...and I'm going to drop this one just a little bit.0169

OK, this is something...I don't know...a point...0175

This is the solid phase; this is the liquid phase; and this is the gas phase; so this is temperature, so at different temperatures and different pressures, your substance (in this case, water)--sometimes it's going to be ice; sometimes it's going to be water; sometimes it's going to be steam.0180

All right, now let's actually label some of the most important points here.0207

When is 1 atmosphere: so, as it turns out, at 1 atmosphere, this is going to be the boiling point.0214

So, the boiling point is going to be 100 degrees Celsius: at 100 degrees Celsius and 1 atmosphere, it is...the phase changes between liquid and gas; that is what that is.0243

OK, now, at 1 atmosphere and 0 degrees Celsius (we drop this down), we have the melting temperature, which is 0 degrees Celsius; at this point, what you end up with--at 1 atmosphere pressure and 0 degrees Celsius, the phase change is going to be solid to liquid, ice to water; that is what this is.0259

All right, so now, let's have some other interesting points here.0290

There is a point here: I'll put it right there and I'll put it right here, and I will do this--I will put Tc, and I will put Pc.0297

Pc is something called the critical pressure, and Tc is exactly what you think--it's the critical temperature.0311

Well, something very, very interesting happens.0322

Oh, wait, let me mark off one other point here: this one and this one--this is a very, very important point.0324

We signify this as T3 and P3; this is called the triple point pressure and the triple point temperature.0336

At this pressure and at this temperature, all three phases exist simultaneously.0345

You can actually have ice, water, and gas all in equilibrium with each other, in a dynamic equilibrium; all will coexist.0351

It has to it turns out, this critical pressure is 0.0060 atmospheres, and the critical temperature is 0.0098 degrees Celsius.0359

That is called the triple point--let's actually write that up here: T3...I'll do a slash...P3...this is called the triple point, and the triple point is where all three phases (gas, liquid, and solid) exist simultaneously.0376

So now, let's talk about Tc and Pc.0396

If I keeping raising the temperature, raising the temperature, and then increasing the pressure and increasing the pressure, something very, very interesting happens.0402

There comes a point where, at a certain pressure and at a certain temperature (in this case, it's going to be 374 degrees Celsius, and here at 218 atmospheres of pressure for water), at which point...there actually...I don't even know how to describe this.0410

There is, all of a sudden, no longer a difference: you don't have enough pressure to actually liquefy.0432

You see, if you keep raising the pressure of this, everything is just going to keep turning into a gas.0439

But, if you keep applying pressure to the system, you can keep turning that gas into a liquid, into a liquid, into a liquid.0443

At some point, you are going to reach a temperature beyond which, no matter what pressure you exert on that system, that gas will not turn into a liquid.0449

But the problem is, it is not a gas anymore, either; it is actually something called a supercritical fluid.0458

It is not a liquid, and it is not a gas; you can consider it, if you will, a fourth phase, because supercritical fluids (things at higher than critical pressures and higher than critical temperatures)--they have some very, very bizarre properties.0464

When I say bizarre, I mean very, very bizarre; you are welcome to either read about them in your books or look them up on the Internet--some really, really amazing things are happening.0480

It's a very fascinating field of chemistry and physics, working at supercritical temperatures and supercritical pressures.0490

Now, that is why this line literally stops here: it is not a gas; it is not a liquid; it is what they call a supercritical fluid.0498

It is like a totally different state of matter, and it behaves in profoundly bizarre ways.0509

That is it: that is called the critical temperature and critical pressure.0515

This is what it looks like for water: now, notice something really, really interesting here: notice that the slope here is actually negative.0520

For most substances, the slope is positive; and the reason it is positive for most substances is: most substances, as the thing becomes a solid--it actually gets more dense.0531

So, as something goes from a liquid to a solid, it becomes more dense--it becomes more tightly packed, as you would expect.0544

But water is different: when water freezes, it actually becomes less dense; it's the reason why ice floats.0550

Because of that density difference between liquid and solid, this has a negative slope.0557

It is not like that for CO2: CO2, in this case, behaves normally, because solid CO2 is more dense than liquid CO2, as you would expect.0563

But water does not behave the way we expect it to behave; that is why this is different.0574

That is it; this is a standard phase diagram; it expresses, at a particular temperature, at a particular pressure, what phases are going to exist--and, of course, the relationships.0581

We have this triple point; we have this critical temperature, critical pressure; that is it.0592

OK, so now, let's do the one for CO2.0600

CO2: OK, so let's go again here and here; so once again, we have temperature, which is going to be in degrees Celsius; we have pressure, which is going to be in atmospheres.0607

And now, we have something that looks like this.0624

This is solid; this is liquid; and this is gas.0638

OK, 1 atmosphere is actually here for CO2; so, at 1 atmosphere pressure, the temperature at which solid becomes a gas is -78 degrees Celsius.0647

So, at -78 degrees Celsius, solid carbon dioxide actually turns into a gas under normal, standard conditions of 1 atmosphere pressure.0667

It sublimes; that is why we call it "dry ice"--it doesn't actually get wet.0677

It goes directly from the solid to the gas phase; it doesn't pass through the liquid phase on its way.0680

1 atmosphere is here for solid CO2.0686

The triple point of CO2 is P3 is equal to 5.1 atmospheres, and I will say the critical pressure is equal to 72.8 atmospheres--very easy to attain--72.8 atmospheres is very easy to do in the lab on a daily basis.0691

We don't really need any specialized equipment for that.0718

The critical temperature is 31 degrees Celsius--again, it's very, very easy to attain a supercritical fluid (supercritical CO2).0722

You raise the temperature to 31 degrees Celsius or a little bit higher, and then you just bring it to 72.8 atmospheres or higher, and you are in this range, where you can't tell the difference.0731

Is it a liquid? Is it a gas?--who knows: it's neither; it's both; it's a supercritical fluid.0740

Just for good measure, we will go ahead and talk about the triple temperature, the triple point, which is -56.6 degrees Celsius.0747

OK, so again, what is important to notice here is that, at 1 atmosphere pressure, which is normal conditions, CO2 sublimes.0761

"Sublime" means going straight from solid to gas phase.0776

That is what this is telling us here; and, as you see, you have a positive slope, because solid CO2 is more dense than liquid CO2, so there isn't any strange behavior.0781

But again, if you were to raise the temperature to, let's say, I don't know...I'm sorry, raise the pressure to 20 atmospheres, and then raise the temperature to...oh, I don't know, maybe 20 degrees Celsius, you will actually get liquid carbon dioxide.0793

I have never seen liquid carbon dioxide, myself; there you go--but it is possible: the phase diagram tells me so.0810

Actually, you can go to any fire extinguisher and just shake it up; that is liquid carbon dioxide.0819

OK, in fact, I will discuss that right now.0825

At 25 degrees Celsius and high pressures (pressures in the range of about 5.1 to 72.8), CO2 is a liquid and used in fire extinguishers.0830

When you open up the valve of a fire extinguisher, the liquid CO2 is all of a sudden exposed to 1-atmosphere conditions.0863

It immediately vaporizes--it immediately turns into a gas.0874

CO2 gas is heavier than air--it actually sinks; when it sinks, what it does is: it actually ends up smothering the fire.0878

It covers it up like a blanket; it literally just smothers it--sits on top of the fire.0887

And, because it is sitting on top of the fire, oxygen gas can't get to the fire; that is how it puts a fire out.0892

Not only that--in the process of going from liquid to vapor, that is actually an endothermic process; well, the energy for that endothermic process is coming from the surrounding air, so it's literally sucking heat out of the air.0900

So, what we feel is cold: because it is cold, that is even...that actually helps to retard the fire even more.0916

You have cooler temperatures, and you have no oxygen getting to the flame.0924

OK, as far as seeing fire extinguishers and looks like you are actually blowing this white smoke at people (or at the fire); that white smoke is not carbon dioxide; that is the (because of the cold temperatures) water in the air, in the atmosphere, that is actually spontaneously condensing.0930

In other words, what you are doing is: you are forming a cloud, right here on the ground; that is it--that is what is going on there.0954

OK, so this was phase diagrams; I just wanted you to sort of see what they are.0960

You will see them on the AP exam; you will see them in your future work; so it's just good to know what they are.0965

All right, now let's go ahead and start talking about solutions.0972

Today, we are just going to talk about...I'll give you a brief introduction to solutions; we are going to talk about the different ways to actually represent solutions.0978

We are going to talk about molarity, mass percent, molality, mole fraction...things like that: the different ways of representing concentration.0985

Up until now, when we say "concentration," we are talking about moles per liter.0992

Well, it's true--the primary unit of concentration is moles per liter--but there are other ways to represent concentration, or the mixture of a solution--how much of a solute is in a solvent.0997

OK, so let us define what we mean by a solution: it is just a homogeneous mixture--that is it.1009

You take some salt; you drop it into water; you stir it up; and all of a sudden, you have a salt solution.1021

Salt is your solute--it is the thing that dissolves; water is your solvent--it's the thing that does the dissolving.1027

That is it.1033

So, a solute is the thing being dissolved, and the solvent is the medium doing the dissolving.1035

The medium...we are mostly going to be concerned with liquid solvents; it doesn't have to be a liquid...the medium doing the dissolving.1054

For example, the soda that you drink--the Coke, the diet Pepsi, the Sprite, things like that: actually, the solvent is water; the solute is actually a gas--it's carbon dioxide gas under high pressure.1071

When you put that under pressure, the carbon dioxide actually dissolves in the water; so you have a gas which is a solute, not a solid like salt.1083

Air--the air that you breathe--it is basically just oxygen gas that is mixed in with nitrogen gas: it is a solution--that is what it is.1094

OK, so let's say a sugar solution (just as a quick example): the sugar is the solute, and the water is the solvent.1106

OK, now, ways of discussing solution composition: how can we numerically represent how much of a solute is in our solution?1127

Well, here is how we do it--composition: OK, the first way is by something called mass percent.1151

Or, you will often see it as weight percent.1165

It is (so the mass percent), these definitions are very, very precise.1172

It is the mass of the solute, divided by the mass of the solution; OK, the mass of the solution is the mass of the solute, plus the mass of the solvent.1181

The total mass of the solution, times 100: that is mass percent.1200

The second one (you already know) is molarity: it is the most common unit used to talk about concentration; it is moles of solute per liters of total solution (liters of solution--total volume--the volume of the solute and the volume of the solvent).1210

Because, again, even if it is a solid solute, that stuff has volume, it actually makes the volume bigger.1243

OK, the third one is something called mole fraction, and there is actually a symbol for it: it is the Greek letter chi.1251

The mole fraction of A is equal to the moles of A, divided by total moles.1260

So, if we happen to have 2 things...well, let's say we want to do the mole fraction of sodium chloride solution...or sugar solution (let's just take sugar; let's stick with sugar): I take the moles of sugar, divided by the total moles (the moles of sugar, plus the moles of the water).1277

It's a fraction: a fraction is always a part over the whole.1295

That is all this is--nothing that you don't already know.1299

And last, something called molality (not molarity, but molality): it is actually equal to the moles of solute (this is an interesting one) over kilograms of solvent.1303

Notice how these two are actually separate: solute and solvent.1323

OK, well, let's just do an example.1328

Example: A solution is made by mixing 2.5 grams of isopropanol with 100 grams of H2O.1332

The density of C3H8O is 0.786 (the C3H8O is the isopropanol, which, by the way, looks like this, in case you want the structure--there is another H here).1366

It is a 3-carbon chain, and in the middle carbon, it has a hydrogen attached to it; it also has a hydroxide attached to it; so that is isopropanol--that is basically rubbing alcohol, is what that is.1390

OK, grams per milliliter...your task is to express the concentration in the four different ways described above.1402

Now, I have to say: some people are kind of sticklers about this; when they say "concentration," they are speaking strictly about moles per liter.1430

But concentration, in its generic term, means how much of a solute is in a particular solution.1437

So, any of these could actually be used for concentration; so it just depends on what we are talking about.1443

If somebody talks about concentration, it is always good to ask, "What unit are we using? Are we using molality? Are we using molarity? mole fraction? mass percent? Something else called normality?" (which we won't discuss)--what?1448

OK, so once again, we have 2.5 grams of isopropanol, which is a liquid, mixed with 100 grams of H2O, also a liquid.1462

All right, so let's go ahead and do our first one, which is mass percent.1472

#1, which is mass percent: well, we said that mass percent is the mass of (let me just write it again) the isopropanol, over total mass, times 100.1476

Well, what is the mass of the isopropanol?--it is 2.5 grams.1496

What is the total mass?--well, the total mass is 100 grams, plus the 2.5 grams, times 100; so it's 2.5/102.5; you end up with 2.44% by mass.1499

2.44% by mass, 2.44% by weight; that means that, if I have 100 grams of that substance, 2.44 grams of it is going to be isopropanol.1518

If I have 50 grams of that substance, 1.22 grams is going to be isopropanol.1534

2.44% of any particular amount is going to be isopropanol; the rest of that solution is going to be water.1541

It is an expression of how much solute there is in our solution.1549

OK, #2, molarity: Well, molarity is the moles of isopropanol, over liters of solution.1553

So, here we have some conversions that we need to make.1570

Let's talk about moles of solute first: moles of isopropanol--well, we have 2.5 grams, and 1 mole of isopropanol is 60 grams; so we end up with 0.0417 mol; so we have the numerator.1573

Now, H2O: well, 100 grams is 100 milliliters, equals 0.100 liter (because water is 1 gram per milliliter in general--it's at 4 degrees Celsius, but not a problem).1593

Now, isopropanol (here we are doing volume): isopropanol--we said we have 2.5 grams, and we said that 1 milliliter of that is 0.786 grams.1611

So, what we have here is 3.18 milliliters, which is equivalent to 0.00318 liters.1631

Our molarity is equal to the moles, 0.0417 mol, divided by this plus this; 0.10318 liters, and we end up with 0.404 molarity.1644

That means, for every liter of solution, it contains .404 moles of that isopropanol.1673

OK, let's see...mole fraction: so, the chi of the isopropanol is equal to, again, the moles of the isopropanol (which we got from the previous one), over the total moles.1685

OK, so we said that our isopropanol contained 0.0417 mol.1711

Let me write these a little bit better here: 0.0417 mol.1720

H2O, on the other hand: we have 100 grams of it, and 1 mole of H2O is 18 grams; we end up with 5.56 mol.1728

Therefore, our chi of isopropanol is equal to 0.0417 mol, divided by 5.56, plus 0.0417; you end up with 0.0074 (I hope you'll forgive me if I don't write 7.4x10-3--I am actually not a big fan of scientific notation, myself--I prefer decimals).1743

That is the mole fraction.1773

And last but not least, molality (which will show up again when we discuss the colligative properties--boiling point, elevation, freezing point, depression, osmotic pressure, vapor pressure of solution, things like that): it is the moles of solute (oh, actually, let's just go ahead and...because we are dealing with isopropanol, let's just say "moles of isopropanol"), divided by the kilograms of water.1777

This is the one that is actually different; you are not actually combining things in the denominator--separate solute and solvent.1804

It equals 0.0417 mol, divided by 0.100 kilogram (right?--100 grams, .1 kilograms), equals 0.417 molal.1810

We say, for molarity, Molar; for molality, we say molal.1832

There we go.1836

OK, so these are the four ways that you are going to see concentration talked about.1840

In this particular chapter, we are going to talk about molarity mostly, but we are also going to be talking about molality, because again, when we discuss vapor pressure and the colligative properties in the next lesson, as it turns out, the mathematical expression requires that the concentration be expressed in molality.1845

So, I will go ahead and stop it there, and next time, we will discuss vapor pressure of a solution, and begin discussing colligative properties; and we will finish off our discussion of solutions.1863

Until then, thank you for joining us here at

We'll see you next time; goodbye.1875