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0:01
- Titrations and titration curve is gonna be the topic of this lesson. My name is Chad and welcome to Chad's Prep, where my goal is to take the stress out of learning science. Now, in addition to high school and college science prep, we also do MCAT, DAT and OAT prep, as well. I'll leave a link in the description for where you can find those courses. Now this lesson's part of my new general chemistry playlist, and if you wanna be notified every time I post one,
0:21
subscribe to the channel, click the bell notification. So in this lesson, we're gonna take really more of a conceptual look at titrations and titration curves. If you're looking for all the pH calculations for titrations, those are gonna be in the next couple of lessons. so I'm just gonna warn you in advance here. So, but a qualitative look at the three different types of titration curves. We're gonna look at strong acid-strong base titrations, weak acid-strong base titrations,
0:41
and then weak base-strong acid titrations, and you'll find out that all of the titrations we're gonna look at here, either the acid or the base or both is going to be strong. We're not gonna take any look at weak acid-weak base titrations at all. It's not something commonly you're gonna ever come across in your general chemistry course. So, all right, so we're gonna start with strong acid-strong base, and the strong acid we're gonna use is HCl, and the strong base we're gonna use is NaOH.
1:06
And first thing you need to realize about a titration is that really commonly, like in industry and stuff, the whole point of doing a titration is to determine the concentration of some acidic or basic species. In our case, we're gonna make that species the HCl. We're gonna try and determine the concentration of HCl in here, and so what we would typically do is we'd take something like an Erlenmeyer flask.
1:30
So, and we'd put inside that Erlenmeyer flask our acid solution, and whatever you're trying to determine the concentration of, we would refer to that as your anolyte.
1:40
So, and then you're gonna set up
1:45
a burette, and inside that burette, in this case, if the anolyte is an acid, then in your burette is gonna be a base, and we're gonna refer to this guy as your titrant. And it could be the other way around. If you're trying to figure out the unknown, some unknown concentration of a base, well, then the base would be the anolyte and you'd use an acid as your titrant. So, but these are two common words you should definitely be familiar with, and the key is the titrant is gonna be standardized,
2:11
and by standardizing it, we're gonna know its exact concentration. That's gonna be important, because by knowing its exact concentration, we'll be able to determine the exact concentration of the anolyte, again, which is usually the whole point of doing a titration.
2:26
So in this case, our anolyte is an acid. It's HCl in this example, and so the pH starts out low. And as we start shooting NaOH into there, the pH is gradually gonna start to increase. But at some point, rather than being a gradual increase, you're gonna get this very rapid increase. So from like this point here to this point here might be a difference of only adding a drop or two of NaOH. And the whole point is to get to this midpoint right here, and I'll call it a midpoint.
2:52
Really, we should properly call it an inflection point. So an inflection point is where the slope is either changing from either increasing to decreasing or decreasing to increasing. And so you can see here all the way up until that point, the slope has been gradually increasing, getting more and more steep, but now it's gonna change to decreasing, getting less and less steep. And if you're into calculus, that means the sign of the second derivative goes from being positive to negative,
3:18
but definitely not something you need to know here. So, but that's an inflection point on this graph. So when you hear somebody refer to this equivalence point as an inflection point, that's what they mean.
3:32
I'll just put that on here. So this is the equivalence point. Sometimes we shorten that to EQ point. So, and a lot of students forget that it's the equivalence point. It is not the equilibrium point. So, and what we mean by the equivalence point is it is the point at which you've added a chemically equivalent amount of acid or base. Well, in our example, HCl and NaOH reacted in a one-to-one ratio, and so a chemically equivalent amount just means an equal number of moles,
3:58
an equimolar amount of NaOH to our HCl. So, that's gonna be true at the equivalence point, and so what that means then is that at that equivalence point, the moles Of HCl are gonna be equal to the moles of NaOH.
4:17
That's gonna be true right at that equivalence point, and only at that equivalence point.
4:23
Cool, and that's gonna be really convenient because, again, we're gonna know the molarity of our NaOH exactly, of our titrant, and we'll be able to figure out, well, what volume of that did we add
4:36
to get to that equivalence point? And once we know the molarity and volume, we can use that to find the moles of NaOH. In fact, another way to write this would be to write the molarity of NaOH
4:47
times the volume Of NaOH,
4:50
'cause molarity times liters is moles. And on the other side of this equation, you could write
4:59
the molarity of the HCl times the volume of the HCl, and now we've kind of made a really convenient equation for what's true at this equivalence point. So, because the truth is, you get to determine how much HCl you start with. You put it in that Erlenmeyer flask. If you wanna start with 10 milliliters, great, then you start with 10 milliliters. You wanna start with 50 millimeters? Great, start with 50 millimeters. It is your choice. Whoever's running the titration
5:24
gets to choose what that volume of HCl's gonna be. Now, the molarity of the NaOH is known, and we'll just measure with that burette how much NaOH it took to get to this equivalence point, so we'll know that volume, as well. And if we know the volume of HCl we start with, and then the molarity and volume of the NaOH, then we can solve for that molarity of the HCl. And again, that's often the point of a titration. And again, this is only true at that equivalence point.
5:50
Oftentimes the entire point of running a titration is to get that equivalence point so we can get the molarity of the anolyte.
5:58
So how do you know if you reach that equivalence point? Well, if you're mapping it out the entire time, you know, and you're adding a little bit of a NaOH and then taking a pH reading and mapping out this curve, well, then you could figure that out, but that's not usually what we do. Normally what we do is we use what's called an indicator to kind of figure this out. So an indicator is something that is gonna colors over a certain pH range. And so it turns out this equivalence point
6:22
is going to occur right at pH seven
6:27
in a strong acid-strong base titration. So we'll find out here that, you know, let's say we start off with 10 moles of HCl. Well, how many moles of NaOH would it take to reach the equivalence point? Well, again, the equivalence point's when we've added a chemically equivalent amount, and since again, they react in a one-to-one ratio, then it would be an equal number of moles. So if you start out with 10 moles of HCl, then you're gonna add 10 moles of NaOH. Now, because these are both strong,
6:52
this reaction goes to completion, and for a reaction that goes to completion, you really wanna look at this from a limiting reagent perspective. And so 10 moles of our acid and 10 moles of our base,
7:06
they're gonna react completely and you're not gonna have any HCl or NaOH left over whatsoever. But what you will form in the end is 10 moles of NaCl. Now you'll also form 10 moles of water, but the whole thing's an aqueous solution, so we don't really care about that. But you're forming 10 moles of NaCl here, and the important thing to realize is that NaCl is a neutral salt. So in the last lesson, in chapter 16, we looked at acidic salts and basic salts and neutral salts,
7:34
and we learned that group one metal ions and group two metal ions, and sodium's group one, were negligible as Lewis acids, whereas most other cations are gonna be acidic. And then we learned that the conjugate base anions of the strong acids, so are the negligible anions. And HCl's a strong acid, so Cl- was a negligible anion. So in NaCl here, having both a negligible cation and a negligible anion, was a neutral salt, and that is ultimately the reason
8:00
why the pH is gonna be seven at the equivalence point in a strong acid-strong base titration. So in this case, it's because the salts you produce in the titration ends up being a neutral salt. That's kind of the idea. When we look at the weak acid-strong base or weak base-strong acid titrations, the pH will not be seven at the equivalence point, and that's not intuitive. You might think, well, if you've added equal amounts of acid and base, shouldn't the pH be seven and neutral.
8:23
No, it turns out. Now, if the acid base are both strong, yes, but not if one's weak and one is strong. And it turns out my personal way of remembering this is I just look at whoever's strong and they win at the equivalence point. So we'll find out, with a weak acid-strong base, the pH is gonna be a little bit basic at the equivalence point, a little bit higher than seven, like seven to 10. And in a weak base-strong acid titration, it's the acid that is strong,
8:47
and so the pH will be a little bit acidic at the equivalence point, probably somewhere between four and seven. Now that's how I remember it, but as we'll see, that's not really the reason why, but we'll come back to that in a bit.
9:00
Okay, so one more thing about our indicator here. So, you want your indicator to change colors right around that equivalence point. Well, it turns out indicators don't just change color over a small pH window. It's actually over a pretty significant jump, usually a couple pH units' jump. But what's nice is that your pH jumps very quickly right across that equivalence point. So again, from down here to somewhere up here, it's usually only a difference of a drop or two,
9:25
and so you wanna choose an indicator that's gonna change color right across that window in the six to eight range maybe in this particular titration. So, and it turns out phenolphthalein is a really common example of a good indicator to use in a strong acid-strong base titration because it will change colors right across that window. And it turns out that phenolphthalein itself is,
9:49
I'll just abbreviate it as an indicator here, it itself is an acid, a weak acid, so, and it has a weak acid form and it has a conjugate base form, which I'll just represent this way. It's actually a rather large molecule that I'm not gonna draw out or anything like that, so, but I'll represent it in these two forms here. And it turns out so that as you add NaOH, it itself also gets titrated. And so it turns out in its acid form, it's colorless. In its conjugate base form, though,
10:16
it has as a pinkish-purplish color. And so as you blow through this equivalence point, again, over the course of just like an extra drop or two of NaOH, the solution goes from being colorless to being pinkish-purplish, and once that happens, you know you've reached the end of your titration, so, and you've reached what's called the endpoint, and your endpoint is your best approximation of that equivalence point. And so these color change indicators are by far
10:39
the most common example of an indicator you're likely to see.
10:44
Okay, so it turns out then, we learned this with buffers in the last lesson, so when you've got a weak acid conjugate base, well, it turns out if the pH equals the pKa of your acid, then these will be present in equal concentrations. But if you go one pH unit lower than that, you'll have 10 times more acid. One pH unit higher than that, you'll have 10 times more conjugate base. And so in this case, if we want the pH in our titration to turn colors, change colors right around pH seven,
11:12
well then the indicator should have a pKa right around seven. So cool. So you want your indicator to have a pKa right around whatever pH you have at the equivalence point. Cool, and it turns out we've got a whole slew of different indicators, and the thing is that they're at least brightly colored in one of the two different versions so that we can use them, like as in the case with phenolphthalein, where it's brightly colored in the base form but colorless in the acid form.
11:38
Some change from red to green and things of the sort. So, but we have a whole host of 'em that we discovered over time and they change colors at different pH ranges, and so we can kind of look up in a table what their pKa's are and choose the appropriate indicator for whatever titration we're doing.
11:53
Okay, so let's take a look at our weak acid-strong base titration. And in this case, the weak acid we're gonna look at is HF, and we're still gonna use NaOH. And again, because NaOH is a strong base, as long as the acid or the base is strong, or both, this reaction will go 100% to completion, and so we're gonna look at it as kind of a limiting reagent problem again, and we'll incorporate that into our pH calculations in the next couple of lessons.
12:18
Now, a big difference here is what you're gonna find out is with a strong acid-strong base titration, so you'll find out when you first start the titration, you're adding NaOH, you get this nice, long linear region. So, but right at the beginning in a weak-strong titration, you're gonna a big change in pH right at the beginning and before it kind of flattens out a little bit. And you'll notice we see the same thing over here, with a weak base-strong acid.
12:40
In this case, we're starting out with the base and adding the acid, so the base is gonna go down, so you get a real sudden pH drop right at the initial point before it kind of flattens out a little bit and goes linear. And so that's characteristic if you've got a weak-strong titration versus a strong-strong titration, one of the key differences you can tell, but it's kind of a minor point, as we'll point out here in a second, 'cause there'll be an easier way to tell.
13:01
Now, you're still going to have an equivalence point here.
13:06
That's the inflection point in both of these here, it turns out.
13:13
And that equivalence point is still when you've added a chemically equivalent amount of titrant to your anolyte. And in this case, our anolyte is the HF, we're starting off with an acidic solution, and the titrant is the NaOH. And so at that equivalence point, you're gonna have the moles of HF equal to, let's put that in black,
13:37
the moles of NaOH in this case
13:41
And what that means again, we could write that in a more convenient form. We could say that the molarity of the HF times the volume of the HF is equal to,
13:54
same thing for the NaOH.
14:12
Cool, and once again, you're gonna know the molarity of NaOH. You can figure out what volume it took to get to the equivalence point. You get to choose what volume of HF you start with, and so you can use this to solve for the molarity of your anolyte, the HF in this particular example. Cool, now what you will find out, though, if we kind of drag this across, though, is that, again, your pH is not gonna be seven at the equivalence point. You're gonna find out
14:36
that it's going to be higher than seven. So, and again, usually not super higher than seven, but somewhere probably in the seven to 10 range, depending on what exact weak acid you've chosen and things of that sort and what concentration it has. So, both play in a factor, but the key is the pH is gonna be a little bit basic. Now, again, my way of remembering this is I look at weak acid-strong base, the base is strong and it wins at the equivalence point. But again, that's not really the reason.
15:01
The reason, so notice if you start off with 10 moles HF
15:06
and you add 10 moles of NaOH,
15:10
so they're gonna react completely and gonna neutralize each other completely so that you have no HF and no NaOH left whatsoever. But in this case, you're gonna form 10 moles of sodium fluoride. And whereas, again, sodium being group one, is still negligible, the fluoride is not. So the fluoride is not the conjugate base of a strong acid, but the conjugate base of a weak acid, and is therefore really a base, and so this is a basic salt, and that is ultimately the reason
15:40
why the pH is gonna be basic. It's 'cause the salt that you produce is a basic salt. Now, if I asked you, why is the pH greater than seven in a weak acid-strong base titration at the equivalence point? So if you said, because the salt that is produced is basic salt, that is 100% true. So, but if you had to choose kind of like which of the following is true on a multiple choice test, they might phrase it that way, but they might phrase it a little bit different.
16:06
So instead of saying that sodium fluoride is a basic salt, they might say that it undergoes hydrolysis, so let me put that word up on the board here somewhere.
16:20
If you look at that word, hydrolysis, hydro refers to water, lysis means the splitting or destruction of, so this is the destruction or splitting of water. Well, it turns out that any chemical reaction that has water as a reactant where water gets used up, kind of water's getting destroyed, if you will, it's getting used up, it's getting consumed, and they call it a hydrolysis reaction. Well, an acid-base reaction that reacts with water,
16:41
where either an acid reacts with water to produce hydronium or a base reactions with water to produce hydroxide, those are examples of hydrolysis reactions. Sometimes we call them acid hydrolysis or base hydrolysis. Well, with this being a basic salt, this is gonna undergo base hydrolysis. And so in this case, your F- that you produced right here is then gonna react with water
17:05
to produce some OH- and some HF.
17:11
And so this is the hydrolysis reaction. This is why the solution is basic at the equivalence point, because the fluoride we produced, part of the sodium fluoride salt that's basic, reacts with water to produce some fluoride. Notice it also implies that you actually don't end up with zero HF because the fluoride, when it undergoes hydrolysis, produces a tiny amount in this equilibrium. The solution technically is not gonna have zero HF. It initially looked like it was going to,
17:37
but you will have a super tiny amount in this case, an amount that's equal to the amount of hydroxide you produce.
17:45
Cool, now we've got something else to address here, and it turns out we didn't have to worry about this on the strong acid-strong base titration, but with the weak-strong titrations, there are not just one important point, the equivalence point on the titration. There are actually gonna be two important points, and the other one is gonna be halfway to your equivalence point. So let's say, for example, that that point right there happened at 20 milliliters.
18:11
What we do is we'd go back to 10 milliliters.
18:17
So, and that point right here would be halfway to the equivalence point. We might call it the half equivalence point or the half neutralization point, and it is a special point. So we didn't have to worry about that here, as it turns out, but we're gonna use this point to find the pKa of our acid. Well, for strong acids, we just say they dissociate completely. So, and that implies that their Ka's are infinity. Well, they're not infinity, they're just really huge numbers.
18:43
So, but we never talk about their Ka's or their pKa's. But for weak acids, we do, and that's why this now becomes relevant. Well, right at this half equivalence point, let's see what's true here for a second now.
18:55
So if it took 10 moles of NaOH to get to the full equivalence point, one-to-one ratio, chemically equivalent amounts, well then, to get halfway there would only be half as much. And in this case, again, this reaction's gonna go to completion, since NaOH is a strong base, and NaOH would be the limiting reagent. And five moles of the NaOH would neutralize five moles of the HF to produce five moles of the NaF. And what you're gonna find out is that you're gonna have five moles of HF
19:25
left in your solution, but you're also gonna have five moles now of the conjugate base, the F-. And notice that's interesting, because you have five moles of a weak acid and five moles of its conjugate base, and you guys learned in the last lesson that when you have a close to one-to-one ratio of a weak acid and its conjugate base, you have a buffer. And notice how flat the pH is right around that region. That is a buffer solution right in there. The pH is not changing a ton,
19:53
so, and the truth is you got pKa, it turns out this is right where the point is pH equals pKa, as well. When your weak acid equals your conjugate base, we learned that's when pH equals pKa. In fact, if we take a look at the Henderson-Hasselbalch one more time real quick,
20:17
when your weak acid and conjugate base are equal, the ratio here is one. The log of one is zero, and pH just equals your pKa plus zero, I-E your pH is equals your pKa. And so, again, right at that half equivalence point, that is where the concentration of HF
20:36
is equal to your concentration of F-,
20:42
and as a result, that is where your pH equals your pKa.
20:50
So, and we saw the pKa for HF in the last lesson. It ended up being 3.2, right around 3.2, and so if this had a nice scale on the pH scale on the left here, on the Y axis, then we could look at this and be like, oh yeah, pKa is right around, you know, just a over three, or maybe we'd get closer, depending on how good this scale was. But it's 3.2, and so you can look at the titration curve of a weak acid-strong base titration and use it not only to approximate
21:17
what's the molarity of the HF that was in there, so, but you could figure out the pKa of the acid. So, in this case, I said we started knowing that we're titrating HF, the anolyte, with NaOH, the titrant, but oftentimes when you do a titration, you don't even know what your acid is. And oftentimes you can do this and then figure out the pKa of your acid, and sometimes that actually can be indicative enough to help you identify what acid it might be.
21:43
All right, now it turns out I said pH equals pKa, and a pKa is always for an acid, so at that half equivalence point, the pH equals the pKa of the conjugate acid. But it's also true that the pOH,
21:57
let's make that look a little better, the pOH equals the pKb of the conjugate base, as well. That is also true at that half equivalence point, as well. We don't usually worry about it as my much 'cause we're usually more concerned with the pKa of the acid than the pKb of the conjugate base, but both are true. So, but in this case, in titrating a weak acid, we probably were more concerned with getting the pKa of the acid, whereas in the next one, when we start titrating a weaker base,
22:20
it might be the other way around. So, but two important points on this curve, and I really want you to know the distinction between those two points. We've got the equivalence point, we got the half of equivalence point, and a lot of students memorize them, what they are and what they mean, and they give the same definition, and they say, well, at the equivalence point, the moles of acid equals the moles of base, and that's a true statement. And then they say, at the half equivalence point,
22:44
the moles of acid equals the moles of base. Well, that's also a true statement, but we're talking about two different bases here. So at the equivalence point, the moles of the acid you're titrating, the anolyte acid, equal the moles of the titrant base, NaOH in this case, whereas at the half a equivalence point, it's the moles of conjugate acid and conjugate base that are equal instead. So be careful you don't just say acid and base and not realize which base you're referring to,
23:09
'cause it's two different bases we're saying are equal to the acid in both cases here, so hopefully you see that distinction. Finally, let's take a look at our weak base-strong acid titration. So in our weak base-strong acid titration, your equivalence point now again is not gonna be seven, but it is the acid that is strong, and so you're gonna find out that your equivalence point's gonna be a little bit acidic. It's going to be below seven now.
23:36
And again, usually somewhere in the four to seven range. And again, the reason, though, it's not because the acid was strong and it wins. Again, that's just my way of remembering it. The key is that the salt you are producing, I was gonna write salt. I wanted to write acidic. I say one thing, can't write the same. All right, I can't write another, anyways. So there's a acidic, that's the key. The salt, we're gonna produce an acidic salt. Now, again, the chloride is the conjugate base
24:01
of a strong acid, so it's a negligible anion, but the ammonium is not a group one or group two metal ion or one of those rarer transition metal ions with a plus one charge. It's a polyatomic ion. It's not even a metal ion, at that. It is acidic. It's a Lewis acid, it's a Bronsted acid, it's acidic. And what do acids do? Well, acids react with water.
24:21
They undergo hydrolysis
24:25
to produce a little bit of hydronium.
24:31
And so if I asked you, what is the reason that the pH is less than seven at the equivalence point in a weak base-strong acid titration, a couple correct answers. You could say that the salt that is produced is an acidic salt, true statement. Or you could get a little more technical with your jargon and you could say that the salt that is produced undergoes hydrolysis to produce hydronium. That's why the pH is gonna be less than seven at the equivalence point.
24:59
Now, once again, if it took 20 milliliters or 30 milliliters, something like this, let's just pick 30 this time, 30 milliliters of our HCl to get to that equivalence point, well, then at the 15 milliliter mark, halfway there,
25:18
you're at the half equivalence point. And the same things were all true here that were true before. So once again, if I start off with 10 moles of my weak base, I would have to add 10 moles of HCl to get to that equivalence point, a one-to-one ration. So how much HCl would I have to add to get halfway to that equivalence point? Only five moles,
25:41
and that makes HCl the limiting reagent, and we lose it all, and we'll lose exactly the same number of moles of NH3, but also gain the same number of moles of NH4 plus the ammonium ion. And so we're still gonna have five moles of ammonia left, but we'll now have formed five moles of the conjugate acid, NH4+, and that's why the moles of the conjugate base and the moles of the conjugate acid are going to be equal. And so in this case, the molarity of NH3 is gonna equal
26:15
the molarity of the ammonium ion, as well.
26:22
So, and as a result, once again, if your conjugate acid and conjugate base concentrations are equal, well, again, that happens when pH equals pKa.
26:35
And again, always true as well, is that pOH equals pKb.
26:41
So if your goal was to get the pKa of ammonium, great, you're good to go. If your goal was to get the pKb of ammonia, well, then rather than looking at the pH, you'd want to convert into a pOH instead.
26:54
Cool, so one thing to note on this one, you're much less likely to see a base getting titrated. So it's just usually kind of secondary to talking about acids getting titrated first. So, and when students do see it, though, they're like, so is the half equivalence point here or is it over here? And the key is remembering that it's halfway to the equivalence point in terms of the volume of titrant added. So you definitely don't wanna have it past that equivalence point. It's definitely before.
27:21
Cool.
27:24
Once again, since your weak acid and conjugate base concentrations are equal right there, that again is right where pH equals pKa and you have a buffer once again. And again, you can go one pH unit higher or one pH unit lower, and the pH doesn't change a whole lot, but get outside that region, and the pH jumps, get right outside that region and the pH will jump in one way, shape, or form, and it's no longer a buffer. And so once again on this titration curve,
27:49
there's a couple of interesting points, the equivalence point, the half equivalence point. And once again, if you wanted to know the pKa of ammonium or the pKb of ammonia, you could use that half equivalence point to figure it out. Cool, that kind of wraps up this lesson. So in the next couple lessons, again, we're gonna be doing all the pH calculations for titrations. In the next one, we'll do strong acid-strong base titrations and we'll look at pH calculations at a variety of points
28:16
along the way in that titration, and then we'll move on to weak acid-strong base titrations, and look at calculating the pH at different points along the way in the titration for those, as well, and we'll see that the weak base-strong acids are pretty analogous to the weak acid-strong base. So, we might do one or two, but we probably won't do the whole gamut like we will for those. Now, if you found this lesson helpful and you wanna support the channel,
28:38
the thumbs up button's pretty much the best thing you can do. If you're looking for general chemistry practice, check out my General Chemistry Master Course. I'll leave a link in the description. A free trial's available. Happy studying.
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