Polyprotic Buffers - Online Tutor, Practice Problems & Exam Prep

Polyprotic buffers, often triprotic, contain three acidic hydrogens and have three corresponding acid dissociation constants (pKa values). The Henderson-Hasselbalch equation varies based on the form of the buffer: for the acid form to the first intermediate, it is $pH=\mathrm{pKa}+\log (\mathrm{intermediate\; 1}/\mathrm{acid\; form})$. Understanding these relationships is crucial for calculating pH in polyprotic systems, such as citric acid.

Polyprotic Buffers

With our discussion of monoprotic buffers, diprotic buffers, we're now left with polyprotic buffers. Here we're going to say, a polyprotic buffer is usually synonymous with a triprotic buffer, where we have 3 acidic hydrogens. We're going to say here a triprotic buffer can be approached in a way similar to diprotic buffers. The key difference is that a triprotic acid now has 3 pKa values or 3 K_a values. Again, when we say polyprotic, we're usually referring to triprotic acids, but there are acids with more than 3 acidic hydrogens.

Those are fewer, so we tend to just stick to 3 acidic hydrogens. Now for polyprotic buffers, remember we have different forms that our polyprotic acid can take. We have the fully acidified version or its fully protonated version, which is H₃A. Here, it has all 3 of its acidic hydrogens. We can talk about removing the 1st acidic hydrogen, and if we're talking about removing the 1st acidic hydrogen, that means we're talking about K_a1.

Removing that first acidic hydrogen gives us our 1st intermediate form, which is H₂A⁻. Then we remove the 2nd acidic hydrogen giving us K_a2 involved. Now we get the 2nd intermediate form, which is HA²⁻. And then finally, we're removing the last acidic hydrogen, which will give us our basic form, A³⁻. Remember in earlier videos where we talked about polyprotic acids in general, if we could talk about K_a going one way in removing acidic hydrogen, we could talk about K_b when adding back acidic hydrogens.

So here, this would be K_b1, this would be K_b2, and this would be K_b3. If you don't quite remember that, make sure you go back and take a look at our polyprotic acid videos. We talk about the relationships between your acid dissociation constants and your base dissociation constants when looking at protic, diprotic, and polyprotic acids. Now with these different forms, we have the Henderson-Hasselbalch equation.

In this first one here, if we're talking about the relationship between the acid form and the 1st intermediate form, then we know we're dealing with K_a1.

pH = pK a1 + log ( intermediate 1 acid form )

Remember, the bottom portion of the Henderson-Hasselbalch equation is the portion that contains more acidic H⁺ ions. The top version, which represents the more basic form, has one less acidic H⁺ ion. Then if we're talking about our second form of the Henderson-Hasselbalch equation, we're talking about pKa₂, which means we're talking about the relationship between our 1^st intermediate and the second intermediate. We've removed the second acidic hydrogen, so that's K_a 2, which is why we're dealing with pKa₂.

pH = pK a2 + log ( intermediate 2 intermediate 1 )

Again, the more acidic form, the one with more hydrogens, goes on the bottom. The more basic form, the one that has less acidic H⁺ ions, goes on top. Then finally, in this form, we're talking about intermediate 2 going to the basic form. So we're dealing with K_a3. Just as before, we put the more acidic form on the bottom and the more basic form on top.

Now here, we could take a common example, citric acid. Citric acid represents a triprotic acid, so it has 3 acidic hydrogens. In these three different scenarios, in this first one, we have 0.10 M of citric acid and then we have 0.15 M of the 1st intermediate form. Here, it's lost one of its acidic hydrogens, and it's been replaced by a sodium ion here.

Here’s what students ask on this topic:

What is a polyprotic buffer and how does it differ from monoprotic and diprotic buffers?

A polyprotic buffer contains multiple acidic hydrogens, typically three, and is often referred to as a triprotic buffer. This means it has three acid dissociation constants (pKa values). In contrast, a monoprotic buffer has only one acidic hydrogen and one pKa value, while a diprotic buffer has two acidic hydrogens and two pKa values. The key difference lies in the number of dissociation steps and the corresponding pKa values, which affect the buffer's ability to resist changes in pH at different stages of hydrogen ion removal.

How do you use the Henderson-Hasselbalch equation for polyprotic buffers?

The Henderson-Hasselbalch equation for polyprotic buffers varies based on the form of the buffer. For the acid form to the first intermediate, the equation is:

$\mathrm{pH}={\mathrm{pK}}_1+\frac{\log ({\mathrm{intermediate}}_1/\mathrm{acid})}{}$

For the first intermediate to the second intermediate, it is:

$\mathrm{pH}={\mathrm{pK}}_2+\frac{\log ({\mathrm{intermediate}}_2/{\mathrm{intermediate}}_1)}{}$

For the second intermediate to the basic form, it is:

$\mathrm{pH}={\mathrm{pK}}_3+\frac{\log (\mathrm{basic}/{\mathrm{intermediate}}_2)}{}$

Understanding which form you are dealing with is crucial for accurate pH calculation.

What are some common examples of polyprotic acids used in buffers?

Common examples of polyprotic acids used in buffers include citric acid, phosphoric acid, and sulfuric acid. Citric acid is a triprotic acid with three acidic hydrogens and three corresponding pKa values. Phosphoric acid is another triprotic acid commonly used in biological systems and industrial applications. Sulfuric acid, although a strong acid, can also act as a polyprotic acid with two dissociation steps. These acids are used in various buffer systems to maintain pH stability across different pH ranges.

How do you calculate the pH of a polyprotic buffer solution?

To calculate the pH of a polyprotic buffer solution, you need to identify the specific form of the buffer you are dealing with. Use the appropriate Henderson-Hasselbalch equation based on the dissociation step:

1. For the acid form to the first intermediate: $\mathrm{pH}={\mathrm{pK}}_1+\frac{\log ({\mathrm{intermediate}}_1/\mathrm{acid})}{}$

2. For the first intermediate to the second intermediate: $\mathrm{pH}={\mathrm{pK}}_2+\frac{\log ({\mathrm{intermediate}}_2/{\mathrm{intermediate}}_1)}{}$

3. For the second intermediate to the basic form: $\mathrm{pH}={\mathrm{pK}}_3+\frac{\log (\mathrm{basic}/{\mathrm{intermediate}}_2)}{}$

Plug in the concentrations or moles of the relevant species to find the pH.

Why is it important to understand the different forms of polyprotic acids in buffer solutions?

Understanding the different forms of polyprotic acids in buffer solutions is crucial because each form has a different pKa value and thus a different buffering capacity. Knowing which form you are dealing with allows you to use the correct Henderson-Hasselbalch equation to calculate the pH accurately. This is essential for applications in chemistry, biology, and medicine where precise pH control is necessary. Additionally, understanding these forms helps in predicting how the buffer will respond to the addition of acids or bases, ensuring effective pH stabilization.