Titration - Online Tutor, Practice Problems & Exam Prep

Titrations are essential for determining the pKa values of weak acids and their concentrations. The titrant, a solution of known concentration, is added to the analyte until neutralization occurs, indicated by a color change. The equivalence point, where moles of titrant equal moles of analyte, varies in pH depending on the acid's strength. For polyprotic acids, multiple inflection and equivalence points correspond to each acidic hydrogen's pKa. The Henderson-Hasselbalch equation is useful for analyzing these relationships in titration curves.

Titrations

In this video, we're going to review titrations. So I'm sure most of you guys have performed titrations in your previous chemistry labs. Recall that a titration is just a lab technique that measures the pH changes of acid-based solutions. Titrations are typically used to determine the \( pK_a \) values of weak acids, as well as the concentrations of weak acids. Titrations can also be used to determine the concentrations of strong acids, but recall from our previous lesson videos that in biological systems, most of the acids are weak acids. Moving forward in our course, we're going to focus most of our attention on the titrations of weak acids. Recall that the way titrations work is that there's an acid-based solution of known concentration called the titrant, and the titrant is gradually added to another solution of unknown concentration called the analyte solution, because this is the solution being analyzed. The titrant is continuously added to the analyte solution until a point of neutralization is reached. This point of neutralization is the exact point where the moles of titrant that are being added are exactly equal to the moles of analyte that are present. The point of neutralization, when it is reached, is indicated by a color change, making it easy to detect visually.

Again, a titration is typically used to determine two different things: the concentration of an acid or a base in a solution, and the \( pK_a \) of a weak acid. Titrations cannot be used to determine the \( pK_a \) of strong acids, but this limitation is acceptable to biochemists because, again, most of the acids in biological systems are weak acids. A titration curve is just a plot of the titration data, which has the analyte pH on the y-axis, and the amount of titrant being added on the x-axis. Remember that the titrant is continuously added to the solution until a point of neutralization is reached. This point of neutralization is called the equivalence point, or also known as the endpoint, because once neutralization has been reached, that is the end of an acid, so that's why it's called an endpoint.

In our example below, we're going to look at the titration of a strong acid with a strong base. The reason we are looking at the titration of a strong acid in this example is that when we're trying to refresh our memories of titrations, it's easiest to examine the titration of a strong acid with a strong base. The setup for a typical titration features an Erlenmeyer flask shown below, which contains a pink solution, the analyte solution. This analyte solution, in this example, is a strong acid. Notice that in this analyte solution we have a pH electrode, which is going to continuously measure the pH of the analyte solution as we start to add titrant. Above, we have a burette instrument, a volumetric instrument that contains the solution of known concentration called the titrant; in this case, this is a strong base. We continue to add the titrant, slowly into the solution below, the analyte solution, until the point of neutralization is reached, which is indicated by a color change. We can then calculate the \( pK_a \) as the stopcock allows us to control the amount of titrant being added. The titration curve for the strong acid with a strong base has pH on the y-axis and the amount of titrant being added on the x-axis, which can sometimes show the volume of the titrant, but here it shows the equivalents of titrant in molarity. A 0.2 molar equivalent of titrant added means that 20% of the analyte solution has been neutralized, a 0.6 molar equivalent means that 60% has been neutralized, and a 1 molar equivalent means that 100% of the analyte solution has been neutralized; this is the equivalence point. At exactly 1 molar equivalent, we have a green dotted line indicating the equivalence point, which for a titration of a strong acid with a strong base always shows up at a pH of 7. We can tell by the titration curve that we are using a strong acid as the analyte and a_b strong base as the titrant because before adding any titrant, the pH of the analyte solution is extremely low, below pH 1. After reaching the equivalence point, the pH rises significantly, indicating the use of a strong base. The equivalence point arrives exactly at a pH of 7. In our next practice problem, we'll analyze the titration curves to predict the type of titration being performed. See you in that practice video.

Which of the following titration curves expresses the titration of a weak acid with a strong base?

• A.
• B.
• C.
• D.

Titration of Monoprotic Weak Acids

So in our last lesson video, we showed an example of the titration of a strong acid with a strong base just to refresh your memories on how titrations work. Now, because most acids in biological systems are weak acids, in this video, we're going to focus our attention on the titration of weak acids. In our last lesson video, we also said that titrations can reveal the pKa values for weak acids. And so, the point on a titration curve that reveals the pKa value of a weak acid is called the inflection point, also known as the midpoint, because that's exactly when half of the acid has been neutralized. So, the point where half of the acid is neutralized is the exact point where the pH of the solution is equal to the pKa value for a weak acid. Recall from our previous lesson videos that when the pH of the solution is equal to the pKa of an acid, that is the exact point where the concentration of conjugate base is equal to the concentration of conjugate acid.

Looking down below at our titration curve, notice that this is the titration of a weak acid with a strong base, meaning that the weak acid here is going to be our analyte solution, and of course, the strong base over here is going to be the titrant. Notice that the equivalence point that we mentioned earlier is being indicated by this blue line and point. This point where half of the molar equivalents of titrant are being added corresponds with a pH value. This pH value is going to be the pH that equals the pKa value for a weak acid. Over here on this chart, you can see that the inflection point, which is also known as the midpoint, is the exact point where the pH of the solution is equal to the pKa value for the weak acid, and this applies to weak acids only.

We already know from our previous lesson video that equivalence points are also known as endpoints because that is essentially the end of an acid because 100% of the acid has been neutralized. This is the exact point where the titrant, or the amount of titrant that has been added. Over here on our titration curve, you can see the equivalence point is being indicated by the green dotted line endpoint here. You can see that it's the exact point where it's exactly equal to the concentration of the titrant, which we said is a strong base, and sodium hydroxide is a strong base. You can see that it's showing up at exactly 1 molar equivalent of titrant that's being added. But, in our previous lesson video where we showed the titration of a strong acid with a strong base, we said that the pH shows up at a pH of 7 for the equivalence point. But that is not always the case. The equivalence point does not always equal a pH of 7. It only equals a pH of 7 when you are performing the titration of a strong acid or base with a strong acid or base.

What you'll see here is that the pH of the equivalence point depends on the concentration of hydrogen ions when exactly 1 molar equivalent of titrant is added. Here, for the titration of a weak acid with a strong base, you can see that when exactly 1 molar equivalent of titrant is added, it corresponds with a pH that is not 7, instead it's about a pH of 8.5. That's something important to keep in mind about the titrations of weak acids, that the equivalence points do not equal a pH of 7. We'll be able to apply some of the concepts that we've learned here moving forward in our practice problems. So I'll see you guys there.

You have an analyte solution of 50 mL of 0.2 M acetic acid (pK_a = 4.8). What volume of 0.05 M NaOH titrant needs to be added to get the final pH = pK_a?

• A. 20 mL
• B. 50 mL
• C. 100 mL
• D. 150 mL

Titration of Polyprotic Weak Acids

So we already know that some acids are polyprotic acids, and all that means is that they have multiple acidic hydrogens. And we know that each acidic hydrogen is going to have its own pKa value. Also, the titration curves of polyprotic acids have multiple inflection points as well as multiple equivalence points. And so, there's going to be a set of an inflection point and an equivalence point for each acidic hydrogen. So the number of acidic hydrogens determines the number of inflection points and the number of equivalence points. And so if there are 2 acidic hydrogens, there's going to be 2 inflection points and 2 equivalence points. If there are 4 acidic hydrogens, then there's going to be 4 inflection points and 4 equivalence points. And so recall from our previous videos that each inflection point, and also recall each inflection is also known as a midpoint. Each inflection point indicates the pKa of an acidic hydrogen. And also recall from our previous videos the Henderson-Hasselbalch equation, which is going to be really helpful for our titration of the acid, which has a chemical formula of H₃PO₄. And phosphoric acid is a polyprotic weak acid, so it actually has 3 acidic hydrogens, and those 3 acidic hydrogens are here. And so notice that the first acidic hydrogen has a pKa of 2.2, the second acidic hydrogen has a pKa of 7.2, and the third has a pKa of 12.7. And so over here, what we have is the titration curve of phosphoric acid with a strong base.

On the y-axis, we have the pH of the analyte solution, and on the x-axis, we have the amount of titrant that's being added. And so notice that because phosphoric acid has 3 acidic hydrogens, there are 3 inflection points shown by the dotted black lines, and there are also 3 equivalence points shown by the green-dotted lines. And so, notice that when the inflection point occurs, it indicates the pKa value of an acidic hydrogen. So the 1st acidic hydrogen we said has a pKa value of 2.2. So notice that the inflection point, which occurs right here, corresponds with a pH value of 2.2, and this is where the pKa is. And so when the pH is equal to 2.2, the concentration of conjugate acid equals the concentration of conjugate base.

Here, because we have H₃PO₄ as our conjugate acid, our H₃PO₄ conjugate acid is going to equal our conjugate base of H₂PO₄^-. And so when we get to our first equivalence point where we add exactly 1 molar equivalent, notice that this is going to be where we completely neutralize H₃PO₄ has been eliminated. So H₃PO₄ is essentially eliminated, or completely neutralized at this equivalence point. And so at the equivalence point, H₂PO₄^- is at its maximum concentration.

Now notice that at the second inflection point, which is shown up here, there is a pH of 7.2, which indicates the pKa value of 7.2. And so when the pH is equal to 7.2, the concentration of conjugate acid is going to equal the concentration of conjugate base. And here, at this point, what we've done is, the conjugate acid is H₂PO₄^-. And so, the concentration of conjugate acid, H₂PO₄^-, is going to equal the concentration of conjugate base, which is HPO₄^2-. And so, that would be at this point here, this midpoint. And so at the second equivalence point over here, what that means is we've added exactly 2 molar equivalents of the titrant to neutralize the conjugate acid. So at this point here, what we've done is we've neutralized H₂PO₄^-. So at this point, H₂PO₄^- is completely gone and HPO₄^2- is at its highest concentration. So then we continue to add titrant, and we get to our 3rd pKa value, our 3rd inflection point.

And so notice that this inflection point occurs at a pH of about 12.7, which indicates that the pKa is 12.7. And so when the pH is equal to 12.7, the concentration of conjugate acid is going to equal the concentration of conjugate base. And so here our conjugate acid is HPO₄^2-. So we can put that in here, HPO₄^2-. And that's going to equal the concentration of conjugate base, which is PO₄^3-. And so, as we continue to add more and more titrant, eventually, we get to our 3rd equivalence point. And our 3rd equivalence point is when we add exactly 3 molar equivalents of titrant. And that means that we've completely eliminated HPO₄^2-, and that PO₄^3- is at its highest concentration of hydronium ions in the solution. In our next video, we'll be able to get a little bit of practice analyzing."

Use the titration curve below. 

What is the predominate species in the solution of phosphoric acid at pH = 5?

• A. H₃PO₄
• B. H₂PO₄^-
• C. HPO₄^-2
• D. PO₄^-3

Titration confirms an acetic acid solution to be 0.1 M. Calculate the pH. (acetic acid K _a = 1.76 x 10^-5 M).

• A. 2.1
• B. 3.6
• C. 2.9
• D. 8.3

Here’s what students ask on this topic:

What is the purpose of a titration in biochemistry?

The purpose of a titration in biochemistry is to determine the pKa values of weak acids and their concentrations. Titrations involve gradually adding a titrant, a solution of known concentration, to an analyte, a solution of unknown concentration, until neutralization occurs. This process helps identify the point where the moles of titrant equal the moles of analyte, known as the equivalence point. Titrations are crucial for understanding the behavior of acids and bases in biological systems, where most acids are weak acids.

How do you determine the pKa value from a titration curve?

To determine the pKa value from a titration curve, identify the inflection point, also known as the midpoint, on the curve. This point occurs when half of the acid has been neutralized, and the pH of the solution equals the pKa value of the weak acid. At this point, the concentration of the conjugate base is equal to the concentration of the conjugate acid. The inflection point is typically marked by a noticeable change in the slope of the titration curve.

What is the equivalence point in a titration?

The equivalence point in a titration is the exact point where the moles of titrant added are equal to the moles of analyte present in the solution. It is indicated by a significant change in the pH of the solution, often marked by a color change if an indicator is used. For strong acid-strong base titrations, the equivalence point typically occurs at a pH of 7. However, for weak acid-strong base titrations, the pH at the equivalence point can be higher than 7.

What are polyprotic acids and how do their titration curves differ?

Polyprotic acids are acids that have multiple acidic hydrogens, each with its own pKa value. Their titration curves differ from monoprotic acids by having multiple inflection points and equivalence points, corresponding to each acidic hydrogen. For example, phosphoric acid (H₃PO₄) has three acidic hydrogens, resulting in three distinct pKa values and three sets of inflection and equivalence points on its titration curve. Each inflection point indicates the pKa of an acidic hydrogen, and each equivalence point marks the complete neutralization of one acidic hydrogen.

How does the Henderson-Hasselbalch equation apply to titrations?

The Henderson-Hasselbalch equation is useful for analyzing titration data, especially for weak acids. The equation is given by:

${\mathrm{pH}}_{}={\mathrm{pKa}}_{}+\frac{\log }{\frac{\mathrm{[A^-]}}{\mathrm{[HA]}}}$

where [A^-] is the concentration of the conjugate base and [HA] is the concentration of the conjugate acid. At the inflection point, where pH = pKa, the concentrations of the conjugate base and acid are equal. This relationship helps in determining the pKa value from the titration curve.