Buffer Solutions (Henderson-Hasselbalch)

Analysis and design of buffer solutions · pH = pKa + log([A⁻]/[HA])

Operation mode

Buffer system

Monosodium / Disodium Phosphate

pKa: 7.2(25 °C)
MW acid: 119.98 g/mol
MW conjugate base: 141.96 g/mol

Parameters

Acid concentration [HA]

Molar concentration of the weak acid

0.0012

Conjugate base concentration [A⁻]

Molar concentration of the conjugate base

0.0012

Total volume

Volume of solution to prepare

110000

Results

Buffer pH

7.2

Buffer capacity (β)

0.1152

mol/(L·pH)

Acid mass

1.2

Conjugate base mass

1.42

Equilibrium details

Ratio [A⁻]/[HA]: 1
Acid fraction (αₕₐ): 0.5
Base fraction (αₐ₋): 0.5

Compatible indicator

Azul de Bromotimol

Range: 6–7.6 · pK_In 7.3

Buffer Capacity and Species Fractions

Capacity β

α(HA)

α(A⁻)

Note: The chart represents the specific contribution of the buffer system. The numerical result above reflects total capacity, including the effect of water autoionization.

Fundamentals & Explanation

What is a buffer solution?

A buffer solution is an aqueous mixture that resists pH changes upon adding small amounts of acid or base. It consists of a weak acid (HA) and its conjugate base (A⁻), or vice versa. Buffers are essential in biochemistry, cell biology, and analytical chemistry to maintain controlled pH conditions.

Henderson-Hasselbalch Equation

\text{pH} = \text{p}K_a + \log_{10}\!\left(\frac{[A^-]}{[HA]}\right)

Derived from the acid dissociation equilibrium ( $K_a = \frac{[H^+][A^-]}{[HA]}$ ), this equation relates pH to the concentrations of the weak acid and its conjugate base. It holds when both concentrations are much larger than $K_a$ and water autoionization is negligible.

Validity assumptions: the equation assumes thermodynamic equilibrium, low ionic strength (activities ≈ concentrations), and no secondary reactions. For polyprotic acids (e.g. citric acid), it models only one equilibrium at a time and results are approximate [3].

Buffer Capacity (β) — Van Slyke Equation

\beta = 2.303 \left( \frac{C \cdot K_a [H^+]}{(K_a + [H^+])^2} + \frac{K_w}{[H^+]} + [H^+] \right)

Buffer capacityquantifies the buffer's resistance to pH changes. The first term represents the conjugate pair contribution, reaching its maximum when $\text{pH} = \text{p}K_a$ (where $[HA] = [A^-]$ ). The $K_w/[H^+]$ and $[H^+]$ terms represent water autoionization, significant only at extreme pH (< 2 or > 12).

In this calculator: the chart displays only the conjugate pair capacity (symmetric bell curve), while the numerical β value reported in the results includes the full Van Slyke equation with water autoionization terms.

Species Fractions (α)

\alpha_{HA} = \frac{[H^+]}{K_a + [H^+]}

\alpha_{A^-} = \frac{K_a}{K_a + [H^+]}

The mole fractions describe the relative proportion of each species at a given pH. The sigmoid curves cross exactly at $\text{pH} = \text{p}K_a$ , where both fractions equal 0.5. The calculator chart overlays β and α to simultaneously visualize capacity and buffer composition.

Calculator Modes

Analysis Mode

Enter known concentrations of [HA] and [A⁻] to obtain the resulting pH, buffer capacity β, and the masses needed for a given volume.

Design Mode

Define a target pH and total concentration C. The calculator solves the inverse Henderson-Hasselbalch to determine [HA] and [A⁻], and converts to grams: $m = [\text{species}] \cdot V \cdot MW$ .

Practical Buffer Design

Golden rule:

Choose a system whose $\text{p}K_a$ is within ±1 unit of the target pH. Outside this range, buffer capacity drops rapidly [1].

Select the buffer system based on the pH range.
Define target pH and total concentration C.
Compute $[A^-]$ and $[HA]$ using the inverse Henderson-Hasselbalch.
Convert to grams: $m = [\text{species}] \cdot V \cdot MW$
Verify that $\beta$ is acceptable for the application.

Standard Conditions

T = 25 °C (298.15 K)

K_w = 1.0 × 10^-14

Ionic strength: low

Solvent: pure water

Effective Range

Optimal pH: pKa ± 1

Max β: pH = pKa

Useful ratio: 0.1 – 10

[A⁻]/[HA] = 1 at pKa

Academic References

[1] Atkins, P. & de Paula, J. (2018). Atkins' Physical Chemistry (11th ed.). Oxford University Press. Ch. 6: Chemical Equilibrium.
[2] Van Slyke, D. D. (1922). On the measurement of buffer values and on the relationship of buffer value to the dissociation constant of the buffer and the concentration and reaction of the buffer solution. J. Biol. Chem. 52, 525–570. doi.org/10.1016/S0021-9258(18)85845-8
[3] Po, H. N. & Senozan, N. M. (2001). The Henderson-Hasselbalch Equation: Its History and Limitations. J. Chem. Educ. 78(11), 1499. doi.org/10.1021/ed078p1499
[4] Good, N. E. et al. (1966). Hydrogen Ion Buffers for Biological Research. Biochemistry 5(2), 467–477. doi.org/10.1021/bi00866a011
[5] CRC Handbook of Chemistry and Physics (104th ed., 2023–2024). CRC Press / Taylor & Francis. Dissociation constant tables.

Buffer Solutions (Henderson-Hasselbalch)

Parameters

Results

Compatible indicator

Buffer Capacity and Species Fractions

Fundamentals & Explanation

What is a buffer solution?

Henderson-Hasselbalch Equation

Buffer Capacity (β) — Van Slyke Equation

Species Fractions (α)

Calculator Modes

Analysis Mode

Design Mode

Practical Buffer Design

Standard Conditions

Effective Range

Academic References

You may also like:

What is a buffer solution?

Henderson-Hasselbalch Equation

Buffer Capacity (β) — Van Slyke Equation

Species Fractions (α)

Calculator Modes

Analysis Mode

Design Mode

Practical Buffer Design

Standard Conditions

Effective Range

Academic References