Acids and bases
Half Equivalence Point Figuring out the pKa of an unknown weak acid from the half equivalence point
⇐ Use this menu to view and help create subtitles for this video in many different languages.
You'll probably want to hide YouTube's captions if using these subtitles.
- Let's review a little bit of all we learned about titration
- curves, and see if we can divine any new information.
- So let me draw a couple of them.
- I'll just do very simple quick and dirty ones.
- And these of course, the x-axis is the amount of strong
- acid you're adding.
- In this case, it's my favorite strong acid.
- It's sodium hydroxide.
- You're increasing the amount of sodium hydroxide solution
- in either case.
- That's the titrator or I think the word is titrand.
- Or it also could be considered the reagent.
- And this is, of course, the scale is pH.
- Over here.
- We'll call this 7.
- Down here, 0.
- And that's 1.
- So I have some mystery acid here, and it looks
- something like this.
- That as I increase my base, my pH increases.
- And then at some point over there.
- And then it levels off.
- My pH is really high.
- And you look at that one.
- And then let me see, I have another one.
- And it look something like this.
- At some point, bam, it just goes like that.
- And then it goes like that.
- So my question is if you look at least two, first of all, is
- one of them a strong acid or weak acid?
- Or is it one or the other?
- And if you look at this, you say, OK.
- Let's look at the equivalence points.
- And the equivalence points are the steepest
- points on these curves.
- On this one, the equivalence point is right about there.
- On this one, the equivalence point is right about there.
- And remember, equivalence point is the point at which
- your hydroxide from your strong base has essentially
- sopped up all of the acid in your solution.
- Right?
- So this is your equivalence point right here.
- Now in this case, we stopped up all of the acid in our
- solution at this equivalence point.
- And our pH 7.
- So we've completely turned into a neutral solution.
- Because we know that we were dealing with a strong acid.
- So this is a strong acid.
- Let me do a different color.
- We were titrating a strong acid.
- How do we know that?
- because at the equivalence point, our strong base has
- completely neutralized it.
- There's nothing that's really of basic
- nature that's left over.
- You do have the conjugate base of the strong acid left over,
- but the conjugate base of a strong acid
- really isn't basic.
- If I have HCl and it disassociates into hydrogen
- and chloride-- and obviously, it only exists in
- hydrogen and chloride.
- This form doesn't exist.
- This isn't an equilibrium reaction.
- This is how it looks in an aqueous solution.
- You're like hey, I sopped up all of this stuff once I'm at
- my equivalence point.
- Don't I have all of these chloride
- conjugate bases there?
- Won't that make my pH go up?
- Be more basic?
- And I say, no.
- Because the conjugate base of a strong acid is pretty much a
- neutral molecule.
- It has no real basic properties.
- If it had some basic properties, this would turn
- into an equivalence.
- You would actually have some movement the other way.
- But you don't.
- If you stick a bunch of chloride anions in water, it's
- not going to start creating hydrogen
- chloride out of the blue.
- So this has no basic properties.
- So once you have sopped up all of the hydrogen,
- your pH is at 7.
- So if you look at the equivalence point, pH at 7,
- you have a strong acid.
- Now in this situation, our equivalence point--
- we're at a higher pH.
- I don't know.
- Maybe that's a pH of 9.
- So we sopped up all of the acid, but we still have a
- basic solution.
- Or, just at that moment, we still have a basic solution
- before we continue to add even more OH to the solution.
- So what must have been happening?
- Well, this must be a weak acid, because a weak acid, the
- reaction looks like this.
- HA and it's in equilibrium with its conjugate base plus
- some hydrogen ions.
- As you continue to sop up this and this, the concentration of
- this base increases, right?
- Your hydroxide from your strong base
- sops this stuff up.
- The equilibrium goes more and more to the right by Le
- Chatelier's Principle to make up for this
- loss of hydrogen ions.
- But the whole time that equilibrium goes to the right,
- and we're pulling these hydrogen ions away, we're
- increasing our concentration of its conjugate base.
- And the conjugate base for a weak acid is a weak base.
- But it has basic properties.
- This is neutral.
- It has no effect on pH.
- This is a weak base.
- It does affect on pH.
- So at the equivalence point, you've sopped up all of this,
- and most of this.
- And I mean, for all purposes, all of it.
- But you're still left with a ton of this.
- Essentially all of this, as many moles of this have been
- converted into this.
- So at this point, let's say when you started off, you had
- A moles of this and B moles-- these were kind of the
- original equilibrium concentrations of this.
- When you're done at the equivalence point, you have
- none of this, and then you have B plus A of this.
- Every mole of this has been converted into at least 1 mole
- of this, plus whatever you had to begin with.
- And because of that, you have a basic equivalence point.
- Your pH will be slightly above 7.
- Let's see if there's anything else we can divine from--
- especially this one here.
- Let me write it down.
- This is a weak acid.
- Let me erase some of this.
- It's getting messy.
- Actually, I'll erase all of this.
- You know that we're titrating with NaOH.
- The hydroxide concentration is going higher and higher.
- But we know, for example, that at this point--
- let me write it right.
- So OH minus is going up.
- You can just view it-- sodium hydroxide's what we're adding,
- but sodium is really just what's kind of carrying the
- hydroxide before we put it into the aqueous solution.
- Once you go in there, the sodium's kind of useless.
- Similarly, if the conjugate-- well, I don't want to go into
- that too much.
- So we're adding hydroxide.
- We get to any equivalence point.
- This is the point where we have used up
- all of our weak acids.
- So let me write some concentrations here.
- Let's say at this point on the left, right here, before I
- started titrating anything, my concentration of my
- acid-- it was A.
- And let's say my concentration of my conjugate base--
- Remember, this was in equilibrium, so it's at B.
- Now, at this point, remember.
- I kept sopping up the hydrogen-- actually, I
- shouldn't have erased that.
- I shouldn't have erased the actual reaction.
- It's all in an aqueous solution.
- Equilibrium with H plus plus A minus on an aqueous solution.
- Now at this point, this is some initial equilibrium.
- We keep taking this up.
- The reaction goes to the right.
- We keep producing more of the A minus.
- Essentially, by the time we are here, our acid
- concentration, let me do that and green.
- Our acid concentration is essentially 0.
- It might be some super small negative number, but let's
- just say for the sake of simplicity, it's at 0 or very
- close to 0.
- What's our conjugate base concentration going to be?
- Let me do that in magenta.
- Our conjugate base concentration, and I know I'm
- getting messy because I'm overwriting this.
- Well, every mole of this that was moving forward in the
- reaction turned into 1 mole of this and 1 mole of that.
- This stuff kept getting sopped up by our titrator, our
- reagent, but we ended up with 1 mole of this so.
- So we went from A moles to 0 of our acid.
- We went from B moles of our conjugate base to B plus A
- moles of our conjugate acid.
- Interesting.
- Now.
- What can we do with this?
- Well, if we can somehow figure out the point along this curve
- where we had an equal amount of our acid and conjugate
- base, there might be something interesting
- that we could do it.
- And actually, I'll tell you what's the interesting thing.
- Let me write that the
- Henderson-Hasselbalch equation.
- I always have trouble pronouncing the second L in
- Hasselbalch, but I'm doing my best.
- But the Henderson-Hasselbalch Equation tells us-- let me do
- it down here.
- Actually, I'm running out of space.
- I'll do it here.
- The pH of-- and remember, this is only true of a weak acid or
- a weak base.
- There is no equilibrium constant for a strong acid or
- strong base.
- So you can only use Henderson-Hasselbalch and what
- I'm about to do now-- I'm going to call it the half
- equivalence point, and I'm going to talk
- about that a second.
- You can only do this with a weak acid or a weak base when
- that's what you're actually titrating.
- Of course you're always titrating with a strong acid
- or strong base, but the solution that you're trying to
- figure out has to be a weak one.
- So that tells us that the pH is equal to the pKa, or the
- negative log of the acid equilibrium constant, plus the
- log of your conjugate base concentration divided by your
- conjugate acid concentration.
- And we proved this a couple of videos ago.
- You essentially just take the log on both sides of the
- equilibrium equation and you do a little
- algebra and you get this.
- Nothing fancy.
- But what's interesting when these two things are equal to
- each other.
- When the concentration of your conjugate base is equivalent
- to the concentration of your weak acid.
- Well then this whole thing is going to be 1.
- Right?
- And what's the log of 1?
- Well, 10 to the 0 power is 1.
- So log base 10 of 1 is 0.
- So this whole thing will be 0.
- So that's interesting.
- When you have your concentration of conjugate
- base is equal to your concentration of your weak
- acid, this whole term turns into 0.
- And then your pH is equal to your pKa.
- So if we can figure out the point on this graph where our
- concentration of our acid and our conjugate base are equal,
- and we figure out the pH of that point, that point will
- also tell us the pKa.
- So if we don't know what acid we're dealing with, all of a
- sudden we'll be able to figure out it's pKa.
- And we'll know something about that acid.
- If we had a pKa table, hey, this is ammonium, or whatever
- we're dealing with.
- So how can we figure out the point at which these two
- concentrations are equivalent?
- What you do is you just say, OK.
- This is the equivalent point.
- This is the point at which we've run
- out of our weak acid.
- You go halfway to there.
- This is called a half equivalence point.
- I'll write that down.
- And you say, at this point, they're roughly
- equal to each other.
- And the reason why say roughly is because you say OK, at this
- point, my concentration of my acid is A over 2.
- And my concentration of my base, at this point-- I
- started with B and A over 2 gets more converted into my
- conjugate base, so I have B plus A over 2.
- So you may say, hey, wait, I still have a little bit more
- of the base here.
- Because I started with some of the base.
- And the reason why you can take this as a point in which
- they're equal is because this term right here is very, very,
- very small for the great majority of acids.
- And actually, when you're doing an experiment like this,
- it doesn't take long to just go right past that point.
- This is almost like your experimental error.
- It doesn't show up.
- And if you don't believe me-- actually, let me just do a
- little side there to make you believe that.
- So we know an equilibrium constant is equal to your
- concentration of hydrogen times a concentration of your
- conjugate base over your concentration
- of your weak acid.
- Let's just do this for ammonium.
- The pKa for ammonium is 9.25.
- That means that the Ka for ammonium is 10
- to the minus 9.25.
- Right?
- You could just take the reverse log of both sides.
- But what number is that?
- 10 to the minus 9.25.
- is equal to 5.6 times 10 to the negative 10.
- So that is equal to, roughly, 10 to the negative 10.
- So if you just put some of this into some concentration,
- or you put some or your weak acid into a solution and you
- let it get to equilibrium--
- If I just do a little algebra.
- Your weak acid times your equilibrium constant is equal
- to your concentration of your hydrogen times
- your conjugate base.
- Now, if they didn't have any hydrogen or conjugate base to
- begin with, every mole of this disassociates into 1 mole of
- that and 1 mole of this.
- So these two things are going to be equal, right?
- So you could even say, it's the same thing as the
- concentration of your weak base squared.
- If you say, hey, this is the same thing as A minus, they're
- going to be equal.
- So if you say that that is equal to your concentration of
- your acid times your equilibrium constant, then you
- say your conjugate base concentration that
- you start off with.
- And this is all approximatating.
- I'm just trying to show you that your initial
- concentration of your conjugate base is much lower
- than your initial concentration of your
- conjugate acid.
- So it equals the square root of your concentration of your
- conjugate acid times the square root of Ka.
- In the case of ammonium, the square root of this is what?
- It's going to be like 2 point something something times 10
- to the minus 5 power.
- So whatever your concentration of your weak acid is, let's
- say it's ammonium in this case, you take the square root
- of that and then you multiply times something with a
- negative 5 power to get the concentration of your
- conjugate base.
- So this is much lower than that.
- These two numbers are much lower than that number for
- most weak acids.
- So because of that, you can ignore the amount of conjugate
- base you started off with.
- And so this point right here, your half equivalence point,
- you can pretty much assume that your concentrations of
- conjugate base and weak acids are equivalent at that point.
- And then by the Henderson-Hasselbalch
- Equation, this term right here is going to be 1.
- The log of 1 is 0.
- And the pKa will be equal to the pH.
- So you measure the pH here and say oh, that's the negative
- log of my equilibrium constant.
- That will be my pKa.
- And until you found out something else that's
- interesting about your molecule.
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
|
Have something that's not a question about this content? |
This discussion area is not meant for answering homework questions.
Discuss the site
For general discussions about Khan Academy, visit our Reddit discussion page.
Flag inappropriate posts
Here are posts to avoid making. If you do encounter them, flag them for attention from our Guardians.
abuse
- disrespectful or offensive
- an advertisement
not helpful
- low quality
- not about the video topic
- soliciting votes or seeking badges
- a homework question
- a duplicate answer
- repeatedly making the same post
wrong category
- a tip or feedback in Questions
- a question in Tips & Feedback
- an answer that should be its own question
about the site
Share a tip
Suggest a fix
Have something that's not a tip or feedback about this content?
This discussion area is not meant for answering homework questions.