Acids and bases
Titration Roundup Making sure you fully understand titration curves
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- I've drawn a bunch of titration curves here.
- So let's see if we can review everything we've learned to
- kind of have a more holistic understanding of interpreting
- these things.
- So the first thing to look at is which of these are the
- titration of acids versus bases?
- And everything I've done now is acids, but the logic for
- base titration is the exact same thing as acid.
- So for example, these are acid titrations.
- We start with low pH's.
- In all of these, this axis is pH.
- I should have drawn that ahead of time before I asked you the
- question, but I think you knew that already.
- So before we add any of the titrator or the reagent, in
- this reaction, we're starting with a low pH.
- So this is kind of our starting point.
- So we have a low pH there.
- We have a low pH there.
- So these are both clearly acids.
- Here, our starting point before we start titrating at
- all, it's a high pH.
- So both of these are bases.
- Let me write that down.
- These are clearly both bases.
- Base titration, and this is an acid titration.
- Now, we haven't covered bases.
- But it's the same exact idea.
- In an acid titration, you start with an acid and you add
- a strong base to it to sop up all of the acid until all of
- the acid is sopped up and you hit the equivalence point.
- You hit the point that all of the acid is sopped up.
- And now, as you add more and more strong base, you're
- making it superbasic.
- So in this acid, our equivalence
- point is over here.
- And in this acid, our equivalence
- point is over here.
- This is how much solution we had to add to sop
- up all of the acid.
- Right there.
- So given what we already know, which one's a strong acid,
- which one's a weak acid?
- Well, this one, when sopped up all of the acid, we have a
- completely neutral solution.
- So this must have been a strong acid.
- There's nothing left.
- Everything has been converted to water in its natural state.
- pH of 7.
- And we might have had some neutral leftover conjugate
- bases there.
- But since it was a strong acid, those conjugate bases
- don't do anything.
- They don't add anything to the pH.
- They're not really basic.
- The chlorine in hydrogen chloride, the chlorine ion,
- doesn't change the pH.
- So this is a strong acid.
- And this one, when we got to the equivalence point-- when
- we had used up all of the acid in a solution, and then we hit
- this in inflection point, where any OH we added was
- significantly increasing the pH-- when we hit that
- equivalence point, our pH was already basic.
- And that's because we had all of the conjugate base of the
- weak acid, which does make the solution more basic.
- So this is a weak acid.
- And in both of these situations, we were increasing
- the concentration of OH minus.
- Maybe by adding sodium hydroxide to the solution, a
- strong base.
- Now, In these situations, we start with a base, and we add
- a strong acid to it.
- Maybe whatever base.
- We're adding hydrogen chloride, something that will
- sop up the OH.
- Here, we want to sop up the OH and bring its concentration
- down, until some point that we have sopped up all of the OH.
- All of the base is gone.
- Or most of it is gone.
- In this situation, we're in a completely neutral situation.
- So when we sopped up all of the base,
- we're completely neutral.
- No basic conjugate bases left.
- So this is a strong base.
- And here, the titration, we're increasing the hydrogen
- solution, or the hydrogen concentration, to
- sop up all the base.
- Same thing here.
- We're sopping up all of the base.
- We start over here.
- But over here, the inflection point happens right over here.
- So we've sopped up all of its base, but some of its
- conjugate acid is still left over, even after we've sopped
- up all of its base.
- So we end up with a slightly negative pH at
- the equivalence point.
- So this is a weak base.
- Let me actually draw that reaction for you.
- Remember, a weak base looks something like this.
- Maybe its A minus is in equilibrium-- that second
- equilibrium arrow is a little too wild for my blood-- is
- equilibrium with AH.
- It grabs hydrogen ions from the surrounding water.
- Everything is in an aqueous solution.
- So after you add hydrochloric acid to this-- remember, HcL
- disassociates completely into hydrogen ions
- plus chlorine anions.
- If you add hydrochloric acid to this, these things are
- going to just completely sop up these things.
- So we keep sopping up those things.
- Our concentration of OH goes down and down and down.
- And as we sop up this, our reaction goes in that
- direction because Le Chatelier's Principle.
- More and more of this is going to get formed
- into this and that.
- Until some point, we're out of that, and we have
- a ton of this left.
- And so our equivalent point is when we're out of this stuff.
- And when we're adding more hydrogens, we're getting
- really acidic really fast. But we have a lot of the conjugate
- acid there in the solution already.
- So we're going to have an acidic equivalence point.
- Now, let me give you an actual problem, just to hit all the
- points home.
- Because everything I've done now has been very hand-wavey,
- and no numbers.
- So let me draw one.
- Let me draw a weak acid.
- And you'll recognize it because you're
- good at this now.
- But I'll deal with some real numbers here.
- So let's say that's a pH of 7.
- We're going to titrate it.
- It starts off at a low pH because it's a weak acid.
- And as we titrate it, it's pH goes up.
- And then it hits the equivalence point and
- it goes like that.
- The equivalence point is right over here.
- And let's say our reagent that we were
- adding is sodium hydroxide.
- And let's say it's a 0.2 molar solution.
- I've been using too round numbers.
- I'll use 700 milliliters of sodium hydroxide is our
- equivalence point.
- Right there.
- So the first question is how much of our
- weak acid did we have?
- So what was our original
- concentration of our weak acid?
- This is just a general placeholder for the acid.
- So original concentration of our weak acid.
- Well, we must have added enough moles of OH at the
- equivalent point to cancel out all of the moles of the weak
- acid in whatever hydrogen was out there.
- But the main concentration was from the weak acid.
- This 700 milliliters of our reagent must have the same
- number of moles as the number of moles of weak acid we
- started off with.
- And let's say our solution at the beginning was 3 liters.
- 3 liters to begin with, before we started titrating.
- Obviously, as we add reagent, we're adding some volume to
- the solution.
- But let's just say that in the beginning, we
- started with 3 liters.
- So how many moles have we sopped up?
- Well, how many moles of OH are there in 700 milliliters of
- our solution?
- Well, we know that we have 0.2 moles per liter of OH.
- And then we know that we don't have--
- times 0.7 liters, right?
- 700 milliliters is 0.7 liters.
- So how many moles have we added to the situation?
- Let's see.
- 2 times 7 is 14.
- And we have 2 numbers behind the decimal.
- So it's 0.14.
- So 700 milliliters of 0.2 molar sodium hydroxide, and we
- have 700 milliliters of it, or 0.7 liters.
- We're going to have 0.14 moles of, essentially, OH that we
- put into the solution, which means that it canceled out
- completely with the same number of moles of our
- original acid.
- So that means that the original concentration of our
- acid is equal to 0.14 moles.
- That's how many moles we had.
- And we know that our original solution before we started
- titrating at all, is 3 liters.
- Remember, the molecules are canceling
- directly with each other.
- So that's why I wanted to figure out how many actual
- atoms, or molecules, of OH did I add.
- Those canceled out with the exact same number of atoms of
- out weak acid.
- And so this is how many atoms or molecules of our weak acid
- we must have started off with.
- And so you divide that by the number of liters, and then you
- have your original molarity.
- So 0.14 divided by 3.
- So you're initial concentration of the mystery
- acid was 0.046 molar.
- Fair enough.
- Now, the other question is, what is the pKa
- of our mystery acid?
- Well, we just go to the half equivalence point.
- So we said, OK.
- What was the pH of our titration
- curve or of our solution?
- We were at the half equivalence point.
- So when we had only added 350 milliliters of our reagent, of
- our strong base, to the solution.
- So you go there, and you say OK, the pH was 5.
- pH is equal to 5.
- And we know, from the last video, that if you take this
- half equivalence point, the pH is equal to the pKa, the
- negative log of our equilibrium constant.
- So there.
- We figured out the equilibrium constant as well.
- It's equal to 5.
- So all of this titration curve and all of this, I'm just
- showing you how experimentally, you can take
- some mystery acid or base.
- You add strong acid or base to it.
- You plot out this curve.
- And then you can pinpoint some of the properties, the
- concentration of your original acid or base.
- And only if you're dealing with a weak acid or base, you
- can figure out it's equilibrium constant.
- Obviously, if you take a strong acid, you say, oh, my
- half equivalence point is here.
- So therefore, this must be the equilibrium or the pKa-- No.
- There is no equilibrium constant for a strong acid.
- And there is no equilibrium constant for a strong base,
- because they're not in equilibrium.
- They disassociate completely.
- Anyway, hopefully you have a good understanding of
- titration now.
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