Buffer Solutions

The Concept of Buffer Solutions

Many fluids in the body — blood, urine, and others — have a very specific pH. A healthy person’s blood, for instance, stays close to pH 7.4. If that pH shifts even a little, it signals something wrong. The same need for pH control shows up in chemical factories, biochemical labs, and even in making medicines and cosmetics. Many formulations must be kept at a fixed pH to stay effective or safe.

So how do you keep pH constant? You cannot just add water — dilution itself changes pH. And if you add a drop of acid or base, the pH usually jumps. But some solutions resist that change. They are called buffer solutions.

You can prepare a buffer of a known pH if you know the $pK_a$ of the weak acid (or $pK_b$ of the weak base) you are using, and if you control the ratio of the salt to the acid (or salt to the base) in the mixture.

Two classic examples:

• A mixture of acetic acid ($CH_3COOH$) and sodium acetate ($CH_3COONa$) acts as a buffer around pH 4.75.
• A mixture of ammonium chloride ($NH_4Cl$) and ammonium hydroxide ($NH_4OH$) acts as a buffer around pH 9.25.

You will study buffer solutions in more detail in higher classes, but the core idea — resistance to pH change — is what matters here.

How a Buffer Works (The Mechanism)

A buffer is always a mixture of either:

1. A weak acid and its salt with a strong base (e.g., $CH_3COOH$ / $CH_3COONa$), or
2. A weak base and its salt with a strong acid (e.g., $NH_4OH$ / $NH_4Cl$).

The key is that the weak acid or base is partially dissociated, while the salt is fully dissociated. This gives the solution a large reservoir of both the weak acid/base and its conjugate.

Consider the acetic acid / sodium acetate buffer. In solution:

• Sodium acetate dissociates completely: $CH_3COONa \rightarrow CH_3COO^- + Na^+$
• Acetic acid dissociates partially: $CH_3COOH \rightleftharpoons CH_3COO^- + H^+$

So the solution contains a lot of undissociated $CH_3COOH$ molecules and a lot of $CH_3COO^-$ ions (from the salt).

Now, what happens if you add a small amount of a strong acid (like $HCl$)? The added $H^+$ ions will react with the large supply of $CH_3COO^-$ ions:

The $H^+$ is consumed, and the pH barely changes.

What if you add a small amount of a strong base (like $NaOH$)? The added $OH^-$ ions will react with the large supply of $CH_3COOH$ molecules:

The $OH^-$ is consumed, and again the pH barely changes.

The Henderson-Hasselbalch Equation

The pH of an acidic buffer is governed by the Henderson–Hasselbalch equation,

(with the analogous $pOH = pK_b + \log([\text{Conjugate acid}]/[\text{Weak base}])$ for a basic buffer). Its full step-by-step derivation, and how to use it to design a buffer of any required pH, is the subject of §6.12.1.

Key Properties of Buffer Solutions (with Derivations)

Three properties follow directly from the Henderson–Hasselbalch equation.

›Proof

Property 1: The pH of a buffer solution depends on the $pK_a$ of the acid and the ratio of the concentrations of the salt and the acid.

This is directly from the Henderson-Hasselbalch equation:

$pH = pK_a + \log\frac{[\text{Salt}]}{[\text{Acid}]}$

The pH is not fixed by the acid alone; you can adjust it by changing the ratio of salt to acid. If $[\text{Salt}] = [\text{Acid}]$, then $\log(1) = 0$, and $pH = pK_a$.

›Proof

Property 2: The pH of a buffer solution does not change on dilution (as long as the dilution is not extreme).

When you dilute a buffer, both $[\text{Salt}]$ and $[\text{Acid}]$ are diluted by the same factor. Their ratio $[\text{Salt}]/[\text{Acid}]$ remains unchanged. Since the Henderson-Hasselbalch equation depends only on that ratio (and $pK_a$, which is constant), the pH stays the same.

For example, if you double the volume, both concentrations are halved, but the ratio stays the same. So $\log([\text{Salt}]/[\text{Acid}])$ is unchanged, and $pH$ is unchanged.

›Proof

Property 3: The pH of a buffer solution changes only slightly upon the addition of a small amount of a strong acid or a strong base.

This is the defining property of a buffer. The Henderson-Hasselbalch equation shows why the change is small.

…