AP Chemistry 8.6: Buffers and Henderson-Hasselbalch

A buffer is a solution that resists large changes in pH when small amounts of acid or base are added.

• A typical buffer contains either:
• weak acid + its conjugate base
• or:
• weak base + its conjugate acid
• Examples include:
• CH₃COOH / CH₃COO⁻
• or:
• NH₃ / NH₄⁺

A buffer does not keep pH perfectly constant. It simply makes the change much smaller than it would be without the buffer.

Consider:

• HA ⇌ H⁺ + A⁻
• The solution contains substantial amounts of both HA and A⁻.

If strong acid is added, the conjugate base removes much of it:

• A⁻ + H⁺ → HA

If strong base is added, the weak acid reacts with it:

• HA + OH⁻ → A⁻ + H₂O
• Therefore the buffer has components available to react with either added acid or added base.

For the weak acid:

• Ka = [H₃O⁺][A⁻]/[HA]
• Rearrange:
• [H₃O⁺] = Ka([HA]/[A⁻])
• Taking the negative logarithm leads to the Henderson-Hasselbalch equation:
• pH = pKa + log([A⁻]/[HA])
• This is one of the most useful equations in Unit 8.

pH = pKa + log(base/acid)

• where:
• base = conjugate base A⁻
• and:
• acid = weak acid HA
• If:
• [A⁻] = [HA]
• then:
• log(1) = 0
• so:
• pH = pKa
• This becomes extremely important during titrations.

Suppose:

• pKa = 4.76
• [A⁻] = 0.200 M
• [HA] = 0.100 M
• Then:
• pH = 4.76 + log(0.200/0.100)
• pH = 4.76 + log(2)
• pH ≈ 5.06
• Because there is more conjugate base than weak acid:
• pH > pKa

The Henderson-Hasselbalch equation depends on:

• [A⁻]/[HA]
• If both concentrations are multiplied by the same factor, the ratio remains the same and the initial pH can remain approximately the same.

However, this does not mean the two buffers have the same capacity.

A more concentrated buffer can neutralize a larger amount of added acid or base.

One method is directly mixing:

• weak acid + salt containing its conjugate base
• For example:
• CH₃COOH + CH₃COONa.

Another method is partial neutralization.

• Suppose you start with a weak acid and add enough strong base to neutralize only part of it.
• Some HA remains, and some A⁻ is produced.
• You now have both members of the conjugate pair, creating a buffer.

A buffer works best when significant amounts of both members of the conjugate pair are present.

• A common useful range is approximately:
• pH = pKa ± 1
• This corresponds roughly to base-to-acid ratios between:
• 0.1 and 10

If one component becomes extremely small, the buffer becomes much less effective.

Buffer capacity describes how much strong acid or strong base a buffer can absorb before its pH changes substantially.

• Capacity increases when there are larger absolute amounts of the buffering components.
• A buffer containing:
• 1.0 mol HA and 1.0 mol A⁻
• has much greater capacity than one containing:
• 0.001 mol HA and 0.001 mol A⁻
• even if both initially have the same pH.

Suppose the buffer contains:

• HA and A⁻.
• Adding H⁺ causes:
• A⁻ + H⁺ → HA
• So:
• A⁻ decreases
• HA increases.

You must perform this stoichiometric reaction before using Henderson-Hasselbalch.

Added OH⁻ reacts:

• HA + OH⁻ → A⁻ + H₂O
• So:
• HA decreases
• A⁻ increases.
• Again:
• stoichiometry first → equilibrium equation second

Do not blindly use the equation for every acid-base problem.

• You need meaningful amounts of both:
• weak acid and conjugate base
• or the corresponding weak-base pair.

It is not the appropriate shortcut for a solution containing only a strong acid or strong base.

Do not call any mixture of an acid and base a buffer.

A useful buffer requires a weak species and a meaningful amount of its conjugate partner.

When strong acid/base is added:

react it first

before using Henderson-Hasselbalch.

Do not confuse buffer pH with buffer capacity.

A buffer needs:

• weak acid + conjugate base
• or:
• weak base + conjugate acid
• and:
• pH = pKa + log(base/acid)
• When:
• base = acid
• then:
• pH = pKa

A buffer generally contains:

• weak acid + conjugate base
• or:
• weak base + conjugate acid
• Use:
• pH = pKa + log(base/acid)
• If:
• base = acid
• then:
• pH = pKa

Adding strong acid:

• conjugate base consumes H⁺

Adding strong base:

• weak acid consumes OH⁻

Best buffering generally occurs near:

• pH ≈ pKa
• and the commonly useful buffer range is roughly:
• pKa ± 1

Higher amounts of both buffer components generally mean:

• greater buffer capacity