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# Buffer Capacity

Did you know that our blood plasma contains solutions called buffers? Their job is to maintain blood pH as close as possible to 7.4! Buffers are crucial because any changes in blood pH can lead to death!  Buffers are characterized by their buffer range and buffer capacity! Interested in knowing what this means? Keep reading to find out!

• First, we will look at the definitions of buffer range and capacity.
• Then, we will learn how to determine buffer capacity.
• After, we will look at the buffer capacity equation and calculation.
• Lastly, we will take a look at some examples involving buffer capacity.

## What is buffer capacity?

Let's begin by defining what buffers are. Buffers are solutions that can resist changes in pH when small amounts of acids or bases are added to them. Buffered solutions are made either by the combination of a weak acid and its conjugate base, or a weak base and its conjugate acid.

According to the Bronsted-Lowry definition of acids and bases, acids are substances that can donate a proton, whereas bases are substances that can accept a proton.

• A conjugate acid is a base that has gained a proton, and a conjugate base is an acid that lost a proton.

$$HA+H_{2}O\rightleftharpoons H^{+}+A^{-}$$

Buffers can be characterized by buffer range and capacity.

The buffer range is the pH range over which a buffer acts effectively.

When the concentration of the buffer components is the same, then pH will be equal to pKa. This is very useful because, when chemists need a buffer, they can choose the buffer that has an acid form with the pKa close to the desired pH. Usually, buffers have a useful pH range = pKa ± 1, but the closer it is to the weak acid's pKa, the better!

Fig. 1: Predicting the pH of a buffer, Isadora Santos - StudySmarter Original.

Unsure about what this means? Check out "pH and pKa" and "Buffers"!

To calculate the pH of a buffer, we can use the Henderson-Hasselbalch Equation.

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

Where,

• pKa is the negative log of the equilibrium constant Ka.
• [A-] is the concentration of the conjugate base.
• [HA] is the concentration of the weak acid.

Let's look at an example!

What is the pH of a buffer solution that has 0.080 M CH3COONa and 0.10 M CH3COOH? (Ka = 1.76 x 10-5)

The question gives the concentration of the weak acid (0.10 M), the concentration of the conjugate base (0.080 M), and the Ka of the weak acid, which we can use to find pKa.

$$pKa=-log_{10}Ka$$

$$pKa=-log_{10}(1.76\cdot 10^{-5})$$

$$pKa=4.75$$

Now that we have everything we need, we just need to plug the values into the Henderson-Hasselbalch equation!

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

$$pH=4.75+log\frac{[0.080]}{0.10}$$

$$pH=4.65$$

The Henderson-Hasselbalch version for weak base buffers is. However, in this explanation, we will only be talking about buffer solutions made of a weak acid and its conjugate base.

Now, let's say that we have a 1-L buffer solution with a pH of 6. To this solution, you decide to add HCl. When you first add some moles of HCl, there might not be any changes in pH, until it gets to a point where the pH of the solution changes by one unit, from pH 6 to pH 7. The ability of a buffer to keep the pH constant following the addition of a strong acid or base is known as the buffer capacity.

Buffer capacity - the number of moles of acid or base that must be added to one liter of the buffer solution in order to lower or raise the pH by one unit.

Buffer capacity depends on the amount of acid and base used to prepare the buffer. For example, if you have a 1-L buffer solution made of 1 M CH3COOH/1 M CH3COONa and a 1-L buffer solution that is 0.1 M CH3COOH/0.1 M CH3COONa, although they will both have the same pH, the first buffer solution will have a greater buffer capacity because it has a higher amount of CH3COOH and CH3COO-.

• The more similar the concentration of the two components, the greater the buffer capacity.

• The greater the difference in the concentration of the two components, the greater the pH change that occurs when a strong acid or base is added.

Which of the following buffers have greater capacity? 0.10 M Tris buffer vs. 0.010 M Tris buffer.

We learned that the higher the concentration, the greater the buffer capacity! So, the 0.10 M Tris buffer will have a greater buffer capacity

Buffer capacity is also dependent on the pH of the buffer. Buffer solutions with a pH at the pKa value of the acid (pH = pKa) will have the greatest buffering capacity (i.e. Buffer capacity is highest when [HA] = [A-])

A concentrated buffer can neutralize more added acid or base than a dilute buffer!

## Determination of Buffer Capacity

Now, we know that the buffer capacity of a solution depends on the concentration of the conjugate acid and conjugate base components of the solution, and also on the pH of the buffer.

An acidic buffer will have a maximum buffer capacity when:

1. The concentrations of HA and A- are large.

2. [HA] = [A-]

3. pH is equal (or very close) to the pKa of the weak acid (HA) used. Effective pH range = pKa ± 1.

Let's solve a problem!

Which of the following buffers have the highest pH? Which buffer has the greatest buffer capacity?

Fig. 2: HA/A- buffers, Isadora Santos - StudySmarter Originals.

Here we have four buffers, each containing a different concentration of weak acid and conjugate base. The green dots are the conjugate base (A-), while the green dots with the purple dot attached to it is the weak acid (HA). Below each drawing, we have the ratio of conjugate base to weak acid, or [A-]:[HA], present in each buffer solution.

The buffer with the highest pH will be the one containing the highest number of A- compared to HA. In this case, it would be buffer 4 since it has a ratio of 4 [A-] to 2 [HA].

The buffer with the highest buffer capacity will be the one with the highest concentration of buffer components and [A-] = [HA]. So, the answer would be buffer 3.

## Buffer Capacity Equation

We can use the following equation to calculate buffer capacity, β.

$$Buffer\ capacity\ (\beta )=\left | \frac{\Delta n}{\Delta pH} \right |$$

Where,

• Δn = amount (in mol) of the added acid or base to the buffer solution.
• ΔpH = Change in pH caused by the addition of the acid or base (final pH - initial pH)

Another equation seen in buffer capacity is the Van Slyke equation. This equation relates buffer capacity to the concentration of the acid and its salt.

$$Maximum\ buffer\ capacity\ (\beta )=2.3C_{total}\frac{Ka\cdot [H_{3}O^{+}]}{[Ka+[H_{3}O^{+}]]^{2}}$$

where,

• C is the buffer concentration. Ctotal = C acid + C conj base

• [H3O+] is the hydrogen ion concentration of the buffer.

• Ka is the acid constant.

For your exam, you will not be asked to calculate buffer capacity using these equations. But, you should be familiar with them.

## Buffer Capacity Calculation

Now, let's say that we were given a titration curve. How can we find buffer capacity based on a titration curve? Buffer capacity will be at its maximum when pH = pKa, which occurs at the half-equivalence point.

Check out "Acid-Base Titrations" if you need a review of titration curves.

As an example, let's look at the titration curve for 100 mL of 0.100 M acetic acid that has been titrated with 0.100 M NaOH. At the half-equivalence point, buffer capacity (β) will have a maximum value.

## Buffer Capacity Examples

The bicarbonate buffer system has an essential role in our bodies. It is responsible for maintaining blood pH near 7.4. This buffer system has a pK of 6.1, giving it a good buffering capacity.

If an increase in blood pH happens, alkalosis occurs, resulting in pulmonary embolism and hepatic failure. If the blood pH decreases, it can lead to metabolic acidosis.

## Buffer Capacity - Key takeaways

• The buffer range is the pH range over which a buffer acts effectively.
• Buffer capacity - the number of moles of acid or base that must be added to one liter of the buffer solution in order to lower or raise the pH by one unit.
• The more similar the concentration of the two components, the greater the buffer capacity.
• At a titration curve, buffer capacity will be at its maximum when pH = pKa, which occurs at the half-equivalence point.

## References

1. Theodore Lawrence Brown, et al. Chemistry : The Central Science. 14th ed., Harlow, Pearson, 2018. ‌
2. Princeton Review. Fast Track Chemistry. New York, Ny, The Princeton Review, 2020. ‌
3. Smith, Garon, and Mainul Hossain. Chapter 1.2: Visualization of Buffer Capacity with 3-D Topos: Chapter 1.2: Visualization of Buffer Capacity with 3-D Topos: Buffer Ridges, Equivalence Point Canyons and Dilution Ramps Buffer Ridges, Equivalence Point Canyons and Dilution Ramps. ‌
4. Moore, John T, and Richard Langley. McGraw Hill : AP Chemistry, 2022. New York, Mcgraw-Hill Education, 2021. ‌

#### Flashcards in Buffer Capacity 15

###### Learn with 15 Buffer Capacity flashcards in the free StudySmarter app

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What is buffer capacity?

Buffer capacity is defined as the number of moles of acid or base that must be added to one liter of the buffer solution to decrease or increase the pH by one unit.

How to calculate buffer capacity?

Buffer capacity can be calculated using two different equations. However, buffer capacity is mostly found by looking at titration curves. Buffer capacity will be maximum at the half-equivalence point.

Which solution has the greatest buffer capacity?

The buffer with the highest buffer capacity will be the one with the highest concentration of buffer components and [A-] = [HA].

How to find buffer capacity from graph.

Maximum buffer capacity can be found at the half-equivalence point, where pH = pKa

How does dilution affect buffer capacity?

The dilution of a buffer solution leads to a decrease in its buffer capacity. A concentrated buffer can neutralize more added acid or base than a dilute buffer!

## Test your knowledge with multiple choice flashcards

The ______ is the pH range over which a buffer acts effectively.

The ideal acidic buffer would be a buffer that has an acid form with the pKa ____ to the desired pH.

Usually, buffers have a useful pH range that is equal to

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