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.

When the concentration of the buffer components is the same, then pH will be equal to pK_a. This is very useful because, when chemists need a buffer, they can choose the buffer that has an acid form with the pK_a close to the desired pH. Usually, buffers have a useful pH range = pK_a ± 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.

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

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

Where,

• pK_a is the negative log of the equilibrium constant K_a.
• [A^-] is the concentration of the conjugate base.
• [HA] is the concentration of the weak acid.

Let's look at an example!

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 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.

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^-])

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 pK_a of the weak acid (HA) used. Effective pH range = pK_a ± 1.

Let's solve a problem!

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. C_total = C _acid + C _{conj base}

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

• K_a is the acid constant.

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 = pK_a, which occurs at the half-equivalence point.

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.