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Titrations and Buffers

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
  • Titrations 0:27
    • Weak Acid
    • Rearranging the Ka Equation
    • Henderson-Hasselbalch Equation
    • Fundamental Reaction of Acids and Bases
    • The Idea Behind a Titration
    • Let's Look at an Acetic Acid Solution
    • Titration Curve
    • Acetate
  • Buffers 26:57
    • Introduction to Buffers
    • What is a Buffer?
    • Titration Curve & Buffer Region
    • How a Buffer Works: Adding OH⁻
    • How a Buffer Works: Adding H⁺
    • Phosphate Buffer System

Transcription: Titrations and Buffers

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

Today we are going to continue our review of chemical basics, and we are going to discuss titrations and buffers.0004

This particular lesson is going to be only a discussion, and I have decided to actually save the example problems for acids, bases, and buffers until the next lesson; and then we'll be done and we'll be ready to jump into biochemistry proper.0011

OK, let’s get started.0025

We said that a weak acid reacts with water only slightly as follows.0030

Let me write weak acid.0037

The basic reaction is HA, and A is any species, that this is just a generic reaction, plus H2O; and when it does, it's going to come to an equilibrium- H3O+ + A-.0042

So, what you going to have in solution is A-, H3O+, which is the same H+, water, of course, that is in solution and HA.0059

Now, it is a weak acid, so most of it actually doesn’t dissociate.0067

Most of the equilibrium is here, which is why the Kas for these things are actually really, really, small.0071

They mean that it doesn’t go very far forward, it’s mostly this way.0075

The Ka for this reaction is going to be H3O+ x A-, which is products over reactants, over the concentration of HA, and of course we don’t include the H2O.0080

Now - very important - this is at equilibrium; this is once the system comes to equilibrium.0097

This is not at the beginning or the end; it’s at equilibrium.0103

OK, let’s go ahead and rearrange this equation.0106

Let’s rearrange the Ka equation and write it like this, and let me also remind you the H3O+ is equivalent to H+.0110

It’s just another way of writing it, so I’m going to use H+ instead of the H3O+.0126

When I rearrange this to solve for the hydronium ion concentration or the H+, I move this over here, and I move this down here.0131

I get the following: I get the concentration of H+ is equal to Ka.0139

Oops, let me start again; excuse me.0148

OK let’s see what we've got here.0156

So, I have got H+ concentration is equal to the Ka, times the HA concentration, divided by A-.0158

Now, I’m going to end up taking the logarithm, the negative logarithm of both sides.0168

I've got -log of H+, equals -log of Ka, plus the -log of HA, over A-.0173

Now, here what I did is Ka, something times something, when I take the logarithm of A x B, it's the logarithm of A plus the logarithm of B, so that is how I did it; I just used the property of logarithms.0192

Well, the negative logarithm is the definition of pH, so this becomes pH equals pKa minus the log of HA over A-, in other words, the acid form over the conjugate base form.0203

Well, generally, you can leave it like this, but generally we don’t.0221

We tend to prefer plus signs, so, if I flip this, if I take the reciprocal of this, I can actually change this to a plus; so I end up with this for the following equation.0225

The pH equals the pKa, plus the log of the concentration of conjugate base A-, that thing - OK, let me go back to black - over the concentration of the actual acid itself, that thing.0235

Now, I'm going to go back to black.0256

This is called the Henderson-Hasslebalch equation.0260

Henderson-Hasslebalch equation is a very, very important equation, probably the single most important one regarding acids, bases and buffers.0265

We are actually going to be talking about this in a minute once I start talking about buffers, but I’m going to do titration first, but I did want to introduce it to you; and this is the equation that you’re going to definitely use particularly when we do our example problems.0273

Now, let’s just talk about what this says.0289

This says that in a weak acid solution, if I ever want to know the pH of that solution, and if I happen to know the pK - I’m sorry - the relationship between the pH, the pKa, and the concentration of acid and conjugate base is expressed this way.0291

I have one thing, hydrogen ion concentration; I have the Ka.0308

I have the conjugate base concentration, and I have the acid concentration.0312

There are four different parameters here.0317

If I have any three of them, I can find the fourth; that is what this equation is.0318

It’s a relationship between these things: hydrogen ion concentration, Ka, acid concentration, conjugate base concentration- very important equation.0322

OK, and again we will return to this in a little bit when we talk about buffers properly.0332

OK.0337

Let me introduce what I call the fundamental reaction of acids and bases, which you already know.0339

You know that if you take an acid plus a base, you get a salt plus water- neutralization reaction.0345

I tend to call it the fundamental reaction of acids and bases, and we'll use this as a beginning to discuss our titration, because that is what a titration is.0351

OK, anytime you put an acid together with a base, essentially what you’re doing is you’re putting an H+ near an OH.0364

Anytime an H+ and an OH- are near each other, they are going to form water.0370

This is the fundamental reaction; this will always happen.0378

OK.0383

This is the idea behind the titration.0384

Titration, it is the use of a known concentration; and here, we are going to be talking about a titration of a weak acid with a strong base.0399

You can do a titration of a strong acid, a strong base, a weak acid with a weak base; but we're talking about weak acid - strong base.0411

That is the most common titration; that is the one people do most often.0418

OK.0423

The use of a known concentration of strong base, in other words OH-, usually in a form of potassium hydroxide or sodium hydroxide, to determine the concentration of weak acid- that is what a titration is.0424

You are trying to figure something out using something that you already know based on a reaction that you know, and the reaction that we use is the H+ + OH- goes to H2O- concentration of weak acid.0450

OK.0466

OH- reacts with any H+ either free or attached to an electronegative atom.0468

In other words, if it’s freely floating around, the OH- is just going to grab it and turn it to water.0490

If it is attached to a nitrogen or an oxygen, the OH- is going to rip that hydrogen ion away to turn it to water, leaving the negative charge behind on the oxygen, free or attached to an electronegative atom; and in our case, the electronegative atoms that we're concerned with are oxygen and nitrogen- O or N.0495

OK.0523

Let us take an acidic acid solution.0525

Let us look at an acidic acid solution- very, very common solution in all chemistry particularly biochemistry.0530

Acidic acid is CH3COOH, and this is what I mean, this H here is attached to this electronegative atom; that is what I mean by that.0542

I’m going to write this as AcOH.0555

OK.0558

I don’t want to write out the cHC2H3O2, whatever that is.0559

This thing right here is going to be my acetate, and then of course, this H is attached to it; that H is attached to it.0566

OK.0573

Let me go ahead and go to blue here.0574

Now, the reaction takes place is the following.0577

Oops.0582

Now, I’ve got some acidic acid solution sitting there.0584

Now, the reaction is as follows: AcOH- standard weak acid.0589

It’s going to react with water.0597

It’s going to come to equilibrium and it’s going to produce some hydronium, and it’s going to produce some acetate- that is the reaction that we know.0598

The KA for this, it is equal to the H+, times the AcO-, over the AcOH; and this particular case happens to be 1.75 x 10-5.0608

This KA is very small; it tells me that not very much of this is actually dissociated.0629

When I drop pure acidic acid in water, this happens, it comes to equilibrium; there is very little that actually come apart.0633

Most of it stays in that form.0642

OK, now, as I add OH- to this solution - so let me go ahead and draw this solution - I have mostly AcOH floating around, so I’m going to put like three of them and I have just a little bit of AcO- floating around, and H+ floating around.0643

OK, when I add OH- to this solution, the fundamental reaction takes place.0674

The OH- reacts with the AcOH.0690

It pulls off that H to form water, which I’m actually going to write as HOH, so that you know that comes from that, this OH is that one, it comes from that, plus AcO-.0696

OK.0715

In other words, some of the AcOH, by using a strong base to rip off that hydrogen ion, it's being converted to acetate.0717

The acidic acid is being converted to acetate.0727

OK.0729

We are titrating it.0732

As you produce more, as you add more OH, you're converting more of the acidic acid to acetate.0737

Now, you have a significant amount of acetate, whereas before, it's just the acidic acid solution, there wasn't really very much floating around; now, you've actually produced a lot by converting the acid to acetate by ripping away that hydrogen of AcOH, and so now, there is a significant amount of both acetate and acidic acid, in other words, the acid and its conjugate base.0745

Now, let’s recall our Henderson-Hasslebalch equation: pKa plus the log of the bases on top, the base version is on top, the acid is on the bottom, so we have AcO- over AcOH.0785

Now, when enough OH- has been added to convert exactly one half of the AcOH to AcO-, when I've added enough hydroxide to convert half of the acid to the acetate, now, the concentration of acidic acid is going to be equal to the concentration of acetate, right?0805

If I have one mole of something, and if I've converted half of that to acetate, now, I have a half a mole of acidic acid left, and I have a half a mole of acetate; now, the concentrations are equal notice what happens, pH equals pKa - well, I’m not going to write all this out I’m just going to show you right here... well, no, that is fine actually I'll just write it out - so pH equals pKa plus the log of AcO- over AcOH, OK, but the concentration of AcO- to AcOH, because this and this are actually equal, it equals 1, and the logarithm of 1 is equal to 0.0852

So what we end up with is pH = pKa.0907

We have a weak acid solution.0913

When we add enough hydroxide, strong base, to that solution to convert half of the original acid to acetate, now, the concentration of acid and conjugate base are the same.0914

Well, this Henderson-Hasslebalch equation, this ratio right here is 1; the logarithm of 1 is 0, so that actually just goes away.0924

What you have left with is pH = pKa.0932

In other words, if you were to measure the pH of that solution with a meter, that is going to equal your pKa.0934

If you take 10 to the negative that, you actually end up recovering your Ka.0940

So, what we have here, this titration, adding a strong base to a weak acid solution to convert some acid to its conjugate base, we have an experimental procedure for actually determining the Ka, the pKa, the Ka of a weak acid- of any weak acid.0944

This is very, very important.0961

We have an experimental procedure, a very easy experimental prodedure for determining pKa or Ka.0963

I personally prefer working with Ka not pKa.0986

I prefer working with hydrogen ion concentration and not pH.0990

That is just a personal preference of mine, but in general, in the biochemical field, a little less so in sort of pure chemistry, but in biochemistry, it's usually pH and pKa, that is the big deal, so get accustomed to how this works.0993

OK.1007

Now, let’s talk about titration curve.1010

That is fine, I guess I can write it over here...yes, that is fine.1017

Let me go back to black here.1023

Now, a titration curve is a plot of pH, which is going to be the Y axis versus amount of OH- added, which is usually going to be in milliliters; that is going to be the X axis and it looks as follows.1028

So, as you add hydroxide to an acidic solution, so you have this acidic acid solution, it has a pH which is less than 7, it’s an acidic solution, you add hydroxide to it, the pH is going to start to rise, rise, rise, rise, rise; it’s going to come a point when you have converted every single bit of acid, you’ve eaten it all up, you’ve ripped away all of the hydrogens to produce water, and now...well, anyway, let’s just sort of draw it and then we'll discuss what’s actually happening.1063

OK, so let me make a good picture here.1095

There is this, and there is that.1099

OK.1103

Let me go 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 1, 2, 3, 4, 5, 6, 7, so this is pH7, so this is our pH scale; and here ,it's going to be OH- added, and again this is going to be in milliliters.1105

I’m not going to specify the scale here, it’s the qualitative, we just want to see what it actually looks like; so you're going to have something that looks like this.1129

Let’s see, let's go ahead and start at the pH2, maybe go this way...so then, something like that.1137

Let’s see what we've got, let's mark a couple of points here.1159

This point, actually right here, when I've added a certain amount of OH, the equivalence point, this is called the equivalence point; and it is when just enough OH- has been added to react with any and all H+ present- whether that H+ is floating around or it's being ripped off the acidic acid.1163

In this case, the equivalence point, there is a certain number of H's that is on acidic acid, when I add enough OH- to that, to react with it and completely convert that H+ to water to neutralize it, now, I’m completely acetate.1210

There is nothing else floating around at this point.1223

It’s just plain old acetate and water, that is this point, the equivalence point; and again the stoichiometry OH- + H+ goes to H2O is one to one- one mole of OH-, one mole of that.1226

Now, we talked about the half equivalence point, this point right here.1239

OK.1242

Let’s go ahead and see what this thing is.1245

So, this is the half equivalence point, and we just talked about what that was- it’s when enough OH- has been added to convert half of the original acid to its conjugate base.1249

OK.1261

Enough OH- has been added to convert one half of the acid to its conjugate base.1265

OK.1288

Now, notice that point right there, that is when I read it off the pH - let me do this in red - this is the pH equals the pKa.1291

I do a titration curve, I add it; with each little bit of hydroxide that I add, I read the pH, read the pH, read the pH.1308

I graph it; I find the equivalence half equivalence point.1315

I read it right of the graph; It gives me my pKa.1318

Perfect.1322

OK.1323

Notice something else here, pH7 is neutral.1324

If I take a strong acid and a strong base, hydrochloric acid is sodium hydroxide, if I neutralize that hydrochloric acid with hydroxide at equivalence, the pH is going to be 7; but notice in this particular case, this equivalence point, the pH is not 7- it's actually above 7.1328

When I titrate a weak acid with a strong base, I end up converting all of the acid to acetate.1346

Well, you would think that the pH would be 7, and in fact, for a microsecond it actually is 7; but something else happens.1353

OK.1360

Now, I’ll write this down here.1362

Notice that at equivalence, we expect a pH of 7, because we have complete neutralization, we expect pH to equal to 7; but since we are titrating a weak base, - I’m sorry we are titrating a weak acid, not a weak base, we're titrating a weak acid, my apologies - now, another reaction is going to take place.1367

So, we just said at equivalence, we've converted all of the acidic acid to acetate.1418

Now, there is no more acidic acid; all of that acid has been neutralized, so there is no free floating acid H+, all we have is acetate.1422

OK.1432

It is all acetate now.1438

Here is the kicker, but AcO- acetate is the conjugate base of a weak acid, which means that it is a strong base; so, it reacts now, with water that is floating around in a solution as follows.1445

Now, there is going to be the base reaction AcOH + HOH; the system is going to come to a new equilibrium.1479

It’s going to come to AcOH + OH-.1490

This was the reaction for a base.1496

If I have the acidic acid solution, if I titrate it, and if I had just enough hydroxide to convert all of the original acidic acid to acetate, yes, at that microsecond, the pH is going to be 7- everything is neutral; but now, that I have acetate floating around, remember acetate, acidic acid is a weak acid, it has a very small Ka, which means it doesn’t want to be acetate, it wants to be acidic acid, AcOH not AcO-, if there is AcO- floating around, it’s going to do everything it can to pull a hydrogen from any source it can to become AcOH.1498

The only other source of hydrogen in the solution is the water, so that is what it does.1531

It actually rips hydrogens away from the water producing hydroxide indirectly.1535

The hydroxide ion concentration goes up, that is why the pH is actually bigger than 7.1541

You are creating a basic solution.1546

So, right here, releasing OH- into solution indirectly, thus, the pH is going to be greater than 7 once the system comes to a new equilibrium.1549

Now, of course this happens instantaneously.1579

We don’t see it, but what’s happening is, again, converting the acid to acetate.1582

Now, free acetate reacts with the water, rips off the hydrogen from the water, some of it converting back to acidic acid.1587

This is the new equilibrium, and when everything is said and done, you’re going to end up with a pH that is actually higher than 7; so when a weak acid is titrated with a strong base, the final pH of the solution at equivalence is going to be greater than 7, not 7.1596

OK, there we go.1613

So, that is titration, and now, let’s go back to black; and now, we're going to talk about buffers- very, very, very important topic, buffers.1614

All your fluids in your tissues are essentially buffer solutions.1630

Your blood is a buffer.1633

The solution inside of your cells is a buffer.1639

A buffer is something that tries to maintain a given pH, so that certain things can take place within that pH medium.1641

It doesn’t like to have big jumps in pH; you don’t want to be a 7.4, 7.3 and all of a sudden jump to 9 or drop to 5.6.1650

Bad things start to happen in the body with very, very small changes in pH, so buffer is there to keep the pH exactly where it’s supposed to be.1658

Let’s go ahead and formalize this.1669

Every biological process, most biological processes is pH dependent.1673

In other words, in order for something to actually happen, the pH of the surrounding medium needs to be a particular value, in order for this thing to happen at its optimal level.1687

OK, it is pH dependent.1696

We need ways to keep a system at a given pH from deviating.1699

If any extra H+ or OH- enters the system, the reactions that are taking place in your body, they tend to produce hydrogen ion, they tend to produce hydroxide ion.1726

Well, we can’t just have hydrogen ion, hydroxide ion just sort of coming and going and having the pH going up and down, and up and down.1747

The body can’t function that way.1754

With the introduction of H+ and OH- from the metabolic processes that are taking place in your body, the buffer actually keeps the pH the same and has ways of dealing with this H+ and OH-.1756

That is what a buffer is.1769

It’s a way of sequestering, of eating up, of locking the H+ and OH-, so they are not floating around freely, changing the pH of the surrounding medium.1770

OK.1781

Now, let’s define what a buffer is.1782

A buffer is a solution of a weak acid and its conjugate base.1787

That’s it, that is all a buffer is -a weak acid and its conjugate, a little bit of the acid, a little bit of the conjugate base in a specified amount.1810

OK.1818

Now, let’s deal with what’s actually happening here.1819

Now, you remember, we just drew a titration curve that looks something like this.1822

This region right here, this is called the buffering region.1829

Notice we keep adding OH, keep adding OH, keep adding OH, well, but you notice, the pH is not rising much, I mean it’s changing a little but it’s pretty flat for the most part- this is called the buffering region.1831

Some of the original acid is being converted to acetate.1850

Now, you have acid and conjugate base floating around in a solution together, and now, it is acting as a buffer until all of the acidic acid is gone.1853

Now, it’s just pure acetate and boom.1862

The minute you add a little bit of hydroxide, the pH just jumps up- this is called the buffering region.1864

In general, if you have the pKa, the optimal, in general, the buffering region is about 1 pH unit up and down from the pKa, so pKa - 1.1870

If I had a pKa of 4, the buffering region, the optimal buffering for that particular weak acid would be from 3 to 5.1885

4 + 1, 4 - 1 sort of it keeps it in that range and that is usually pretty good.1894

It is called the buffering region- pKa plus or minus one.1900

OK.1904

I will only just write that out.1906

The flat region of a titration curve is called - let me actually be specific, the flat region of a titration curve for a weak acid, I know that is repetitive I know that we're only going to deal with titrations of weak acids but it's OK - the titration curve for weak acid is called the buffer region or the buffering region; it doesn't really matter.1909

During this region, we have a buffer solution, so that we can create a buffer solution by starting with the acid and adding hydroxide to it; or we can just create a buffer solution by dropping in some acidic acid or maybe some sodium acetate - some of the acid, some of the conjugate base directly - we can do it either way.1960

OK.1983

Now, let’s go ahead and draw a little solution here.1987

Now, I've got this solution, and I have some AcOH and I have some AcO-, I have some AcOH and I have some AcO-, and let’s just try it one more, AcOH and I have some AcO-.1994

It doesn’t necessarily need to be equal amounts, but the ideal is, if they are equal, that is the ideal buffer.2007

It has the greatest buffer capacity when the concentration of acid and conjugate base are the same.2013

OK.2018

Now, let me go to blue here.2019

Now, adding H+ or OH- to this solution changes the pH, and if I add hydrogen ion to it, the pH is going to drop.2023

The hydrogen ion concentration is going to go up, the pH is going to drop because it's -log, that is why I prefer to work directly with hydrogen ion concentration instead of pH.2040

If I drop OH- into it, the pH is going to go above, it’s going to go higher, it's going to get more basic.2049

OK.2055

Here is how a buffer works.2059

Yeah, that is fine I can do this on this page.2072

OK.2073

Actually, you know what, I think I’m going to go ahead and go to the next page.2075

So, we have this solution, now, suppose I add hydroxide to this solution, somehow hydroxide is introduced to that buffer solution, here is the reaction that takes place: the hydroxide is going to react with the acid, and it’s going to form water, HOH, plus acetate.2084

So now, basically, this AcOH, because it's floating around in solution, is going to eat this up, and is going to lock it up, this water, instead of letting it float around freely to change the pH.2113

OH- is eaten up so it can’t float around freely to change the pH.2127

OK, so that takes care of the hydroxide.2150

Well, what if I add hydrogen ion instead; what if somehow some hydrogen ion is introduce into this?2153

OK, so suppose I introduce hydrogen ion, well, now, what does the buffer do?2159

Well, in this case, now, the hydrogen ion is going to react with the acetate and it's going to form AcOH.2170

Now, this one is going to be locked up as this, to keep it from floating around and changing the pH.2183

H+ is trapped by AcO- so it cannot float freely and change the pH.2191

That is what a buffer does; it has the acid, it has the base, whether I add hydroxide or whether I add hydrogen ion, in either case, it will react with one of them to sequester it, to lock it in, to eat it up, so that it is not floating around freely changing the pH- that is how a buffer works.2214

OK.2232

Now, and as we said, when the concentration of acid and conjugate base in a buffer solution are equal, that is the ideal buffer, that has the highest buffer capacity.2235

OK, so let’s see.2246

Now, let's go ahead and close this out.2250

Actually, I think I’m going to go to one more page here.2252

Now, weak acids and weak bases, they buffer our cells and tissues, because again, this is biochemistry, we're talking about the chemistry of biological systems.2259

Now, I’m going to talk about one of the buffering systems, it's called the phosphate buffer system; and this is the buffer system that operates inside of our cells.2282

The phosphate buffer system, it acts inside of the cell.2300

Inside the cell, we want to keep the pH in a certain region, somewhere about 7.2, 7.3 maybe 7.1, somewhere in the range of about 7 - 7.4.2310

The phosphate buffer system is perfect for that because H2PO4- is in equilibrium with H+ + HPO42-.2324

The pKa of this thing right here, this reaction, so we have dihydrogen phosphate and we have hydrogen phosphate and the relationship is when this loses a proton it turns into this, when this gains a proton it turns into that.2342

The pKa is 6.86.2358

So, this is the acid, and this is the conjugate base.2362

This is the hydrogen ion donor, and this is the hydrogen ion acceptor.2367

So, What we need to have in the cell, there is some of this and there is some of this- that is what’s going on here.2374

Now, we said that the buffering range is pKa plus or minus 1, so the range for this particular buffer system, for the phosphate buffer system if pKa happens to be 6.86, well, it is going to be about 5.86 to 7.86.2381

It's perfect, the normal pH inside the cells somewhere in the range of about 7 to 7.4, it falls in that range, that is why this is the perfect buffer.2403

This is why cells use this as the buffer inside the cell.2415

If all of a sudden, because of the metabolic process that takes place inside the cell, there is a rise in hydrogen ion concentration, well, the conjugate base will eat up the hydrogen ion to convert it to phosphate, so that the hydrogen ion is not floating around freely changing the pH.2421

If for some odd reason, there is a whole bunch of hydroxide because of some metabolic process that is pumped into the cell, well, this hydroxide is going to rip off a hydrogen ion here, it's going to change to water, and it’s going to convert to the hydrogen phosphate.2438

In other words, the equilibrium is going to shift to the right to use up the hydroxide.2453

If acid ends up entering the cell because of metabolic processes, the equilibrium is going to shift to the left to use up the H+.2458

So, in either case we're keeping H+ and OH- from building up in the cell, and the phosphate buffer system, that is what take cares of it- this is the reaction that takes place in the cell.2467

OK, that’s it.2479

That is our discussion of titrations and buffers.2480

In the next lesson, we're actually going to be concentrating just on examples for titrations and buffers, mostly buffers.2484

Thank you for joining us here at Educator.com.2489

We'll see you next time, bye-bye.2491