AP Chemistry Acids and Bases

Welcome back to Educator.com; welcome back to AP Chemistry.0000

Last time we finished off our discussion of equilibrium, a very, very important topic, and now we are going to go on to probably the second central topic of chemistry, which is acids and bases.0005

They're very, very important in all aspects of chemistry, particularly in biochemistry, because much of the reaction that takes place in your body is, of course, acid-base reactions.0016

We are going to spend some time discussing acids and bases and writing reactions and talk about what is going on qualitatively, and then, we will also deal with it quantitatively, and we are going to introduce a new equilibrium constant, called the K_a or the K_b.0026

Now, fortunately, it isn't really anything new; it isn't new in the sense that it is a different way of writing the equilibrium constant.0043

It is just a different symbol for it; it is still exactly what you learned with equilibrium, and everything that we learned with equilibrium will again play the same part.0049

We will be doing ICE charts, so we will get plenty of practice in this.0058

If you feel like you don't have a solid grasp of equilibrium, acids and bases are a wonderful place to continue to practice that until you get a solid grasp of it.0062

Let's go ahead and get started with some definitions.0071

OK, what we are going to be using: there are a couple of models for acid-base behavior, and the primary model--at least, the one that is used most often--is something called the Bronsted-Lowry acid-base model.0075

Let's just talk about what that is; we'll just define it.0087

Bronsted-Lowry...the name itself doesn't really matter all that much--for historical reasons, I suppose it's nice to give credit to the people who deserve credit--but it is the model that is important: acid-base model.0093

Now, an acid is a hydrogen ion donor, and a base is a hydrogen ion acceptor--a very, very simple definition, and let's talk a little bit about what this means.0109

So, an acid is a compound that has an H⁺ that can come off--that can potentially come off.0133

I'll write "potentially come off"--in other words, it has a hydrogen ion to donate, if it needs to donate it.0161

More often than not, it will actually donate it--it will give up the hydrogen ion.0170

A base is something (I shouldn't say something--it's a compound--yeah, right, it's just "something")...is a compound that can potentially take that (not that; it will be that, but let's be as general as possible)...that can take an H⁺ ion.0176

That is it: so, a base is a compound that has a hydrogen attached to it, but the hydrogen can potentially separate from that compound, and just float around freely as hydrogen ion.0221

That is, in fact, the acid: when we speak about an acid, that is what an acid is: it is just free hydrogen ions floating around in solution--that is what does the damage.0233

A base is something that has the capacity to either take a hydrogen ion from something (an acid) that has it to give--in other words, rip it off--or, if there are free hydrogen ions floating around, a base can actually grab onto it.0241

That is it: so an acid is a hydrogen ion donor; a base is a hydrogen ion acceptor.0260

Acid-base chemistry--they come in pairs; when there is some acid, there is some base, usually; so we will see what that means in just a minute.0266

OK, there are two ways to write the reaction of an acid in water--or with water, I should say: to write the reaction of an acid with water.0277

And again, an acid is something that you are actually dropping in water, and once it is in water, it actually tends to come apart.0304

Here is what actually happens: we will just write H, and we will write A; so H is the H that actually comes off; this A can be anything--it's just a generic other part of the molecule.0312

...Plus H₂O, goes to H₃O, plus A^-.0326

What has happened is that the H has gone from this HA over, and attached itself to the H₂O; it has actually attached itself to the oxygen, and it is H₃O⁺, now.0335

H₂O is neutral; H⁺ is plus charge--that is why now, this has a plus charge; and because this was HA, it's a neutral ionic compound, but this H left its electron when it left (it left as H⁺), it has an A^-.0346

There is another way to write this reaction, which is the way that I am certainly accustomed to doing it, and in certain circumstances, it helps to write it this way as opposed to this way.0365

It is why we actually have two ways of doing it, because it depends on the problem and how convenient it is to write one way or the other.0375

HA...it's the actual dissociation reaction: when you put this in water, it becomes free ion, H⁺ ion, and free A^- ion.0382

This is a little bit more descriptive of what is really going on, in the sense that HA dissolves, like sodium chloride dissolves, and it breaks up into a hydrogen ion and the other ion (whatever the rest of the molecule is).0393

What is really happening is: there is an actual transfer.0409

This is the acid; it has the hydrogen to give up--it has the hydrogen to donate.0413

In this case, water is acting as the base; it has the capacity to take that hydrogen, or to accept that hydrogen.0418

So, when we write it this way, we actually talk about an acid conjugate base pair, which I will actually get to in just a minute; but I just want to sort of talk about these two equations, and how to represent them.0426

When we talk about an acid dissociating, or an acid reacting with water, we can either write it this way, or we can write it this way.0443

This H₃O⁺ and this H⁺ are the same thing.0452

This H⁺ is just an H⁺; when it is attached to an H₂O, we write it as H₃O⁺, but the chemistry is the same.0456

Now, let's go ahead and write the equilibrium constant for this.0466

The K_eq--well, we said the K_eq is the concentration of product, concentration of product, divided by concentration of reactant, concentration of reactant.0470

This is liquid water; it doesn't show up--remember, liquids and solids don't show up in the equilibrium constant.0483

This is going to be: the concentration of H₃O⁺ in moles per liter, raised to its coefficient (which is 1), the concentration of A^-, raised to its coefficient (which is 1), divided by the concentration of HA; this is aqueous.0488

OK, water doesn't show up; when we have an acid written like this, or (let me actually write this version of it: H⁺, A^-, over HA) when we are dealing with an acid, we don't call it K_eq; we call it K_a.0507

This is the acid dissociation constant; it is the equilibrium constant for the reaction of an acid with water, or for the reaction of an acid dissolved in water.0530

When you dissolve it in water, we think about it as just a dissociation, like any ionic compound.0543

But what is really happening--it is actually reacting with water.0547

The acid is giving up the H; the water is acting as the base, accepting the H.0550

In some sense, when you look at this, this equation, this equilibrium--what it expresses, what it represents...it represents a competition between water and the conjugate base for this H.0555

In other words, does the H stay with the A, or does it go with the water?0570

If it goes with the water, that means the reaction is over on this side: H₃O⁺ is formed.0574

If the H doesn't want to leave the A--if it wants to stay with the A--that means most of the reaction is on this side.0580

That is what the K_a measures.0586

So, the equilibrium constant is called the acid dissociation constant.0588

It is the same as any other equilibrium, except it is representing what is happening when the acid reacts with water, when the acid is dropped into water.0595

That is it; so, from now on, when we are discussing acid-base chemistry, it is going to be K_a.0605

Later on, when we discuss bases, we are going to have an analogous equation, and it is going to be K_b.0610

But it is just an equilibrium constant.0615

And what does an equilibrium constant represent? It represents the extent to which a reaction has moved forward.0619

Once it reaches equilibrium, how much of this, how much of this, how much of this?--it's a measure of the extent of reaction.0626

How far forward has it gone? How far has it not gone?--that is all it is a measure of.0634

The higher the K_a, that means the dissociation; that means it's to the right, because the numerator is a bigger number.0639

OK, now, let's talk about polyprotic acids really quickly.0648

For acid dissociation, 1 H⁺ leaves at a time.0656

For example, if I have the acid H₃PO₄, which we know of as phosphoric acid, it doesn't do this: H₃PO₄--it doesn't just dissociate into 3 H⁺s plus PO₄^3-.0683

It doesn't do that; that is not how acids behave.0699

This doesn't happen; what does happen is that 1 H⁺ leaves at a time, so the dissociation of phosphoric acid is three steps, and it looks like this.0704

H₃PO₄ + H₂O is going to be in equilibrium with H₃O⁺ + H₂PO₄^-.0722

That is the first dissociation; there is some K_a associated with that first equilibrium.0733

And then, H₂PO₄ has two more Hs to give up; so, H₂PO₄ (actually, you know what, I think I'm going to write it as just a regular dissociation--I'm sorry; I think it will be a little more clear) now gives up another one.0739

It gives up 1 at a time: H⁺, and it becomes HPO₄^2-; there is an equilibrium associated with that.0762

OK, and then we have HPO₄; it has another H⁺ to give up, and now it's PO₄^3-; there is a third acid dissociation constant.0773

And each one of these is actually different; these phosphoric acid dissociates to differing degrees--these are not the same number.0787

In other words, this equilibrium might be really far forward; this equilibrium may be really far this way; it just depends.0796

The key idea is: for a polyprotic acid (polyprotic just means having more than one hydrogen to give up), it gives them up one at a time.0805

Very, very important: for acids, it releases one at a time; it doesn't happen all at once.0813

So, H₂PO₄: it doesn't just release both hydrogens--it releases one completely, and the second one comes off very little, in fact--so, just something that you should know.0819

OK, so let's talk about acid strength.0830

Acid strength: Acid strength is defined by the position of the equilibrium constant--or by the position of equilibrium; in other words, which is measured by the equilibrium constant.0837

It's measured, it's defined, by the position of the equilibrium; and the equilibrium, we said, was some acid plus water, going to hydronium ion...or just H₃O⁺...0856

We call it hydronium, by the way--let me just write that name down: H₃O⁺ is called a hydronium.0874

Anything with a positive charge tends to have an -onium ending; it's the same as H⁺--you can treat them the same.0882

So, the acid strength is defined by the position of the equilibrium; if the equilibrium lies really far to the right, that means, if this acid has completely given up all of its Hs over to water, it is a strong acid.0891

So, the farther to the right the equilibrium is, that means it is a stronger acid.0903

We talk about a strong acid being something that actually does not want to keep its H's; it wants to give them up completely.0914

It wants to be A^-, and it wants its H to be H⁺.0922

It does not want to be together.0928

OK, now, let's talk about...let's see; so, actually, let me write that again.0930

Let me say: farther to the right, stronger acid--so, when we talk about acid strength, we are talking about relative strength; it's always...we are comparing it to something.0942

Stronger acid--well, that means a higher K_a, right?--because the K_a is products over reactants; well, farther to the right means there is more product and very little reactant--a really big numerator, a really small denominator, and a huge number--stronger acid.0958

OK, now let's go back to blue here.0976

A strong acid implies a weak conjugate base.0983

Acids and bases come in conjugate pairs--"conjugate base"; we get the conjugate base by just pulling off the hydrogen from the acid.0988

So, let's write our equation again: HA + H₂O is in equilibrium with H₃O⁺ + A^-.0999

This is the acid; this is its conjugate base.1010

I pulled off the H; that leaves my conjugate base.1021

If I take a base (in this particular case, again, this is the acid--this has the H to give up; water is acting as the base--it is going to take that H, or accept it, if it wants to), when it accepts the H and it becomes H₃O⁺, this is called the conjugate acid.1026

That is it; if you have an acid, you pull of the H; you are left with a conjugate base.1048

If you have a base, and if you add a hydrogen ion to it, you have its conjugate acid.1053

That is it--nothing more than that; no more, no less: don't read any more into that.1060

OK, so a strong acid means a weak conjugate base, which is exactly what you would expect.1064

A strong acid does not want to hold onto its H's; it will give them up completely; that means it has a weak conjugate base.1070

A weak conjugate base means that it doesn't want this H; that is the whole idea.1077

A strong base wants the H--will take the H; it's a competition.1084

A weak acid has a strong conjugate base.1091

A weak acid is one that does not want to give up its H's; and the reason it doesn't want to give up its H's is because its conjugate base is so strong that it literally holds onto its H's without letting go.1104

That is the idea; so, weak acid means conjugate base.1116

When you are thinking about this, you have to pick a perspective; you have to pick a point of reference; that is the whole idea.1121

We decide to take the reference point as the acid itself; we call it strong; we call its conjugate base weak.1127

That means the conjugate base doesn't want the H; it gives it up.1134

A weak acid is one that does not want to give up its H; that means that its conjugate base is very, very strong--it will not release its H.1139

So, it's really a question of perspective; you need a point of reference; and the point of reference that we have taken is the acid.1149

We talked about a strong acid and a weak acid: a strong acid has a weak conjugate base; a weak acid has a strong conjugate base.1157

OK, for strong acids, no K_a exists...no K_a is listed, we should say.1172

So, for example, hydrochloric acid is a very strong acid; its dissociation (it's not even in equilibrium)--it completely breaks up into free H⁺ and free Cl^-.1184

You won't find any of this at all.1195

Well, the K_a for this is H⁺(Cl^-)/HCl.1198

Well, since there is a whole bunch of this and a whole bunch of that, and virtually none of this, this denominator is really tiny; the numerator is really big.1207

So, you have a K_a which is huge; in fact, the K_a is so huge that we can't even measure this.1216

Because we can't measure the Cl concentration accurately, we don't even list a K_a for it; it's just off the charts.1222

Strong acids--full dissociation; that is the idea.1228

Once again, strong acid means full dissociation.1233

That means this H and Cl completely come apart; in solution, you will never find any Cl attached to an H.1240

It will free Cl^- and free H⁺.1249

That is what makes it a strong acid; because there is so much H⁺ floating around freely, that is what does the damage.1252

So, when we say "strong acid," we are talking about a chemical property.1259

Strong acids do damage because there is so much H⁺; there is so much H⁺ because the H and Cl do not want to stay together--they want to be separate.1263

Strong acid--full dissociation: that's very important.1274

OK, let's do an example to get a sense, or a feel for what is going on, for some numbers here.1279

So, Example 1: HF, which is hydrofluoric acid, has a K_a of 7.2x10^-4.1290

It's a small number; it's a weak acid--it's not very far forward.1301

Most of it is in this form; OK, so let me write the dissociation: HF goes to H⁺ + F^-.1305

When I measure this, this, and this, and I put these on top of that--the K_a--I get this number.1314

It's pretty tiny; a tiny K_a means that most of this equilibrium will be found on this side, the reactant side.1320

In other words, there is very little dissociation; most of it just stays HF.1327

Hydrocyanic acid, HCn--it has a K_a of 6.2x10^-10--wow, really, really small.1333

So, when I see HCn--when I drop some of that in water (that is Cn^-), this would be the dissociation.1343

This is so tiny that this is telling me that most of this reaction is over on this side.1351

I won't find a lot of free H⁺ and Cn^-; I'll find some--I was able to measure it--but most of it is this.1356

That is what the small K_a means; a small K_a means it hasn't dissociated very much.1362

A big K_a means it has dissociated a lot more.1368

Between these two, this is bigger; this is smaller; this is a stronger acid, because its K_a is bigger--it has dissociated more.1371

It is still a weak acid, but compared to hydrocyanic, it's stronger than hydrocyanic.1383

That is the difference; when we speak about the strength of acids, we are often going to be comparing; it's relative.1390

We are going to be talking about 2 or 3 or 4 species.1396

Now, the question is: which one has the stronger conjugate base?--that is the question.1402

Which acid has the stronger conjugate base?1409

Well, for HF, the conjugate base is--just take off the H; this is the conjugate base.1421

For HCn, it is the acid minus the H; that is the conjugate base.1427

Which has the stronger conjugate base? Well, the stronger conjugate base comes from the weaker acid, right?1433

Weak acid=strong conjugate base; OK, between these two, the weaker acid is the hydrocyanic acid.1445

In other words, it's a weak acid because it doesn't dissociate very much; that is confirmed with this really, really small K_a.1456

It doesn't dissociate very much; it's a weaker acid; it has a stronger conjugate base.1464

In other words, the base is so strong that it doesn't want to release its hydrogens; it wants to hold on to it.1470

That is what a strong base does: a strong base grabs onto its hydrogens and holds onto it.1476

A strong acid wants to give up its hydrogens; that is why we have strong acid, weak base--yes, stronger acid, weaker base; weaker acid, stronger base.1482

So, in this case, F^- is a weaker conjugate base than Cn^-.1495

That is it; we are using K_a values to decide, depending on what species we are talking about.1509

This K_a means HF is a stronger acid than HCn.1515

It means its conjugate base is weaker than Cn^-; that is what is going on here.1520

OK, so now, let's discuss water as an acid and a base.1526

Let's define something called amphoteric: an amphoteric substance is one that can behave as an acid or a base.1538

It should be "and a base," because it actually does both; "as an acid or a base"--in other words, something that can go both ways.1561

Well, let's look at the dissociation of water.1571

I'm going to write it slightly differently.1575

I'm going to write the first water: so now, we are talking about water as a species dissolved in water.1577

It's plain old water; I know it's a little weird, but think about it this way.1583

I'm going to write it as HOH + H₂O.1587

These are both water, but I wanted to emphasize what is happening.1591

This HOH, believe it or not, actually dissociates just a little bit; it breaks up into H⁺ and OH^-.1596

Well, this H goes over here to become H₃O⁺ + OH^-.1602

Another way of writing this is HOH, as free dissociation, without involving the water species, breaks up into H⁺ + OH^-1611

Well, let me rewrite it: HOH is in equilibrium with a little bit of H⁺ and a little bit of OH^-.1622

The K_eq for this is equal to...well, this is liquid water; liquid doesn't show up in the equilibrium concentration; this is aqueous; this is aqueous; this is floating around, in other words, and this is floating around in the water, to a certain degree.1634

It is equal to the H⁺ concentration times the OH^- concentration--the products.1650

Well, as it turns out, for water, we actually call it K_w.1656

We have done the experiment; and, as it turns out experimentally, we have actually measured, at 25 degrees Celsius...experimentally, at 25 degrees Celsius, the hydrogen ion concentration is equal to the hydroxide ion concentration; that is what this equation says.1662

For each H that is produced, one OH is produced.1685

They have the same concentration; it equals 1.0x10^-7 moles per liter.1688

The concentration of H⁺ and OH^- in standard, neutral, run-of-the-mill water, is 1.0x10^-7.1696

Well, what does that mean?--K_w is H⁺ times OH^-, so K_w equals 1.0x10^-7 squared, equals 1.0x10^-14.1706

Water has a K_a of 1.0x10^-14.1723

We give it a special name; we call it K_w for water--it's very, very important that you know this.1728

K_w is 1.0x10^-14 at 25 degrees Celsius--always.1734

OK, what does this mean?--it does have a meaning.1743

This means (and here is where it gets really, really important): in any, in any aqueous solution, at 25 degrees Celsius, no matter what is in it--no matter what--no matter what is in it (in the solution), the product of H⁺ and OH^- must always equal 1.0x10^-14.1753

OK, we need to stop and think about this, because this is really important.1811

Any aqueous solution, no matter what is in it--sodium chloride, potassium phosphate, the complex ion, magnesium hydroxide, phosphoric acid, permangenic acid--anything--if I were to measure the hydrogen ion concentration and the hydroxide ion concentration, they have to--the products have to equal--have to equal 1.0x10^-14.1816

That is what this says; at any given moment, an aqueous solution (in other words, water--something that is in water)--the product of the hydrogen ion and the OH^- ion concentration always 1x10^-14.1842

That doesn't mean that each one is 1x10^-7; that is just for neutral water.1858

It just says that, if...so this is equal to the H⁺ concentration times the OH^- concentration--that means, if the H⁺ concentration rises, the OH^- concentration has to drop in order to retain the constant value of 1.0x10^-14.1863

So again, they don't have to equal each other; their product has to be a constant.1883

If one goes up, the other goes down; that is the relationship--that is the mathematical relationship.1888

OK, their product has to be 10^-14; and it is going to be very, very important in just a minute.1894

So, let's just...if the concentrations do equal each other, we call it neutral.1899

If the hydrogen ion concentration is bigger than the OH^- concentration, we call it acidic.1910

That is where we get the idea of "acidic"; so, when you say that orange juice is acidic, that means that, if you take some orange juice, and if you measure the concentration of H⁺ versus the concentration of OH^-, the H⁺ concentration is going to be higher.1919

But, the product of the two concentrations is still going to be 10^-14.1934

If the H⁺ concentration is less than the OH^- concentration, we call that solution basic.1940

That's it; OK, so let's do an example.1948

Nice, simple math: Calculate H⁺ and OH^- (I'm really, really sorry about my handwriting; I know) concentration for the following solutions.1956

OK, let's see: Oh, "at 25 degrees Celsius."1982

A: We have: 1.5x10^-5 molarity OH^-.1991

Well, we know what the concentration of OH^- is; it's right there--it's 1.5x10^-5.2000

Well, we know that the H⁺ concentration, times the OH^- concentration, at 25 degrees Celsius, equals 1.0x10^-14, so we just plug it in to find the H⁺ concentration.2010

H⁺ concentration equals 1.0x10^-14, divided by the OH^- concentration; I have just done a simple division.2026

1.0x10^-14 (ten to the negative fourteen, not fifteen), divided by OH^-, which is 1.5x10^-5, and I get a concentration of 6.7x10^-10.2038

Which one is a higher concentration? OH^- is 10^-5; H⁺ is 10^-10; the OH^- is a bigger concentration--the solution is basic.2058

It will still hurt you, so don't...it doesn't mean that a base won't hurt you; an acidic solution will hurt you--a basic solution will also hurt you.2072

OK, the idea is: we want a neutral solution.2080

By the way, blood pH is just about...we will get to that in a minute; sorry about that.2083

OK, so let's do another one; let's do a 2 Molar solution--2.0 Molar solution of H⁺.2091

Well, again, we have the H⁺ concentration: in this case, a 2.0 Molar solution, a solution that contains 2 molarity H⁺; that is the hydrogen ion concentration.2101

Well, we know that the H⁺ concentration, times the OH^- concentration, equals 1.0x10^-14; therefore, the OH^- concentration equals 1.0x10^-14, divided by 2.0, which was that.2112

And we end up with an OH^- concentration of 5.0x10^-15--a very, very small number; in this case, the hydrogen ion concentration hugely, hugely out-values the OH^- concentration.2132

This is acidic--I would say highly acidic; that is it; very, very dangerous.2149

OK, let's do another one here.2158

Example 3 (or, actually, I'm not sure if it's Example 3, but...I'll just do an example): At 100 degrees Celsius, the K_w equals 5.13x10^-13.2163

So remember: we said that, at different temperatures, the equilibrium constant is different.2183

At 25 degrees Celsius, the K_w is 1.0x10^-14; but if I change the temperature to 100 degrees Celsius, now it has gone up to 5.13x10^-13.2187

It has gone up.2199

The question to you is: Is this reaction, a dissociation of water into H⁺ plus OH^---is it endo- or is it exo-thermic?2202

OK, well, let's see what happens here: at 100 degrees Celsius, they are telling me that the K_w equals 5.13x10^-13.2227

They want to know if this reaction is endo- or exothermic.2240

Well, let's see what we did: we increased the temperature, and by increasing the temperature, we actually pushed the reaction forward, because that is what this K_w is telling us.2243

This K_w of 5.13x10^-13 is bigger than the 1.0x10^-14, right?--negative 13 is bigger than negative 14.2256

That means that the equilibrium has actually shifted to the right; that means more product has been produced.2267

That means that the reaction shifted to the right when I increased the temperature.2273

Well, if it increases to the right when I increase the temperature, that means that temperature, or heat, must have been one of the reactants, because, if it's one of the reactants, and if I increase this temperature, the system is going to want to offset what I do to it (which is an increase) by decreasing the temperature.2283

Well, in order to decrease the temperature, it has to use up this extra heat that I have pumped into it.2311

In order to use up the heat, it has to shift the reaction that way; it has to produce more H and more OH^-, which is exactly what it did, because now the equilibrium constant has gone up.2317

When an equilibrium constant goes up, that means the reaction has moved to the right.2329

The numerator of the equilibrium constant has increased; so, in this case, because heat is on the left side of this equilibrium arrow, this is an endothermic reaction.2333

So notice, we used our discussion of equilibrium and Le Chatelier's Principle to actually find out, qualitatively, that this is an endothermic reaction.2346

In order to push this reaction forward--in order to produce more H⁺ and more OH^-, I actually have to increase the temperature, which means that it is an endothermic reaction.2356

I don't know what the ΔH is, but I do know that it is going to be positive for this reaction.2368

OK, B: what is the H⁺ and OH^- concentration in a neutral solution at 100 degrees Celsius?2375

Well, we just said that K_w is equal to the concentration of OH^- times H⁺ at 100 degrees Celsius.2398

We gave it already; it's 5.13x10^-13.2407

Well, in a neutral solution--go back a slide or two--neutral means that the OH^- concentration is equal to the H⁺ concentration.2412

So, if I call this X and call that X, I end up with: X squared is equal to 5.23x10^-13.2425

I get: X is equal to 7.16x10^-7 molarity.2435

At 100 degrees Celsius, there is 7.16x10^-7 moles of H⁺ per liter of water, and 7.16x10^-7 moles of OH^- per liter of water.2444

That is all that is going on here; molarity is moles per liter.2461

OK, let's see what else we can do.2466

Now, we are going to close this discussion off by introducing the pH scale.2474

Now, I have to (I probably shouldn't say this, but I'm going to go ahead and do it, because I tell all my students this)...working with concentrations is perfectly valid--concentration is something we always work with; concentration of H⁺, concentration of OH^-, concentration of Cl^-...2479

With acids and bases, because these concentrations tend to be really, really small, as you have noticed (you know, 10^-7, 10^-6...), chemists have come up with a way to have numbers that actually are a little more easy to deal with--normal numbers like 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.2499

So, they have created this thing called a pH scale.2516

Here is what it means: the p of anything is equal to negative log of the concentration of that anything.2519

So, in other words, if I talk about pH, that is equal to the negative log of the hydrogen ion concentration.2532

If I talk about pOH, that is equal to the negative log of the hydroxide ion concentration.2540

If I say pK_a (so this p function means whatever it is...p of whatever--just take the negative log of that whatever), pK_a is the negative log of K_a.2546

It is a way of taking numbers that are really odd, like 6.6x10^-3, and turning them into actual numbers that you can deal with: 3.16--something like that.2562

Personally, I don't care for it myself; I like dealing strictly with what we are dealing with.2571

We are dealing with concentrations; the equilibrium constant is expressed in concentrations; so, I think it is perfectly valid to deal with concentrations.2578

But again, this is so deeply entrenched in chemistry that literally nobody talks about concentration anymore when they speak about acid-base.2588

They speak about pH and pOH and pK_a.2596

That is the only reason; but they are actually the same thing.2599

It is not like we are introducing a new concept; we are just introducing a way of changing the numbers of concentrations that tend to be really small, and turning them into numbers that make more sense, that look better--not make more sense, just look better, aesthetically.2605

OK, so one more example: if I said, "What is the pCl^-?" well, that is going to be the -log of the Cl^- concentration, if we happen to be talking about Cl^-.2618

It is just a p function, and it is the negative log of the concentration we are talking about.2630

OK, let's do an example.2636

What is the pH and pOH of a solution which is 1.4x10^-3 Molar hydroxide?2642

OK, well, they want the pH, and they want the pOH.2668

Well, I know the pH is the negative log of the hydrogen ion concentration; pOH is the negative log of the hydroxide ion concentration.2672

Well, they give me the hydroxide ion concentration, so why don't I just deal with that one first.2681

pOH is equal to negative log of the OH^- concentration, which is negative log of 1.4x10^-3.2685

I just stick in this in the calculator; I take the logarithm of it; I change the sign; and I end up with 2.85.2699

So notice, 2.85 is a much more attractive number than 1.4x10^-3; at least, that is what many people think.2709

I, personally, don't think so, but that is fine; I'm a chemist; we deal with pHs; we'll deal with pHs.2716

But, don't think it is something different; it is not.2722

If you want to, you are more than welcome to deal strictly in concentrations, and if you ever have to find a pH, just at the last minute take the negative log of it: no harm, no foul.2724

Now, we want the pH; well, the pH--we know that the H concentration, times the OH^- concentration, is equal to 1.0x10^-14.2735

The H⁺ concentration equals 1.00x10^-14 (well, let me just stick with 1.0; let's just do 2 significant figures here), divided by 1.4x10^-3.2748

That is going to equal 7.2x10^-12, and then, when I take the pH of that (that is going to be the negative log of the H concentration), -log of 7.2x10^-12 equals 11.14.2767

11.14 pH; 2.85 pOH: notice something--what is 11.14 plus 2.85? Yes, you guessed it--it's about 14.2791

Now, let's explain why.2806

We said that K_w is equal to the hydrogen ion concentration, times the hydroxide ion concentration.2812

Let's take the negative log of both sides.2822

-log of K_w is equal to -log of this whole thing: H⁺, OH^-...2824

Well, -log of K_w is pK_w; that is it--equals -log of H⁺, right?--plus the negative log of OH^-.2836

You end up with pH plus pOH; well, pK_w is the negative log of 1.0x10^-14, equals pH plus pOH.2860

Because K_w is 1.0x10^-14, the negative log of that is 14; that is our final relationship.2884

So, for any aqueous solution at 25 degrees Celsius, pH plus the pOH of the solution equals 14.2895

This is just a restatement of the fact that the H⁺ concentration times the OH^- concentration equals 1.0x10^-14.2914

These are the same thing, except one deals with these numbers (these scientific notation numbers, the small ones); one deals with numbers that are a little bit more tractable.2928

In any aqueous solution, the product--the product--of the hydrogen ion and hydroxide concentrations is 10^-14.2937

The pH plus the pOH of that solution is equal to 14.2948

OK, so we have introduced acid and base; actually, we have introduced acid mostly; we have talked a little bit about base, mostly in the context of conjugate base.2955

We have talked about the dissociation of acids and what happens in water.2964

We have introduced the idea of an equilibrium constant for that acid dissociation.2970

We have introduced the idea of water acting as both acid and base, an amphoteric substance.2976

And we have introduced the very, very important property that the product of the hydrogen ion and the hydroxide ion concentrations is 10^-14; or, if we want to use the p scale, we can talk about the pH and the pOH equaling 14 for any aqueous solution at 25 degrees Celsius.2981

Next time, we will continue our discussion of acids and bases, and we will actually get into some of the more equilibrium-type problems that are involved.3000

Thank you for joining us here at Educator.com and AP Chemistry.3008

We'll see you next time; goodbye.3010