We're being asked to find the pH at the equivalence point of a titration between an acid and a base. Not only are we to find pH, but also the volume of the HNO3 needed to reach this equivalence point. Now the students typically find that the calculation of the pH at the equivalence point is the most challenging. It is certainly the lengthiest. You will always need to do a couple reactions in a couple different tables in order to work these. So let's begin with part A. In part a, we're going to have a flask and in this flask is the pyradine. Okay, so we're going to put the pyradine into this flask. And we're given the molarity and the volume of this pyradine. Now, I know that pyradine is a weak base because it gives me the KB4 that is a give away that it's a weak base. I will then have a burette. And in the beret, we will put the nitric acid, so we're going to place that into the beret and slowly add it to this flask until we reach the equivalence point. So let's begin by writing the reaction. Whenever I see a strong acid given to me, I will use H3O plus to represent that strong acid. And the weak base peredine is C6H5N. Now you could just use a B to represent a weak base, but I'll write the whole formula since I know the whole formula. The strong acid pushes it to completion, and the acid will donate to the base to give C6H5N and then the H plus is on there. So there's the formula of the conjugate acid of that weak base. And water will be the next product formed. So that's the reaction. Since this is a one-way reaction, we will use an ICF table for this reaction. And in this ICF table, we know we have to put moles. So we're going to set out and figure out the moles. Any time we're given the molarity and the volume of the substance, we can obtain the moles of that substance. So let's get the moles of that base. The moles of the base will be the molarity, which is 0.060 times the volume, which is 2.65, and I'm going to sneak my liters in there. There's the liters and this will give me the moles of base equal to 0.159. And I'll plug that in here. Now, they did not give me the molarity in the volume of the HNO3. They only gave me the molarity. So how do I get the moles? Well, it comes from the word equivalence point. By definition, the equivalence point is when the moles of acid equal the moles of base, according to this balanced equation. So before the reaction happens, there's none of this. And there's lots and lots of water, but we don't need numbers for it. Now in an ICF table, we will consume the smallest quantity. And always, when it's at the equivalence point, you're consuming the same quantity of those two things. You're producing this amount of the conjugate acid and we have 0s and we have 0.159. Okay, so now we have completed our table. The next thing that's going to be helpful for us to calculate is the volume of that acid. Well I know two things about the acid. How many moles that there were in that acid, so let's write that number. I have 0.159 moles of the acid. And I know the molarity of the acid, which is moles per liter. So I can take 0.447 moles per liter and obtain the volume of the acid and that is 2.65 And we have it in, oops, not 2.65, my bad. It is 0.356 liters of the acid that had to be added. So that answers this portion, what is the volume of the acid needed in order to reach the equivalence point? Since I knew the moles needed, and I know the molarity, I can get the volume of the acid. And in this case, the acid is HNO3. Okay, so the other part is to calculate the pH. Now this will always be needed when you're at the equivalence point and you're calculating the pH of the titration at the equivalence point. Next thing you have to do is consider this F line and say, what is present? After it reaches this F, the final reaction. And we have present this many moles of this substance, which we have established is an acid. So you will always follow an ICF table with an ICE table for the reaction of the weak thing sitting over on that side, which in this case is a weak acid. It's re-establishing its equilibrium in water, giving me C6H5N, the acid donates to the water, and H3O+. I have to plug into an ICE table molarity. Now what is the molarity of this acid? Well, I know two things. I know the moles of the acid, 0.159 moles. And I know the volume of the solution. That is 2.65 liters for the base that was put into the solution and 0.356 liters for the acid that was put into the solution. This is going to be giving me a concentration of that acid as 0.0529 molar, and that's what goes in the table, 0.0529. Okay, so in an ICE table, in which we know how much acids we're putting in here, we know that some of it, but not all of it, will react because it's in equilibrium. And I will produce these products, so I'll have 0.0529-x, and x and x. Okay, so now I'm ready to solve for x because if I could solve for x, I would know the H3o+ concentration and I could obtain the pH. Well I'll need a KA value since this is a weak acid. I'll need a KA. Well I wasn't given a KA, I was given a KB. So I'll take the k w over the k b. And that will be equal to x squared over 0.0529- x. Well this is a very small k, when you divide these two values, you get a very small k. So, we can assume that x will be negligible and can ignore that term. And you might want to stop the video and solve for x. When you do, you should obtain that x is 5.6 times 10 to the minus 4. And that is small so it's a legitimate assumption that we made and then we can obtain the pH from there. pH would be the negative log of this number. So you take the negative log of that value, you will obtain the value of 3.25 and that's the pH. Add the equivalent to point between a weak base and a strong acid. So we gotta consider, before we finish, is this a good pH, is it a reasonable pH? Well, any time you're doing a titration where the acid is strong, but the acid is weak, it's going to have a pH at the equivalence point less than seven. So that is a legitimate value that we have obtained here for this problem.
