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I've drawn a bunch of titration curves here.

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So let's see if we can review everything we've learned to

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kind of have a more holistic understanding of interpreting

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these things.

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So the first thing to look at is which of these are the

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titration of acids versus bases?

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And everything I've done now is acids, but the logic for

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base titration is the exact same thing as acid.

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So for example, these are acid titrations.

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We start with low pH's.

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In all of these, this axis is pH.

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I should have drawn that ahead of time before I asked you the

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question, but I think you knew that already.

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So before we add any of the titrator or the reagent, in

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this reaction, we're starting with a low pH.

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So this is kind of our starting point.

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So we have a low pH there.

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We have a low pH there.

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So these are both clearly acids.

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Here, our starting point before we start titrating at

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all, it's a high pH.

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So both of these are bases.

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Let me write that down.

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These are clearly both bases.

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Base titration, and this is an acid titration.

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Now, we haven't covered bases.

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But it's the same exact idea.

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In an acid titration, you start with an acid and you add

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a strong base to it to sop up all of the acid until all of

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the acid is sopped up and you hit the equivalence point.

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You hit the point that all of the acid is sopped up.

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And now, as you add more and more strong base, you're

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making it superbasic.

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So in this acid, our equivalence

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point is over here.

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And in this acid, our equivalence

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point is over here.

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This is how much solution we had to add to sop

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up all of the acid.

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Right there.

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So given what we already know, which one's a strong acid,

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which one's a weak acid?

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Well, this one, when sopped up all of the acid, we have a

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completely neutral solution.

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So this must have been a strong acid.

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There's nothing left.

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Everything has been converted to water in its natural state.

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pH of 7.

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And we might have had some neutral leftover conjugate

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bases there.

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But since it was a strong acid, those conjugate bases

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don't do anything.

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They don't add anything to the pH.

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They're not really basic.

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The chlorine in hydrogen chloride, the chlorine ion,

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doesn't change the pH.

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So this is a strong acid.

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And this one, when we got to the equivalence point-- when

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we had used up all of the acid in a solution, and then we hit

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this in inflection point, where any OH we added was

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significantly increasing the pH-- when we hit that

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equivalence point, our pH was already basic.

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And that's because we had all of the conjugate base of the

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weak acid, which does make the solution more basic.

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So this is a weak acid.

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And in both of these situations, we were increasing

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the concentration of OH minus.

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Maybe by adding sodium hydroxide to the solution, a

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strong base.

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Now, In these situations, we start with a base, and we add

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a strong acid to it.

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Maybe whatever base.

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We're adding hydrogen chloride, something that will

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sop up the OH.

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Here, we want to sop up the OH and bring its concentration

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down, until some point that we have sopped up all of the OH.

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All of the base is gone.

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Or most of it is gone.

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In this situation, we're in a completely neutral situation.

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So when we sopped up all of the base,

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we're completely neutral.

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No basic conjugate bases left.

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So this is a strong base.

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And here, the titration, we're increasing the hydrogen

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solution, or the hydrogen concentration, to

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sop up all the base.

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Same thing here.

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We're sopping up all of the base.

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We start over here.

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But over here, the inflection point happens right over here.

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So we've sopped up all of its base, but some of its

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conjugate acid is still left over, even after we've sopped

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up all of its base.

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So we end up with a slightly negative pH at

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the equivalence point.

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So this is a weak base.

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Let me actually draw that reaction for you.

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Remember, a weak base looks something like this.

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Maybe its A minus is in equilibrium-- that second

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equilibrium arrow is a little too wild for my blood-- is

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equilibrium with AH.

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It grabs hydrogen ions from the surrounding water.

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Everything is in an aqueous solution.

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So after you add hydrochloric acid to this-- remember, HcL

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disassociates completely into hydrogen ions

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plus chlorine anions.

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If you add hydrochloric acid to this, these things are

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going to just completely sop up these things.

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So we keep sopping up those things.

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Our concentration of OH goes down and down and down.

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And as we sop up this, our reaction goes in that

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direction because Le Chatelier's Principle.

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More and more of this is going to get formed

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into this and that.

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Until some point, we're out of that, and we have

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a ton of this left.

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And so our equivalent point is when we're out of this stuff.

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And when we're adding more hydrogens, we're getting

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really acidic really fast. But we have a lot of the conjugate

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acid there in the solution already.

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So we're going to have an acidic equivalence point.

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Now, let me give you an actual problem, just to hit all the

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points home.

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Because everything I've done now has been very hand-wavey,

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and no numbers.

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So let me draw one.

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Let me draw a weak acid.

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And you'll recognize it because you're

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good at this now.

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But I'll deal with some real numbers here.

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So let's say that's a pH of 7.

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We're going to titrate it.

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It starts off at a low pH because it's a weak acid.

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And as we titrate it, it's pH goes up.

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And then it hits the equivalence point and

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it goes like that.

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The equivalence point is right over here.

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And let's say our reagent that we were

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adding is sodium hydroxide.

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And let's say it's a 0.2 molar solution.

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I've been using too round numbers.

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I'll use 700 milliliters of sodium hydroxide is our

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equivalence point.

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Right there.

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So the first question is how much of our

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weak acid did we have?

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So what was our original

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concentration of our weak acid?

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This is just a general placeholder for the acid.

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So original concentration of our weak acid.

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Well, we must have added enough moles of OH at the

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equivalent point to cancel out all of the moles of the weak

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acid in whatever hydrogen was out there.

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But the main concentration was from the weak acid.

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This 700 milliliters of our reagent must have the same

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number of moles as the number of moles of weak acid we

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started off with.

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And let's say our solution at the beginning was 3 liters.

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3 liters to begin with, before we started titrating.

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Obviously, as we add reagent, we're adding some volume to

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the solution.

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But let's just say that in the beginning, we

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started with 3 liters.

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So how many moles have we sopped up?

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Well, how many moles of OH are there in 700 milliliters of

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our solution?

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Well, we know that we have 0.2 moles per liter of OH.

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And then we know that we don't have--

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times 0.7 liters, right?

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700 milliliters is 0.7 liters.

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So how many moles have we added to the situation?

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Let's see.

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2 times 7 is 14.

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And we have 2 numbers behind the decimal.

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So it's 0.14.

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So 700 milliliters of 0.2 molar sodium hydroxide, and we

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have 700 milliliters of it, or 0.7 liters.

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We're going to have 0.14 moles of, essentially, OH that we

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put into the solution, which means that it canceled out

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completely with the same number of moles of our

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original acid.

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So that means that the original concentration of our

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acid is equal to 0.14 moles.

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That's how many moles we had.

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And we know that our original solution before we started

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titrating at all, is 3 liters.

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Remember, the molecules are canceling

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directly with each other.

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So that's why I wanted to figure out how many actual

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atoms, or molecules, of OH did I add.

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Those canceled out with the exact same number of atoms of

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out weak acid.

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And so this is how many atoms or molecules of our weak acid

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we must have started off with.

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And so you divide that by the number of liters, and then you

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have your original molarity.

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So 0.14 divided by 3.

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0.046.

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So you're initial concentration of the mystery

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acid was 0.046 molar.

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Fair enough.

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Now, the other question is, what is the pKa

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of our mystery acid?

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210
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Well, we just go to the half equivalence point.

211
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So we said, OK.

212
00:09:32,740 --> 00:09:35,830
What was the pH of our titration

213
00:09:35,830 --> 00:09:37,970
curve or of our solution?

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00:09:37,970 --> 00:09:39,300
We were at the half equivalence point.

215
00:09:39,299 --> 00:09:46,259
So when we had only added 350 milliliters of our reagent, of

216
00:09:46,259 --> 00:09:48,309
our strong base, to the solution.

217
00:09:48,309 --> 00:09:52,669
So you go there, and you say OK, the pH was 5.

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00:09:52,669 --> 00:09:55,409
pH is equal to 5.

219
00:09:55,409 --> 00:09:57,469
And we know, from the last video, that if you take this

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00:09:57,470 --> 00:10:04,440
half equivalence point, the pH is equal to the pKa, the

221
00:10:04,440 --> 00:10:07,080
negative log of our equilibrium constant.

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00:10:07,080 --> 00:10:07,800
So there.

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00:10:07,799 --> 00:10:10,589
We figured out the equilibrium constant as well.

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It's equal to 5.

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00:10:11,970 --> 00:10:15,430
So all of this titration curve and all of this, I'm just

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showing you how experimentally, you can take

227
00:10:18,460 --> 00:10:20,340
some mystery acid or base.

228
00:10:20,340 --> 00:10:22,600
You add strong acid or base to it.

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You plot out this curve.

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00:10:23,769 --> 00:10:26,620
And then you can pinpoint some of the properties, the

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00:10:26,620 --> 00:10:29,149
concentration of your original acid or base.

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And only if you're dealing with a weak acid or base, you

233
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can figure out it's equilibrium constant.

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00:10:35,409 --> 00:10:38,899
Obviously, if you take a strong acid, you say, oh, my

235
00:10:38,899 --> 00:10:42,209
half equivalence point is here.

236
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So therefore, this must be the equilibrium or the pKa-- No.

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There is no equilibrium constant for a strong acid.

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00:10:49,610 --> 00:10:52,289
And there is no equilibrium constant for a strong base,

239
00:10:52,289 --> 00:10:53,179
because they're not in equilibrium.

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They disassociate completely.

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Anyway, hopefully you have a good understanding of

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00:10:59,460 --> 00:11:01,250
titration now.

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