Weak acid–strong base titrations

- [Instructor] Acetic acid is an example of a weak acid and sodium hydroxide is an example of a strong base. If we are titrating a sample of acetic acid with sodium hydroxide, acetic acid would be the analyte, the substance that we are analyzing, and sodium hydroxide would be the titrant. When acetic acid reacts with sodium hydroxide, the products are an aqueous solution of sodium acetate and water. Next, let's look at the complete or overall ionic equation for this reaction. Because the acetic acid is a weak acid, it does not ionize completely in aqueous solution. Therefore, for our complete ionic equation, we simply write a acetic acid. We don't show it as being ionized. However, sodium hydroxide is a strong base that associates 100% in aqueous solution. Therefore, we would show it as its ions, Na+ and OH-. Since sodium acetate is a soluble salt in aqueous solution, it would consist of sodium cations and the acetate anion. And we would also include water in our overall or complete ionic equation. For our net ionic equation, we leave out spectator ions. Since sodium cations are on the left and the right side, when we take those out, we're left with the net ionic equation for this weak acid-strong base titration. So acetic acid reacts with hydroxide anions to form the acetate anion and water. Next, let's look at the titration curve for our weak acid-strong base titration, pH is on the y-axis and since we're adding our strong base to our solution of weak acid, milliliters of base added is on the x-axis. Let's use particulate diagrams to help us figure out what's going on in this titration. Keep in mind that these particulate diagrams are only meant to represent what's going on in the solution during the titration and water molecules will be left out for clarity. Looking at our first particulate diagram, there's only acetic acid present, only two particles of acetic acid present. Therefore, this is before any base has been added. So on our titration curve, we're right here at zero milliliters of base added. Next, let's add some sodium hydroxide to our initial solution of acetic acid. So for sodium hydroxide, the pink sphere represents the sodium cation. So we think about adding in the sodium cation and also a hydroxide anion. Remember from our net ionic equation, hydroxide anion reacts with acetic acid to form the acetate anion and water. Since water is left out of our particulate diagrams, we don't see it here in this second particulate diagram. However, we do see the acetate anion that formed when the hydroxide anion reacted with the acetic acid particle. In the second particulate diagram, we also see the sodium cation that was added and also the particle of acetic acid that was present initially. Because we started with two particles of acetic acid and we have only one left in the second particulate diagram, that means that half of the initial acid has been neutralized. So this second particulate diagram is meant to represent the half equivalence point in the titration. Next, let's add enough sodium hydroxide to neutralize the other half of acid that was initially present in solution. The acetic acid particle reacts with the hydroxide anion to form water and the acetate anion. Since water is left out of our particulate diagram, we don't see water in this third particulate diagram. However, we do see the acetate anion that was formed. We also see these sodium cation that was added. And at the half equivalence point, we already had a sodium cation and an acetate anion, so we can see those in our third particulate diagram as well. If we compare the third particulate diagram to the first particulate diagram, all of the acid that was initially present has been neutralized. Therefore, the third particulate diagram represents the equivalence point of the titration. We can estimate the equivalence point on our titration curve by looking for the area where we see a sharp increase in pH. So right about in here. And if we draw a little line, about halfway up that line approximately, is a good place to mark the equivalence point. So this is a good estimate of our equivalence point. And if we go over to where that intersects in the y-axis, we can estimate the pH for this weak acid-strong base titration. It looks to be a little bit over eight, so between eight and nine somewhere. So the pH of the solution at the equivalence point is greater than seven. The reason why the pH is greater than seven is because at the equivalence point, there are acetate anions in solution and acetate anion react with water to form hydroxide anions and acetic acid. The pH of water at 25 degrees Celsius is seven, but because we've increased the concentration of hydroxide anions in solution, the pH will be greater than seven at the equivalence point. This is called anion hydrolysis and is the reason why the pH is greater than seven at the equivalence point for a weak acid-strong base titration. Going back to our titration curve to the equivalence point, if we drop down to the x-axis, we can see that the equivalence point has been reached after 50 milliliters of base have been added. So if it takes 50 milliliters of base to reach the equivalence point, it should take half that volume to reach the half equivalence point. Therefore, the half equivalence point is reached after 25 milliliters of base has been added. So if we go up here to our titration curve, we can mark the location or the approximate location of the half equivalence point. So let me draw a line here from half equivalence point to the point on our titration curve. Let's go back to our third particulate diagram which represents the equivalence point and let's add some more sodium hydroxide into the solution. Because there's no more acid present to react with the sodium hydroxide in our fourth particulate diagram, we can see the sodium cation and the hydroxide anion that we added. At the equivalence point, we also had two sodium cations. So here they are on the fourth particulate diagram and two acetate anions which are also present. So the fourth particulate diagram represents excess base past the equivalence point. As a quick summary of our titration curve, we started out with only weak acid so the pH was relatively low. As we add base, the pH increases slowly, and we get to the half equivalence point where half of the weak acid that was initially present has been neutralized. Notice how the pH is changing very slowly in this region of the titration curve. As we continue to add more and more base, the pH keeps on increasing. And around the equivalence point, we see a dramatic increase in the pH. Once we go past the equivalence point, we're in the region of excess base and the pH keeps increasing as we add more and more hydroxide anions. During the titration of a weak acid with a strong base, a buffer solution is actually formed. So let's look at more detail at the buffer region or the buffer zone on our titration curve. The buffer region occurs around the half equivalence point. And we can see on our titration curve, there are very small changes in pH as we add hydroxide anions in this region. That's because the weak acid that's present in solution is neutralizing the added base and protecting against a dramatic change in pH. We can calculate the pH at the half equivalence point because we know at the half equivalence point, half of the initial acid that was present has been neutralized and turned into the conjugate base. Therefore, at the half equivalence point, the concentration of weak acid is equal to the concentration of the conjugate base. We can use the Henderson-Hasselbalch equation to find the pH. If the concentration of weak acid is equal to the concentration of the conjugate base, then the ratio of their concentrations is equal to one. And the log of one is equal to zero. Therefore, the pH is equal to the pKa value of the weak acid at the half equivalence point. So if we wanted to find the pKa value of a weak acid from our titration curve, we would simply find the half equivalence point and go over to the y-axis to estimate the pKa value. Because at this point, the pH of the solution is equal to the pKa value of the weak acid. Next, let's think about how the titration curve can tell us about the relative concentrations of weak acid and conjugate base. We know that the pH is equal to the pKa value at the half equivalence point right here on our titration curve. And we know at the half equivalence point, the concentration of weak acid is equal to the concentration of conjugate base. Therefore, if we think about a point just to the left of the half equivalence point, so right here on our titration curve, I'll call this point P, we know that the pH at that point is less than the pKa value of the weak acid. And we know that the initial point on our titration curve was almost all weak acid. Therefore, since point P is in between the initial point where we have almost all acid and the half equivalence point where we have equal amounts of weak acid and conjugate base, point P must have more weak acid than conjugate base. Therefore, we can say when the pH is less than the pKa value. The concentration of weak acid is greater than the concentration of conjugate base. We could have also figured this out using the Henderson-Hasselbalch equation. However, it's often simpler just to think about the shape of the titration curve. Next, let's think about a point just to the right of the half equivalence point. So I'm gonna call this point, point Q. At point Q, the pH of the solution is greater than the pKa value of the weak acid. So for trying to determine the relative concentrations of weak acid and conjugate base at point Q, remember that point Q is in between the half equivalence point and the equivalence point, which is right about here on our titration curve. And at the equivalence point, there's no more weak acid present. All of the weak acid has been neutralized and only the conjugate base, A-, remains. Since point Q is in between the half equivalence point where there are equal amounts of weak acid and conjugate base, and the equivalence point where there's only conjugate base, at point Q, there must be more conjugate base than weak acid. Therefore, we can say when the pH of the solution is greater than the pKa value of the weak acid, the concentration of weak acid is less than the concentration of the conjugate base. Or we could say the concentration of conjugate base is greater than the concentration of weak acid. Finally, let's talk about why a buffer forms on this titration curve. When we first start off, we have almost all weak acid, and therefore we do not have a buffer. However, as base is added to the solution, the weak acid is converted into its conjugate base. And when there are significant amounts of the weak acid and its conjugate base, we have a buffer solution. So that's right about here on our titration curve. And we can see the buffer is resisting large changes to pH in this region. However, as we continue to add base, the concentrations of weak acid and conjugate base change. And eventually, we no longer have a buffer solution. So the pH changes more dramatically at this point. So the buffer region or the buffer zone is only right around the half equivalence point on our titration curve.