Biochemistry Dilution & Osmotic Pressure

Hello and welcome back to Educator.com, and welcome back to Biochemistry.0000

So, the last lesson, we started a review of some general chemical principles that are going to lay the foundation for the work that we do in biochemistry.0004

For the next couple of lessons, we are going to continue that.0012

Today, we're going to be discussing dilution and osmotic pressure.0015

The notion of osmosis is profoundly important in biological systems.0019

The cell is a semi-permeable membrane, and the relationship that a cell has with its surroundings outside the cell, inside the cell, is all based on the difference in concentration; so, osmosis is huge in biological systems.0025

OK.0042

Let's just go ahead and jump in.0043

Let's begin with dilution.0047

You all know from experience what dilution is.0051

Basically, you are changing a given concentration by the addition of solvent.0054

If you have some solution and it has a certain concentration, if you add more solvent to it, the concentration of the solute is going to diminish; because remember, molarity is moles of solute over liters of solution, right, mol/L.0081

If the number of moles of solute stays the same in there, but all of a sudden I up the liters of solution by adding more solvent to it, well, this is a fraction: as the denominator increases, the concentration decreases.0104

That is what dilution is.0117

OK.0121

Once again, you want to change a given concentration by the addition of solvent.0122

You are trying to dilute the solute.0126

Let's go ahead and do an example.0129

This is a very, very important example.0134

This is something that all of you are going to do at one time or another, if you haven't already.0137

A student is given a stock solution - let me erase this, actually - of hydrochloric acid which is 11.8mol.0142

How can he prepare 500mL of a 1.5M HCl solution from this stock?0176

Basically, he has this solution which is 11.8mol but what he needs is, he needs to create 500mL of 1.5M, so, how is he going to do this?0203

Let's think about what he is going to do.0217

Basically, what he needs to do is put in a certain amount of stock solution of a given molarity, and he needs to dilute that by adding water, bringing it up to 500mL, and then making sure that that 500mL is 1.5M.0220

The question becomes, "How much of the stock is he actually going to pull out of the stock solution to put into this beaker, and then on top of that, add the water to bring it to 500mL, to turn this into a 1.5M solution?".0244

That is what we are doing here.0258

OK.0260

The basic dilution equation is as follows.0261

The basic dilution equation says that the initial molarity of something times its initial volume is equal to its final molarity times its final volume.0271

This is also written as m₁v₁ = m₂v₂.0285

This M is molarity, not mass - very, very important.0304

The molarity times the volume that we start off with, in other words, of the stock solution once we've diluted it, the final molarity, the final volume- this is the equation that we want to work with.0306

Again, we're concerned with - let me go to red - we want to know how much stock do we have to pull from the stock solution to dilute that up to 500mL.0318

That is what we are trying to do.0330

OK.0332

Well, Let's take a look at what it is that we actually have.0333

We know that we need this, this, this and this.0336

Of course, with any equation that has four different parameters, you can be given any of the other three, in order to find the fourth.0341

The problem itself is going to dictate which parameter that you are actually looking for.0346

In this case, let's see what it is that we have, and then we'll find out what parameter we need.0352

Well, we know what the final volume is going to be so the final volume, that one equals 500mL or 0.5l depending on which units you're going to use, as long as the units are consistent.0357

We have the final volume, and we also have the final molarity.0372

We are looking for a solution which is 1.5M.0377

I'm just going to make my M the way that I'm comfortable doing it.0386

Here, how's that?0388

Our final molarity is going to be 1.5M.0389

OK.0395

What's our initial molarity?0397

We are using a stock solution.0400

The initial molarity is 11.8mol, so, that's going to be 11.8.0402

The only thing that we are missing is the initial volume.0408

In other words, I need to find how much of the stock solution I'm going to dilute to 500mL.0412

I'm going to put in a certain amount of stock solution that's this, my initial volume of my stock; and on top of that, I am going to add water to bring that final volume to 500.0419

So, that is what I do.0429

Well, This is nice and easy, very basic equation.0431

We will just go ahead and put it in.0433

So, we have initial volume times initial molarity, which is 11.8 equal - you know what I'm going to do, I'm actually going to use the units here and because I want you to see what cancels and what doesn't.0436

So we have V_i x 11.8mol/L, that is the initial volume; and molarity is equal to the final volume, which is going to be 0.500L because we are dealing with moles per liters, so the units have to match so that they can cancel, and the final volume, that's this one.0450

The molarity is 1.5mol/L.0478

I just switched them around.0483

Here, I have M first and V second; here I have V first and M second.0485

Sorry about that.0490

I hope that doesn't confuse you.0491

That is it, now, let me go ahead and solve for my initial volume.0492

V_i is going to equal 0.0636L or 63.6mL.0498

63.6mL is the amount of stock solution that I am going to pull,0510

I'm going to add that to a beaker, and then I'm going to bring the volume up.0518

Let me go ahead and write out the procedure.0521

Take 63.6mL of stock solution, stock HCl and pour into a volumetric flask.0529

I'm sorry, a 500mL volumetric flask.0547

Now we want to be as precise as possible, I mean you can use a beaker if you want but again, you are trying to create a solution, so, you want to use a 500mL volumetric flask.0551

Those are flasks that are specifically calibrated to create a very, very accurate volume: 500mL, 250mL, 1000mL, 50mL.0560

They have a certain mark on them to tell you where to stop adding water; at that point, you are exactly where you should be.0571

So, you pour this 63.6mL of stock into a 500mL volumetric flask, then add solvent, add water until the mark, which is 500mL and then just mix thoroughly.0578

There you go.0606

That's it.0607

The dilution equation: the initial molarity times the initial volume equals the final molarity times the final volume; therefore, parameters here, in order to find the one that you want, you have to have the other three.0611

That's it.0626

OK.0629

Now, the idea behind this equation m₁v - let me write the equation again, let me go back to black here- the idea behind this m₁v₁ = m₂v₂, is that when you're diluting something, when you're adding solvent to something, you're not changing the solute amount.0630

The amount of solute, whether it's floating around in 100mL of solution or floating around 1000mL of solution, it's still the same amount that is floating around in solution; there just happens to be a hell of a lot more solvent now in which it can float around, so the number of moles of solute actually stays the same.0654

That's what this equation is based on.0674

Let me write this as mol/L x L = mol/L x L.0677

What liter cancels, leaving you the initial number of moles, is going to equal the final number of moles.0687

That's the whole idea here.0692

That's what this equation is based on.0695

The amount of solute doesn't change.0696

The moles of solute floating around are the same.0698

The only thing that changes is the volume.0701

Given this, I am going to go ahead and do this problem again in an alternate way just for that sake of doing it in an alternate way.0704

I personally do it this second way.0713

I don't use the m₁v₁ equation, but I know a lot of kids actually prefer the M in equation to work with; but I think about it like this in terms of keeping the amount of solute constant.0715

This is going to be example two, and let me do this one in blue, and either procedure is fine.0727

Different people find different ways of looking at a particular problem, but it's nice to know, in this particular case, we can give you an equation and you can work with it.0735

But, if you know it's actually happening underneath, if you know that it's based on the fact that the moles are the same, then you have another way of thinking about it.0747

You can reason it out stoichiometrically.0753

Well, what is it that we wanted?0762

We want 500mL of a 1.5M HCl solution.0764

OK.0774

That means, we are going to concern ourselves with moles- 500mL of 1.5M solution, so that's 0.5L x 1.5mol/L.0776

That means, we need to have 0.75mol of HCl floating around in our solution.0791

Well, 0.75mol of HCl x 1L, our stock solution has 11.8M of HCl floating around per liter.0802

When I do this division, I get 0.0636L or 63.6mL of stock solution.0819

This tells me that I need 63.6mL of stock solution.0832

I put that in a beaker or volumetric flask.0840

I add enough water to bring it to 500mL.0842

Now, I've created my 1.5M HCl acid solution.0845

It's based on the fact that all I've added is solvent.0849

The solute concentration, the amount of HCl floating around, is constant; and I've just done it that way.0853

I've gone from volume into molarity to moles, and then from moles, using molarity, back to volume.0860

That's it, so it's just an alternate way of doing it.0865

OK.0869

That is dilution- very, very, very important.0870

Now, let's go on and discuss a new topic.0876

I'm going to discuss colligative properties.0882

Of the colligative properties, we're really only going to be concerned with one of those properties- osmotic pressure.0885

That is going to be the thing that is most important in biological systems.0888

Let me just start off with some basic definitions, and then we'll jump in to osmotic pressure and do some examples.0893

OK.0898

I think I am going to actually go forward one page here.0900

The colligative properties are properties of a solution that depend only - very important - only on the number of free particles of solute floating around in solution, not the identity of the particles.0903

The colligative properties are certain properties that a solution has that is based strictly on the number of things that are floating around in there.0910

Let's say if I create a sugar solution and there's a certain amount of sugar molecules, let's say 500 sugar molecules floating around in a certain volume of solvent, that's just a sugar solution with 500 particles of sugar.0928

Well, let's say I take another molecule, whatever it is, some protein, and I have 500 protein particles floating around in that solution; well, that solution is going to behave the same way simply because there are 500 of each particle.0933

It's the number of particles that matters; it doesn't matter whether it's sugar or salt or glucose or protein or something else.0952

The colligative properties don't care about what the identity of the species is.0959

All they care about is how many of those particles are floating around freely in solution, running interference with that solvent, because now the solvent isn't pure anymore.0965

It isn't just solvent molecules interacting with each other, it's solvent molecules that have a bunch of things floating around in it; and those things, the fact that they are there, they change the property of the solvent.0973

OK.0984

I should say one thing, but recall, very, very important: covalent compounds and soluble ionic compounds do not dissolve the same way.0986

Covalent compounds, it's one for one; one covalent compound dissolved and becoming aqueous releases one free particle, but as salt dissociates it to free particles - so it just depends on what the salt is made of- when it dissociates one unit of salt, sodium chloride produces two particles.1079

One unit of magnesium chloride produces three particles.1099

One unit of aluminum chloride produces four particles.1103

It's the total number of particles that are floating around that affect the colligative particles.1108

Now, and again, I'll just repeat what I just said.1122

One molar glucose solution has 6.02 x 10²³ free particles floating around in there; however, a 1M magnesium chloride solution has 3 x 6.02 x 10²³ free particles.1129

This is what we have to remember: what is it actually that we're dissolving, what is the solute.1165

If it is an ionic compound that dissolves, we need to keep track of the number of things that it is actually producing, number of free particles that are floating around.1172

If it is covalent, it's just one; it's not a problem.1179

OK.1183

Pure water has certain properties, for example, its boiling point.1188

We know that water boils at 100°C - pure water.1203

It has a freezing point at sea level by the way, which again, we are here, we are not up in space or down under the earth or anything.1212

We know that water freezes at 0°C.1224

It has a vapor pressure of 24 Torr, Torricelli, or 24 mmHg - it's the unit of pressure.1230

I'll just go ahead and write Torr at 25°C.1245

If I take a glass of water and I cover it up, well, at 25°C, some of that water is actually going to escape into the gas phase because it's not going to be just pure liquid.1257

There is enough motion, there is enough heat, there is enough energy in the water to actually kick off some of the water molecules in the gas phase.1267

Here, let me draw this out.1276

This is the liquid water; however, some of the water molecules are going to escape in the gas phase.1279

The ones that are here in the gas phase, they're bouncing around the walls of the glass; they create a certain pressure- that's what the vapor pressure is.1288

At certain temperature, there are certain parts of the solvent that actually exist in the gas phase in equilibrium with the liquid phase.1298

It contributes a little bit of pressure- that's what vapor pressure is.1309

It's not going to concern us, but I just thought you should know where this comes from.1312

OK.1317

Now, here is the interesting part.1318

Adding a solute - in other words, free particles - changes the values of these properties.1323

So, just by virtue of dropping in some salt into water, all of a sudden I change its boiling point now, of the solution.1349

Now, the solution has a new freezing point and it has a new vapor pressure.1355

Now, the solution has a new boiling point, freezing point and vapor pressure.1363

OK.1380

Now we come to osmotic pressure.1381

Adding a solute to a pure solvent- in other words creating a solution - it creates a new property for the solution.1385

That property, we call osmotic pressure.1419

And, this is what we are going to talk about now, osmotic pressure- profoundly, profoundly important in biological systems.1426

Osmosis is ubiquitous in biological systems.1432

Well, I'll go ahead and talk about it now and we'll talk about it more biologically later.1439

Here is what happens.1443

I'm going to draw something here.1444

I'm going to take a little bit of something called a "U tube", something like that.1448

It's just a tube that is in a shape of a U, and down at the bottom, I'm going to have something called a semi-permeable membrane.1457

OK.1468

Let me go ahead and label that.1470

This is a semi-permeable membrane, and what that means is that solvent molecules can pass back and forth through that membrane, but solute molecules cannot pass.1472

It's like a filter is what it is: allows certain molecules to pass, others not to pass.1484

In this case, it allows the solvent itself to pass but nothing else.1489

So, this is a semi-permeable membrane- like a cell wall.1497

This is the model for a cell wall.1503

A cell wall is a semi-permeable membrane; certain things can pass naturally, other things cannot pass without being given permission.1508

OK.1516

On one side, I have pure solvent.1517

This over here, this is going to be pure solvent.1521

Over here on this side, this is going to be the solution.1528

And of course, because it has solution, I'm going to use Xs to designate solute particles, so we have a bunch of solute particles floating around in that solution.1537

OK.1547

Here is what's interesting.1548

I was going to go ahead and write this out, but I think I'd rather just say it and describe it because I think it'll make more sense.1550

Now, with this semi-permeable membrane, when I create this situation, and now, here is what happens.1555

Intuitively, you have a sense on what's going to be going on.1562

These solute particles, there's a whole bunch of particles here in this solution and there's nothing over here.1565

By nature, these solute particles are going to try to distribute themselves evenly across all of these volume that they have available, but this is a semi-permeable membrane, these solute particles can't pass through this membrane, so what happens is that it actually induces water from the solvent side, that way, it actually pulls water into it in order to dilute this until there is an equal distribution.1571

However, as water passes into this compartment, well, this water level is going to drop because water is passing and it's going to reach a new level.1600

Actually, let me do this in red.1614

This water level is going to drop and it's going to come down here, and of course this water level is going to rise until it comes to about here.1623

OK.1632

Now, when a solution is separated from a pure solvent by a semi-permeable membrane, the solute particles want to naturally distribute themselves, but they're not going to so what they end up doing if they can't go to the water, they are going to pull the water to them so water ends up moving across this membrane into this compartment and the volume of water rises.1633

It's going to rise, it's going to rise, it's going to rise but at a certain point, it can only rise so far because now this water has weight, this extra water that is coming in it has weight so what it's doing is it's actually pushing down on this thing, trying to keep it from rising.1657

So, there's this water moving in this way, pushing the water level up, but at some point there is the extra weight of water that's actually now pushing it down; there comes a point where it reaches an equilibrium.1676

Once this stops that level and that level, what we define is the osmotic pressure, is the pressure that's required to actually keep this water flow from actually happening.1687

OK.1700

In other words, the volume of the solution, of the extra water keeps more water from coming in.1702

At some point it reaches an equilibrium where this weight is pushing down, this is pushing this weight trying to move in, well, the amount of pressure that actually keeps water from moving in to begin with, we define that as the osmotic pressure.1708

It's a measure of the extent to which the solution is actually pulling water into it in order to dilute it.1725

That's what it is, and we can actually measure this, so it is an osmotic pressure.1734

It's as if this water is actually pushing this solution that's why we call it osmotic pressure but really what it is, it's the pressure that I have to maintain on this to make sure that no water passes across the membrane.1740

I hope that makes sense.1757

OK.1759

Now, like I said we have a way of actually representing this numerically and that's what's nice, we want some number that we can use.1761

So, let's go ahead and define our osmotic pressure.1771

It is equal to iMRT or osmotic pressure, we use a pi symbol, you'll see that, iMRT.1776

The variables that you use don't matter as long as you understand what it is that the variables represent.1792

Let's go ahead and use this one because that's probably the one you see in your book.1797

It's pretty standard now to have osmotic pressure represented by this symbol π.1800

OK.1807

So, let's go ahead and talk about what this means, so let me go to the next page, let me go to blue, actually let me go back to black.1808

We have the osmotic pressure is equal to i x M x R x T.1816

Let's talk about what these things mean, the i, the M, the R, the T.1822

OK.1826

M is the molarity of the solute.1827

R- that's the gas constant.1839

That is 0.08206 and the unit is Latm/molK.1845

Remember that from the ideal gas law?1857

T is the absolute temperature, in other words, the temperature in Kelvin - very, very important - has to be in Kelvin; it's what absolute temperature means.1860

Now, i is something called the van't Hoff factor and this is really, really easy.1873

Van 't Hoff factor is just the number of particles produced upon dissolving.1882

So, let's just do a couple of examples of i just to make sure that we understand that part.1898

OK.1909

So, glucose, C₆H₁₂O₆ solid, when it dissolves in water, it produces C₆H₁₂O₆ aqueous.1910

It doesn't come apart.1924

One molecule releases one free particle; one mole releases one mole.1925

i = 1, it's the number of free particles produced upon dissolving.1931

Magnesium chloride, solid, when it dissolves you produce 1 magnesium particle and you produce 2 chloride particles: i = 3, 1 + 2 = 3.1938

That's it, that's all that's going on here.1959

OK.1962

Let's go ahead and do an example.1963

Yes, it's fine, I'll go ahead and start here.1969

Example number 3: At 25°C, what would be the osmotic pressure of our 0.686M lactic acid solution?1975

Remember the solution from the previous lesson?2009

We want to know what kind of osmotic pressure it produces.2014

In other words, if I were to take this lactic acid solution and separate it via a semi-permeable membrane from pure water, what pressure do I need to apply to the lactic acid solution to prevent any water from actually flowing into it?2019

What is the extent to which it's actually pulling in water across the semi-permeable membrane to dilute its particles?2038

What would that pressure be?2044

Well, let's go ahead and work that out.2046

OK.2049

Let's see what we've got.2050

Well, again, in example it's is always nice to write out your equation so π = i x MRT or you'll also see it this way, iCRT.2051

C stands for concentration.2065

Concentration has to be in mol/l as far as osmotic pressure is concerned but you're going to see C, you're going to see M.2067

Again, the letters, irrelevant, what's important is that you understand the properties.2074

OK.2079

Well, so lactic acid is a covalent compound where a covalent compound i = 1, the van 't Hoff factor.2081

So, the osmotic pressure equals 1 times its molarity, well the molarity is 0.686, that's mol/L.2089

I'm going to go ahead and use all the units so you see how they cancel.2101

R is 0.08206, that is Latm/molK, and then of course we're at 25°C so that is going to be 298K.2104

K cancels K, mole cancels mole, liter cancels liter, the unit we're left is atmosphere, perfect, it's a unit of pressure, everything is good,2123

When we go ahead and do this, we end up with the following: the osmotic pressure is 16.8 atm.2136

If I have a solution of lactic acid which is 0.686M, and if I actually separate that solution - let me go ahead and draw my other U tube here, OK - so here I have my lactic acid solution, here I have just pure water and this is semi-permeable membrane that allows water to pass and not solute particles.2145

So, I have the water level, I have a bunch of lactic acid particles.2170

Now, 16.8 atm, what that means is that I need to apply 16.8 atm of pressure on top of this solution to prevent water from actually flowing from the pure solvent into the solution side- that's the osmotic pressure.2177

Simply by virtue, the fact that I have a bunch of particles floating around here, a solution, versus no particles around here, it actually causes water to be pulled in to that solution.2197

The pressure that I have to apply, because again, I need something physical that I can measure, so that's why this is osmotic pressure, I need to apply - that's a hell of a lot of pull, that's very, very strong tendency to pull - I need to apply 16.8 atm of pressure to prevent that from happening.2208

16.8 atm of pressure is no joke, that's a hell of a lot of pressure.2225

There you go, that's osmotic pressure.2231

Now, a little bit of information: this is 16.8 atm, this is just a little more than twice the osmotic pressure of blood, and the osmotic pressure of blood happens to be 7.7 more or less, 7.7 atm.2234

Then again, we have other units of pressure but atmosphere, because of the R, so osmotic pressure will often be expressed in atmosphere.2277

We can convert later - it's not a problem - to Torricelli, or kilopascal or pascal or whatever we need, but it is expressed in atmospheres.2285

Blood has a lot of things dissolved in it, so if you separate blood from water by a semi-permeable membrane, it will actually pull the water across that membrane into it in order to dilute it.2293

7.7 atm, that's how much pressure I have to apply to the blood to keep the water from flowing in.2309

7.7 atm is a hell of a lot of pressure.2315

OK.2321

So, that's dilution and osmotic pressure.2322

In the next lesson, we are actually going to continue our discussion of osmosis because there is a little bit more to say about it.2324

Thank you so much for joining us here at Educator.com.2329

We'll see you next time, bye-bye.2333