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Let's say I have some weak acid.

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I'll call it HA.

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A is a place holder for

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really a whole set of elements that I could put there.

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It could be fluorine, it could be an ammonia molecule.

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If you add H it becomes ammonium.

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So this isn't any particular element I'm talking about.

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This is just kind of a general way of writing an acid.

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And let's say it's in equilibrium with, of course,

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and you've seen this multiple times, a proton.

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And all of this is in an aqueous solution.

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Between this proton jumping off of this

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and its conjugate base.

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And we also could have written a base equilibrium,

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where we say the conjugate base could disassociate,

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or it could essentially grab a hydrogen from the water

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and create OH.

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And we've done that multiple times.

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But that's not the point of this video.

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So let's just think a little bit about

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what would happen to this equilibrium

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if we were to stress it in some way.

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And you can already imagine

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that I'm about to touch on Le Chatelier's Principal,

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which essentially just says, look,

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if you stress an equilibrium in any way,

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the equilibrium moves in such a way

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to relieve that stress.

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So let's say that the stress that I apply to the system

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--Let me do a different color.

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I'm going to add some strong base.

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That's too dark.

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I'm going to add some NaOH.

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And we know this is a strong base

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when you put it in a aqueous solultion,

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the sodium part just kind of disassociates,

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but the more important thing,

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you have all this OH in the solution,

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which wants to grab hydrogens away.

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So when you add this OH to the solution,

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what's going to happen for every mole that you add,

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not even just mole,

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for every molecule you add of this into the solution,

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it's going to eat up a molecule of hydrogen.

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Right?

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So for example, if you had

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1 mole oh hydrogen molecules in your solution

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right when you do that,

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all this is going to react with all of that.

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And the OHs are going to react with the Hs

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and form water,

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and they'll both just kind of

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disappear into the solution.

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They didn't disappear, they all turned into water.

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And so all of this hydrogen will go away.

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Or at least the hydrogen that was initially there.

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That 1 mole of hydrogens will disappear.

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So what should happen to this reaction?

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Well, know this is an equilibrium reaction.

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So as these hydrogen disappear,

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because this is an equilibrium reaction

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or because this is a weak base,

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more of this is going to be converted

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into these two products

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to kind of make up for that loss of hydrogen.

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And you can even play with it on the math.

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So this hydrogen goes down initially,

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and then it starts getting to equilibrium very fast.

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But this is going to go down.

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This is going to go up.

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And then this is going to go down less.

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Because sure, when you put the sodium hydroxide there,

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it just ate up all of the hydrogens.

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But then you have this

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-- you can kind of view as

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the spare hydrogen capacity here to produce hydrogens.

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And when these disappear,

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this weak base will disassociate more.

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The equilibrium we'll move more in this direction.

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So immediately, this will eat all of that.

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But then when the equilibrium moves in that direction,

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a lot of the hydrogen will be replaced.

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So if you think about what's happening,

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if I just threw this sodium hydroxide in water.

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So if I just did NaOH in an aqueous solution

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so that's just throwing it in water

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-- that disassociates completely

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into the sodium cation and hydroxide anion.

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So you all of a sudden immediately

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increase the quantity of OHs

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by essentially the number of moles of

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sodium hydroxide you're adding,

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and you'd immediately increase the pH, right?

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Remember. When you increase the amount of OH,

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you would decrease the pOH, right?

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And that's just because it's the negative log.

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So if you increase OH, you're decreasing pOH,

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and you're increasing pH.

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And just think OH-- you're making it more basic.

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And a high pH is also very basic.

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If you have a mole of this, you end up with a pH of 14.

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And if you had a strong acid, not a strong base,

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you would end up with a pH of 0.

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Hopefully you're getting a little bit familiar

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with that concept right now,

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but if it confuses you,

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just play around with the logs a little bit

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and you'll eventually get it.

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But just to get back to the point,

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if you just did this in water,

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you immediately get a super high pH

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because the OH concentration goes through the roof.

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But if you do it here

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--if you apply the sodium hydroxide to this solution,

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the solution that contains

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a weak acid and it's conjugate base,

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the weak acid and its conjugate base,

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what happens?

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Sure, it immediately reacts with all of this hydrogen

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and eats it all up.

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And then you have this extras supply here

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that just keeps providing more and more hydrogens.

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And it'll make up a lot of the loss.

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So essentially, the stress won't be as bad.

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And over here, you dramatically increase the pH

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when you just throw it on water.

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Here, you're going to increase the pH by a lot less.

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And in future videos, we'll actually do the math of

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how much less it's increasing the pH.

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But the way you could think about it is,

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this is kind of a shock absorber for pH.

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Even though you threw this strong based

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into this solution,

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it didn't increase the pH

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as much as you would have expected.

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And you can make it the other way.

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If I just wrote this exact same reaction

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as a basic reaction

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--and remember, this is the same thing.

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So if I just wrote this as, A minus

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--so I just wrote its conjugate base--

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is in equilibrium with the conjugate base

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grabbing some water from the surrounding aqueous solution.

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Everything we're dealing with right now

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is an aqueous solution.

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And of course that water that it grabbed from

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is not going to be an OH.

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Remember, are just equivalent reactions.

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Here, I'm writing it as an acidic reaction.

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Here, I'm writing it is a basic reaction.

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But they're equivalent.

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Now.

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If you were to add a strong acid to the solution,

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what would happen?

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So if I were to throw hydrogen chloride into this.

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Well hydrogen chloride, if you just throw it

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into straight up water without the solution,

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it would completely disassociate into

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a bunch of hydrogens and a bunch of chlorine anions.

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And it would immediately make it very acidic.

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You would get to a very low pH.

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If you had a mole of this

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--if your concentration was 1 molar,

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then this will go to a pH of 0.

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But what happens if you add hydrochloric acid to

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this solution right here?

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This one that has this weak base

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and its conjugate weak acid?

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Well, all of these hydrogen protons that

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disassociate from the hydrochloric acid

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are all going to react with these OHs you have here.

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And they're just going to cancel each other out.

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They're just going to merge with these and turn into water

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and become part of the aqueous solution.

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So this, the OHs are going to go down initially,

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but then you have this reserve of weak base here.

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And Le Chatelier's Principal tells us.

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Look, if we have a stressor

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that is decreasing our overall concentration of OH,

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then the reaction is going to

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move in the direction that relieves that stress.

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So the reaction is going to go in that direction.

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So you're going to have more of our weak base

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turning into a weak acid and producing more OH.

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So the pH won't go down as much as you would expect

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if you just threw this in water.

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This is going to lower the pH,

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but then you have more OH that could be produced as

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this guy grabs more and more hydrogens from the water.

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So the way to think about it is it's kind of like

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a cushion or a spring in terms of what

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a strong acid or base could do to the solution.

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And that's why it's called a buffer.

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Because it provides a cushion on acidity.

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If you add a strong base to water,

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you immediately increase its pH.

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Or you decrease its acidity dramatically.

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But if you add a strong base to a buffer,

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because of Le Chatelier's Principal,

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essentially, you're not going to affect the pH as much.

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Same thing.

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If you add and acid to that same buffer,

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it's not going to affect the pH

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as much as you would have expected

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if you had thrown that acid in water

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because the equilibrium reaction can always

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kind of refill the amount of OH that you lost

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if you're adding acid,

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or it can refill the amount of hydrogen you lost

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if you're adding a base.

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And that's why it's called buffer. It provides a cushion.

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So it give some stability to the solution's pH.

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The definition of a buffer is

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just a solution of a weak acid in equilibrium

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with its conjugate weak base.

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That's what a buffer is, and it's called a buffer

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because it provides you this kind of cushion of pH.

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It's kind of a stress absorber,

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or a shock absorber for the acidity of a solution.

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Now, with that said,

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let's explore a little bit the math of a buffer,

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which is really just the math of a weak acid.

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So if we rewrite the equation again,

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so HA is in equilibrium.

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Everything's in an aqueous solution.

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With hydrogen and its conjugate base.

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We know that there's an equilibrium constant for this.

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We've done many videos on that.

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The equilibrium constant here is equal to

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the concentration of our hydrogen proton

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times the concentration of our conjugate base.

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When I say concentration, I'm talking molarity.

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Moles per liter divided by

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the concentration of our weak acid.

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Now.

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Let's solve for hydrogen concentration.

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Because what I want to do is

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I want to figure out a formula,

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and we'll call it the Hendersen-Hasselbalch Formula,

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which a lot of books want you to memorize,

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which I don't think you should.

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I think you should always just be able to

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go from this kind of basic assumption and get to it.

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But let's solve for the hydrogen

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so we can figure out a relationship

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between pH and all the other stuff that's in this formula.

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So, if we want to solve for hydrogen,

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we can multiply both sides

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by the reciprocal of this right here.

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And you get hydrogen concentration.

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Ka times

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--I'm multiplying both sides times a reciprocal of that.

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So times the concentration of our weak acid

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divided by the concentration of our weak base

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is equal to our concentration of our hydrogen.

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Fair enough.

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Now.

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Let's take the negative log of both sides.

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So the negative log of all of that stuff,

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of your acidic equilibrium constant,

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times HA, our weak acid divided by our weak base,

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is equal to the negative log of

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our hydrogen concentration.

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Which is just our pH, right?

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Negative log of hydrogen concentration is

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--that's the definition of pH.

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I'll write the p and the H in different colors.

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You know a p just means negative log.

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Minus log. That's all. Base 10.

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Let's see if we can simplify this any more.

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So our logarithmic properties.

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We know that when you take the log of something

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and you multiply it,

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that's the same thing as taking the log of this

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plus the log of that.

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So this can to be simplified to minus log of our Ka minus

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the log of our weak acid concentration divided by

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its conjugate base concentration.

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Is equal to the pH.

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Now, this is just the pKa of our weak acid,

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which is just the negative log of

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its equilibrium constant.

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So this is just the pKa.

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And the minus log of HA over A.

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What we can do is we could make this a plus,

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and just take this to the minus 1 power. Right?

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That's just another logarithm property,

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and you can review the logarithm videos

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if that confused you.

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And this to the minus 1 power just means invert this.

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So we could say,

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plus the logarithm of our conjugate base concentration

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divided by the weak acid concentration

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is equal to the pH.

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00:13:43,110 --> 00:13:44,540
And this right here,

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this is called the Hendersen-Hasselbalch Equation.

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And I really encourage you not to memorize it.

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00:13:51,700 --> 00:13:54,270
Because if you do attempt to memorize it,

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within a few hours, you're going to forget

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00:13:57,000 --> 00:13:58,470
whether this was a plus over here.

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00:13:58,480 --> 00:13:59,880
You're going to forget this,

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00:13:59,900 --> 00:14:01,850
and you're going to forget whether you

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00:14:01,870 --> 00:14:03,360
put the A minus or the HA

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00:14:03,390 --> 00:14:04,750
on the numerator or the demoninator,

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00:14:04,770 --> 00:14:06,040
and if you forget that, it's fatal.

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The better thing is to just start

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from your base assumptions. And trust me.

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00:14:10,270 --> 00:14:11,610
It took me a couple minutes to do it,

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00:14:11,630 --> 00:14:13,240
but if you just do it really fast on paper,

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00:14:13,270 --> 00:14:14,940
you don't have to talk it through the way I did

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00:14:14,970 --> 00:14:18,060
--it'll take in no time at all to come to this equation.

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00:14:18,070 --> 00:14:19,410
It's much better than memorizing it,

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00:14:19,430 --> 00:14:22,350
and you won't forget it when you're 30 years old.

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00:14:22,370 --> 00:14:24,750
But what's useful about this?

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00:14:24,760 --> 00:14:28,830
Well, it immediately relates pH to our pKa,

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00:14:28,840 --> 00:14:31,370
and this is a constant, right, for an equilibrium?

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00:14:31,400 --> 00:14:35,120
Plus the log of the ratios between the acid

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00:14:35,140 --> 00:14:37,050
and the conjugate base.

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00:14:37,080 --> 00:14:40,410
So the more conjugate base I have,

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and the less acid I have,

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the more my pH is going to increase. Right?

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00:14:45,490 --> 00:14:47,770
If this goes up and this is going down,

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00:14:47,790 --> 00:14:49,100
my pH is going to increase. Which makes sense

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00:14:49,110 --> 00:14:51,270
because I have more base in the solution.

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00:14:51,280 --> 00:14:52,870
And if I have the inverse of that,

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might be just going...