Titration roundup

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. 0.046. 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.