Buffers

A buffer solution resists changes in pH when small amounts of strong acid or base are added. Every buffer contains a conjugate acid–base pair in appreciable concentrations — either a weak acid with its conjugate base (e.g., CH₃COOH / CH₃COO⁻) or a weak base with its conjugate acid (e.g., NH₃ / NH₄⁺).

Buffers are prepared by mixing a weak acid with a salt of its conjugate base (e.g., acetic acid + sodium acetate), or by partially neutralizing a weak acid with a strong base (or a weak base with a strong acid). The key requirement is that both members of the conjugate pair are present at concentrations large enough to absorb added acid or base without being depleted.

Solutions of strong acids or strong bases alone cannot act as buffers because they lack the conjugate partner needed to neutralize additions of the opposite type.

The buffering mechanism relies on two equilibrium reactions that consume added H⁺ or OH⁻:

• Added acid (H⁺): the conjugate base reacts: A⁻ + H⁺ → HA. This converts the strong acid into the weak acid of the buffer pair, which ionizes only slightly.
• Added base (OH⁻): the weak acid reacts: HA + OH⁻ → A⁻ + H₂O. This converts the strong base into the weak conjugate base.

In both cases, the strong acid or base is replaced by the much weaker member of the buffer pair. Because only the ratio [A⁻]/[HA] determines pH (via the Henderson–Hasselbalch equation), and that ratio changes only modestly when small amounts of strong acid or base are added, the pH shifts far less than it would in an unbuffered solution.

Compare: adding 0.010 mol HCl to 1 L of pure water drops pH from 7.00 to 2.00 — a five-unit change. The same addition to an acetate buffer at pH 4.74 shifts pH by only about 0.09 units.

The Henderson–Hasselbalch equation provides a direct way to calculate the pH of a buffer:

pH = pK_a + log([A⁻] / [HA])

where pK_a = −log K_a of the weak acid, [A⁻] is the concentration of the conjugate base, and [HA] is the concentration of the weak acid. The equation is derived from the K_a expression by taking the negative logarithm of both sides.

Key relationships: when [A⁻] = [HA], the log term equals zero and pH = pK_a — the point of maximum buffering capacity. When [A⁻] > [HA], pH > pK_a; when [A⁻] < [HA], pH < pK_a.

This equation assumes the “x is small” approximation is valid — that is, the concentrations of HA and A⁻ are large enough that equilibrium shifts from ionization are negligible compared to the initial amounts.

When a strong acid or base is added to a buffer, handle the problem in two stages:

1. Stoichiometry first: treat the neutralization as going to completion. Strong acid converts A⁻ to HA; strong base converts HA to A⁻. Calculate the new moles of each buffer component after this reaction.
2. Equilibrium second: use the Henderson–Hasselbalch equation with the updated mole (or concentration) values to find the new pH.

Always work in moles, not concentrations, during the stoichiometry step, because volumes may change when solutions are mixed. Convert back to concentrations (or use the mole ratio directly in Henderson–Hasselbalch, since volume cancels) for the equilibrium step.

If the moles of added strong acid exceed the moles of A⁻ (or the moles of added strong base exceed the moles of HA), the buffer is overwhelmed and the excess strong acid or base determines the pH directly.

Buffer capacity measures how much strong acid or base a buffer can absorb before its pH changes significantly (typically by one unit). Two factors govern capacity:

• Total concentration of the conjugate pair — a 1.0 M buffer can neutralize ten times more acid or base than a 0.10 M buffer at the same pH.
• Ratio of components — capacity is greatest when [A⁻] ≈ [HA] (ratio near 1:1). An imbalanced buffer has less capacity on the depleted side.

When enough strong acid or base is added to completely consume one of the buffer components, the buffer is said to be overwhelmed or “broken.” Beyond this point, the solution behaves like an unbuffered system and pH changes sharply with each additional drop of titrant.

In practice, the buffer capacity can be estimated as the number of moles of the lesser component, since that component will be exhausted first.

The effective buffer range is the pH interval over which a buffer meaningfully resists pH change, typically pK_a ± 1. Within this range, the ratio [A⁻]/[HA] stays between 0.1 and 10, and the Henderson–Hasselbalch log term varies from −1 to +1. Outside this range, one component is nearly exhausted and buffering action fails.

To design a buffer at a target pH, select a weak acid whose pK_a is as close as possible to that pH. Then adjust the ratio [A⁻]/[HA] using the Henderson–Hasselbalch equation to fine-tune the exact pH value. Weak acids with pK_a < 7 are best for acidic buffers; weak bases (or weak acids with pK_a > 7) are best for alkaline buffers.

Common buffer systems include acetate (pK_a 4.74) for pH ∼4–5, phosphate (pK_a2 7.20) for pH ∼6–8, and ammonia (pK_a of NH₄⁺ = 9.25) for pH ∼8–10.

Buffers are essential in living organisms where even small pH changes can disrupt enzyme activity and protein structure. Human blood is maintained near pH 7.4 by the carbonate buffer system: H₂CO₃ / HCO₃⁻.

When acid enters the bloodstream, bicarbonate ion neutralizes it: HCO₃⁻ + H⁺ → H₂CO₃. The carbonic acid decomposes to CO₂ and water, and excess CO₂ is expelled through the lungs. When base enters, carbonic acid reacts: H₂CO₃ + OH⁻ → HCO₃⁻ + H₂O. This open system (CO₂ can be exhaled or retained) extends the effective buffer range beyond the typical pK_a ± 1 window.

Normal blood pH variations are less than 0.1 unit. Deviations of 0.4 or more from pH 7.4 can be fatal, making the carbonate buffer one of the most critical chemical systems in the body. Additional buffering is provided by phosphate and protein buffer systems inside cells.

To design an effective buffer, start with target pH, then choose a conjugate pair with pK_a near that value:

1. Select acid/base pair with pK_a ≈ target pH (within ±1 is ideal).
2. Set total concentration high enough for needed buffer capacity.
3. Choose ratio [A⁻]/[HA] using Henderson–Hasselbalch.
4. Stress-test by simulating expected acid/base additions.

Common mistakes: using Henderson–Hasselbalch before neutralization stoichiometry after strong-acid/base addition, using a pair far from the target pH, and ignoring dilution effects in biological or lab prep contexts. Practical rule: if expected additions are large relative to buffer component moles, capacity failure is likely even when initial pH is correct.