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Let's review a little bit of all we learned about titration

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curves, and see if we can divine any new information.

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So let me draw a couple of them.

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I'll just do very simple quick and dirty ones.

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And these of course, the x-axis is the amount of strong

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acid you're adding.

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In this case, it's my favorite strong acid.

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It's sodium hydroxide.

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You're increasing the amount of sodium hydroxide solution

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in either case.

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That's the titrator or I think the word is titrand.

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Or it also could be considered the reagent.

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And this is, of course, the scale is pH.

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Over here.

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We'll call this 7.

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Down here, 0.

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And that's 1.

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So I have some mystery acid here, and it looks

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something like this.

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That as I increase my base, my pH increases.

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And then at some point over there.

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And then it levels off.

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My pH is really high.

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And you look at that one.

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And then let me see, I have another one.

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And it look something like this.

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At some point, bam, it just goes like that.

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And then it goes like that.

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So my question is if you look at least two, first of all, is

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one of them a strong acid or weak acid?

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Or is it one or the other?

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And if you look at this, you say, OK.

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Let's look at the equivalence points.

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And the equivalence points are the steepest

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points on these curves.

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On this one, the equivalence point is right about there.

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On this one, the equivalence point is right about there.

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And remember, equivalence point is the point at which

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your hydroxide from your strong base has essentially

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sopped up all of the acid in your solution.

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Right?

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So this is your equivalence point right here.

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Now in this case, we stopped up all of the acid in our

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solution at this equivalence point.

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And our pH 7.

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So we've completely turned into a neutral solution.

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Because we know that we were dealing with a strong acid.

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So this is a strong acid.

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Let me do a different color.

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We were titrating a strong acid.

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How do we know that?

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because at the equivalence point, our strong base has

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completely neutralized it.

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There's nothing that's really of basic

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nature that's left over.

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You do have the conjugate base of the strong acid left over,

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but the conjugate base of a strong acid

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really isn't basic.

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If I have HCl and it disassociates into hydrogen

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and chloride-- and obviously, it only exists in

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hydrogen and chloride.

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This form doesn't exist.

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This isn't an equilibrium reaction.

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This is how it looks in an aqueous solution.

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You're like hey, I sopped up all of this stuff once I'm at

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my equivalence point.

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Don't I have all of these chloride

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conjugate bases there?

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Won't that make my pH go up?

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Be more basic?

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And I say, no.

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Because the conjugate base of a strong acid is pretty much a

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neutral molecule.

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It has no real basic properties.

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If it had some basic properties, this would turn

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into an equivalence.

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You would actually have some movement the other way.

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But you don't.

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If you stick a bunch of chloride anions in water, it's

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not going to start creating hydrogen

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chloride out of the blue.

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So this has no basic properties.

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So once you have sopped up all of the hydrogen,

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your pH is at 7.

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So if you look at the equivalence point, pH at 7,

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you have a strong acid.

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Now in this situation, our equivalence point--

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we're at a higher pH.

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I don't know.

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Maybe that's a pH of 9.

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So we sopped up all of the acid, but we still have a

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basic solution.

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Or, just at that moment, we still have a basic solution

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before we continue to add even more OH to the solution.

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So what must have been happening?

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Well, this must be a weak acid, because a weak acid, the

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reaction looks like this.

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HA and it's in equilibrium with its conjugate base plus

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some hydrogen ions.

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As you continue to sop up this and this, the concentration of

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this base increases, right?

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Your hydroxide from your strong base

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sops this stuff up.

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The equilibrium goes more and more to the right by Le

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Chatelier's Principle to make up for this

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loss of hydrogen ions.

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But the whole time that equilibrium goes to the right,

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and we're pulling these hydrogen ions away, we're

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increasing our concentration of its conjugate base.

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And the conjugate base for a weak acid is a weak base.

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But it has basic properties.

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This is neutral.

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It has no effect on pH.

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This is a weak base.

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It does affect on pH.

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So at the equivalence point, you've sopped up all of this,

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and most of this.

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And I mean, for all purposes, all of it.

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But you're still left with a ton of this.

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Essentially all of this, as many moles of this have been

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converted into this.

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So at this point, let's say when you started off, you had

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A moles of this and B moles-- these were kind of the

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original equilibrium concentrations of this.

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When you're done at the equivalence point, you have

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none of this, and then you have B plus A of this.

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Every mole of this has been converted into at least 1 mole

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of this, plus whatever you had to begin with.

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And because of that, you have a basic equivalence point.

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Your pH will be slightly above 7.

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Let's see if there's anything else we can divine from--

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especially this one here.

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Let me write it down.

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This is a weak acid.

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Let me erase some of this.

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It's getting messy.

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Actually, I'll erase all of this.

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You know that we're titrating with NaOH.

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The hydroxide concentration is going higher and higher.

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But we know, for example, that at this point--

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let me write it right.

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So OH minus is going up.

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You can just view it-- sodium hydroxide's what we're adding,

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but sodium is really just what's kind of carrying the

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hydroxide before we put it into the aqueous solution.

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Once you go in there, the sodium's kind of useless.

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Similarly, if the conjugate-- well, I don't want to go into

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that too much.

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So we're adding hydroxide.

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We get to any equivalence point.

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This is the point where we have used up

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all of our weak acids.

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So let me write some concentrations here.

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Let's say at this point on the left, right here, before I

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started titrating anything, my concentration of my

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acid-- it was A.

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And let's say my concentration of my conjugate base--

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Remember, this was in equilibrium, so it's at B.

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Now, at this point, remember.

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I kept sopping up the hydrogen-- actually, I

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shouldn't have erased that.

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I shouldn't have erased the actual reaction.

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It's all in an aqueous solution.

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Equilibrium with H plus plus A minus on an aqueous solution.

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Now at this point, this is some initial equilibrium.

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We keep taking this up.

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The reaction goes to the right.

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We keep producing more of the A minus.

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Essentially, by the time we are here, our acid

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concentration, let me do that and green.

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Our acid concentration is essentially 0.

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It might be some super small negative number, but let's

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just say for the sake of simplicity, it's at 0 or very

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close to 0.

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What's our conjugate base concentration going to be?

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Let me do that in magenta.

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Our conjugate base concentration, and I know I'm

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getting messy because I'm overwriting this.

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Well, every mole of this that was moving forward in the

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reaction turned into 1 mole of this and 1 mole of that.

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This stuff kept getting sopped up by our titrator, our

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reagent, but we ended up with 1 mole of this so.

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So we went from A moles to 0 of our acid.

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We went from B moles of our conjugate base to B plus A

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moles of our conjugate acid.

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Interesting.

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Now.

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What can we do with this?

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Well, if we can somehow figure out the point along this curve

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where we had an equal amount of our acid and conjugate

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base, there might be something interesting

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that we could do it.

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And actually, I'll tell you what's the interesting thing.

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Let me write that the

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Henderson-Hasselbalch equation.

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I always have trouble pronouncing the second L in

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Hasselbalch, but I'm doing my best.

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But the Henderson-Hasselbalch Equation tells us-- let me do

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it down here.

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Actually, I'm running out of space.

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I'll do it here.

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The pH of-- and remember, this is only true of a weak acid or

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a weak base.

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There is no equilibrium constant for a strong acid or

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strong base.

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So you can only use Henderson-Hasselbalch and what

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I'm about to do now-- I'm going to call it the half

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equivalence point, and I'm going to talk

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about that a second.

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You can only do this with a weak acid or a weak base when

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that's what you're actually titrating.

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Of course you're always titrating with a strong acid

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or strong base, but the solution that you're trying to

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figure out has to be a weak one.

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So that tells us that the pH is equal to the pKa, or the

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negative log of the acid equilibrium constant, plus the

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log of your conjugate base concentration divided by your

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conjugate acid concentration.

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And we proved this a couple of videos ago.

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You essentially just take the log on both sides of the

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equilibrium equation and you do a little

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algebra and you get this.

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Nothing fancy.

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But what's interesting when these two things are equal to

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each other.

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When the concentration of your conjugate base is equivalent

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to the concentration of your weak acid.

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Well then this whole thing is going to be 1.

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Right?

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And what's the log of 1?

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Well, 10 to the 0 power is 1.

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So log base 10 of 1 is 0.

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So this whole thing will be 0.

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So that's interesting.

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When you have your concentration of conjugate

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base is equal to your concentration of your weak

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acid, this whole term turns into 0.

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And then your pH is equal to your pKa.

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So if we can figure out the point on this graph where our

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concentration of our acid and our conjugate base are equal,

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and we figure out the pH of that point, that point will

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also tell us the pKa.

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So if we don't know what acid we're dealing with, all of a

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sudden we'll be able to figure out it's pKa.

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And we'll know something about that acid.

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If we had a pKa table, hey, this is ammonium, or whatever

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we're dealing with.

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So how can we figure out the point at which these two

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concentrations are equivalent?

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What you do is you just say, OK.

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This is the equivalent point.

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This is the point at which we've run

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out of our weak acid.

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You go halfway to there.

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This is called a half equivalence point.

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I'll write that down.

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And you say, at this point, they're roughly

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equal to each other.

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00:11:20,129 --> 00:11:22,090
And the reason why say roughly is because you say OK, at this

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00:11:22,090 --> 00:11:28,100
point, my concentration of my acid is A over 2.

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00:11:28,100 --> 00:11:32,050
And my concentration of my base, at this point-- I

271
00:11:32,049 --> 00:11:35,259
started with B and A over 2 gets more converted into my

272
00:11:35,259 --> 00:11:39,189
conjugate base, so I have B plus A over 2.

273
00:11:39,190 --> 00:11:41,010
So you may say, hey, wait, I still have a little bit more

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00:11:41,009 --> 00:11:41,700
of the base here.

275
00:11:41,700 --> 00:11:43,460
Because I started with some of the base.

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00:11:43,460 --> 00:11:46,230
And the reason why you can take this as a point in which

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00:11:46,230 --> 00:11:50,029
they're equal is because this term right here is very, very,

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00:11:50,029 --> 00:11:52,919
very small for the great majority of acids.

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00:11:52,919 --> 00:11:55,479
And actually, when you're doing an experiment like this,

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00:11:55,480 --> 00:11:59,680
it doesn't take long to just go right past that point.

281
00:11:59,679 --> 00:12:01,649
This is almost like your experimental error.

282
00:12:01,649 --> 00:12:02,669
It doesn't show up.

283
00:12:02,669 --> 00:12:05,149
And if you don't believe me-- actually, let me just do a

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00:12:05,149 --> 00:12:07,449
little side there to make you believe that.

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00:12:07,450 --> 00:12:10,710
So we know an equilibrium constant is equal to your

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00:12:10,710 --> 00:12:14,000
concentration of hydrogen times a concentration of your

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00:12:14,000 --> 00:12:16,480
conjugate base over your concentration

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00:12:16,480 --> 00:12:17,955
of your weak acid.

289
00:12:17,955 --> 00:12:20,759


290
00:12:20,759 --> 00:12:23,360
Let's just do this for ammonium.

291
00:12:23,360 --> 00:12:27,000
The pKa for ammonium is 9.25.

292
00:12:27,000 --> 00:12:30,169
That means that the Ka for ammonium is 10

293
00:12:30,169 --> 00:12:32,349
to the minus 9.25.

294
00:12:32,350 --> 00:12:32,740
Right?

295
00:12:32,740 --> 00:12:36,350
You could just take the reverse log of both sides.

296
00:12:36,350 --> 00:12:37,560
But what number is that?

297
00:12:37,559 --> 00:12:49,099
10 to the minus 9.25.

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00:12:49,100 --> 00:12:54,860
is equal to 5.6 times 10 to the negative 10.

299
00:12:54,860 --> 00:13:00,560
So that is equal to, roughly, 10 to the negative 10.

300
00:13:00,559 --> 00:13:05,849
So if you just put some of this into some concentration,

301
00:13:05,850 --> 00:13:08,149
or you put some or your weak acid into a solution and you

302
00:13:08,149 --> 00:13:11,240
let it get to equilibrium--

303
00:13:11,240 --> 00:13:12,519
If I just do a little algebra.

304
00:13:12,519 --> 00:13:17,169
Your weak acid times your equilibrium constant is equal

305
00:13:17,169 --> 00:13:19,740
to your concentration of your hydrogen times

306
00:13:19,740 --> 00:13:21,590
your conjugate base.

307
00:13:21,590 --> 00:13:24,360
Now, if they didn't have any hydrogen or conjugate base to

308
00:13:24,360 --> 00:13:27,783
begin with, every mole of this disassociates into 1 mole of

309
00:13:27,783 --> 00:13:28,830
that and 1 mole of this.

310
00:13:28,830 --> 00:13:32,060
So these two things are going to be equal, right?

311
00:13:32,059 --> 00:13:36,629
So you could even say, it's the same thing as the

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00:13:36,629 --> 00:13:39,279
concentration of your weak base squared.

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00:13:39,279 --> 00:13:43,899
If you say, hey, this is the same thing as A minus, they're

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00:13:43,899 --> 00:13:45,129
going to be equal.

315
00:13:45,129 --> 00:13:49,320
So if you say that that is equal to your concentration of

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00:13:49,320 --> 00:13:53,410
your acid times your equilibrium constant, then you

317
00:13:53,409 --> 00:13:56,029
say your conjugate base concentration that

318
00:13:56,029 --> 00:13:56,919
you start off with.

319
00:13:56,919 --> 00:13:58,049
And this is all approximatating.

320
00:13:58,049 --> 00:13:59,370
I'm just trying to show you that your initial

321
00:13:59,370 --> 00:14:02,379
concentration of your conjugate base is much lower

322
00:14:02,379 --> 00:14:03,809
than your initial concentration of your

323
00:14:03,809 --> 00:14:04,979
conjugate acid.

324
00:14:04,980 --> 00:14:08,050
So it equals the square root of your concentration of your

325
00:14:08,049 --> 00:14:11,079
conjugate acid times the square root of Ka.

326
00:14:11,080 --> 00:14:14,180
In the case of ammonium, the square root of this is what?

327
00:14:14,179 --> 00:14:18,000
It's going to be like 2 point something something times 10

328
00:14:18,000 --> 00:14:20,809
to the minus 5 power.

329
00:14:20,809 --> 00:14:25,439
So whatever your concentration of your weak acid is, let's

330
00:14:25,440 --> 00:14:27,680
say it's ammonium in this case, you take the square root

331
00:14:27,679 --> 00:14:29,909
of that and then you multiply times something with a

332
00:14:29,909 --> 00:14:32,029
negative 5 power to get the concentration of your

333
00:14:32,029 --> 00:14:32,769
conjugate base.

334
00:14:32,769 --> 00:14:34,860
So this is much lower than that.

335
00:14:34,860 --> 00:14:37,570
These two numbers are much lower than that number for

336
00:14:37,570 --> 00:14:39,290
most weak acids.

337
00:14:39,289 --> 00:14:45,069
So because of that, you can ignore the amount of conjugate

338
00:14:45,070 --> 00:14:46,980
base you started off with.

339
00:14:46,980 --> 00:14:50,629
And so this point right here, your half equivalence point,

340
00:14:50,629 --> 00:14:54,389
you can pretty much assume that your concentrations of

341
00:14:54,389 --> 00:14:57,720
conjugate base and weak acids are equivalent at that point.

342
00:14:57,720 --> 00:14:59,480
And then by the Henderson-Hasselbalch

343
00:14:59,480 --> 00:15:02,840
Equation, this term right here is going to be 1.

344
00:15:02,840 --> 00:15:05,170
The log of 1 is 0.

345
00:15:05,169 --> 00:15:08,549
And the pKa will be equal to the pH.

346
00:15:08,549 --> 00:15:11,870
So you measure the pH here and say oh, that's the negative

347
00:15:11,870 --> 00:15:13,149
log of my equilibrium constant.

348
00:15:13,149 --> 00:15:14,990
That will be my pKa.

349
00:15:14,990 --> 00:15:18,279


350
00:15:18,279 --> 00:15:20,799
And until you found out something else that's

351
00:15:20,799 --> 00:15:22,089
interesting about your molecule.

352
00:15:22,090 --> 00:15:23,340