Buffer Calculator

Calculate buffer solution concentrations for desired pH using Henderson-Hasselbalch equation

What Is a Buffer Solution?

A buffer solution resists changes in pH when small amounts of acid or base are added. Buffers consist of a weak acid and its conjugate base (or a weak base and its conjugate acid) in equilibrium. This property makes buffers essential in biology, medicine, and chemical analysis where stable pH is critical.

Buffer TypeComponentsExamplepH Range
Acidic bufferWeak acid + conjugate baseAcetic acid + sodium acetatepH < 7
Basic bufferWeak base + conjugate acidAmmonia + ammonium chloridepH > 7
Phosphate bufferH₂PO₄⁻ / HPO₄²⁻PBS (phosphate buffered saline)6.2–8.2
Bicarbonate bufferH₂CO₃ / HCO₃⁻Blood buffer system6.1–8.1
Tris bufferTris base + Tris-HClMolecular biology applications7.0–9.0

Henderson-Hasselbalch Equation

pH = pKa + log([A⁻]/[HA])

Where:

  • pH= Hydrogen ion concentration (log scale)
  • pKa= -log(Ka) of the weak acid
  • [A⁻]= Concentration of conjugate base
  • [HA]= Concentration of weak acid

The Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation relates buffer pH to pKa and the ratio of conjugate base to weak acid concentrations. It's derived from the acid dissociation equilibrium.

FormEquationWhen to Use
For acidspH = pKa + log([A⁻]/[HA])Weak acid + salt buffer
For basespOH = pKb + log([BH⁺]/[B])Weak base + salt buffer
AlternativepH = pKa + log(mol A⁻/mol HA)When using moles instead of M
At equal conc.pH = pKaWhen [A⁻] = [HA], log(1) = 0

Key insight: The equation shows that buffer pH depends primarily on pKa, with the concentration ratio providing fine-tuning of ±1 pH unit.

Henderson-Hasselbalch Derivation

Ka = [H⁺][A⁻]/[HA] pKa = -log(Ka) pH = pKa + log([A⁻]/[HA])

Where:

  • Ka= Acid dissociation constant
  • [H⁺]= Hydrogen ion concentration

Buffer Capacity and Effectiveness

Buffer capacity (β) measures how much acid or base a buffer can neutralize before its pH changes significantly. Higher capacity means better resistance to pH changes.

FactorEffect on CapacityOptimal Condition
Total concentrationHigher concentration → higher capacityUse highest practical concentration
Ratio [A⁻]/[HA]Closer to 1:1 → higher capacityRatio between 0.1 and 10
pH vs pKaCloser to pKa → higher capacitypH within ±1 of pKa
VolumeMore volume → more total bufferScale to application

Buffer range: A buffer is effective within approximately pKa ± 1 pH unit. Outside this range, buffering capacity drops significantly because one component dominates.

Buffer Capacity Formula

β = ΔC / ΔpH or β = 2.303 × C × Ka[H⁺] / (Ka + [H⁺])²

Where:

  • β= Buffer capacity (mol/L per pH unit)
  • ΔC= Moles of strong acid/base added per liter
  • ΔpH= Resulting pH change
  • C= Total buffer concentration

Common Buffer Systems and Their pKa Values

Different buffers are selected based on the desired pH range and compatibility with the application.

Buffer SystempKa at 25°CUseful pH RangeCommon Applications
Citric acid/citrate3.13, 4.76, 6.402.1–7.4Food science, pharmaceuticals
Acetic acid/acetate4.763.8–5.8Chemical analysis, food
MES6.155.2–7.1Biochemistry (Good's buffer)
Phosphate (H₂PO₄⁻/HPO₄²⁻)7.206.2–8.2Biochemistry, cell culture
HEPES7.556.6–8.5Cell culture, biochemistry
Tris8.077.0–9.0Molecular biology, electrophoresis
Borate9.248.2–10.2Electrophoresis, cosmetics
Ammonia/ammonium9.258.3–10.3Chemical analysis

Good's buffers: MES, HEPES, MOPS, PIPES, and Tris are biological buffers designed to minimize interference with biochemical reactions.

How to Prepare a Buffer Solution

Buffers can be prepared by several methods, each suited to different situations.

MethodProcedureAdvantageWhen to Use
Mix acid + saltDissolve weak acid + its sodium saltPrecise control of both componentsMost accurate preparation
Partial neutralizationAdd strong base to weak acid until target pHUses fewer reagentsWhen salt unavailable
From acid + base formsMix acid and base forms of buffer compoundCommon for Tris, HEPESBiological buffers
pH adjustmentMake approximate buffer, adjust pH with HCl/NaOHQuick and practicalRoutine lab work

Best practice: Prepare buffer at the temperature where it will be used—pKa values (and thus pH) are temperature-dependent.

Buffer Systems in Biology

Living organisms rely on multiple buffer systems to maintain precise pH for proper enzyme function and cellular processes.

Buffer SystemLocationNormal pHComponents
Bicarbonate bufferBlood plasma7.35–7.45H₂CO₃ / HCO₃⁻ (CO₂ regulation)
Hemoglobin bufferRed blood cells7.35–7.45Hb-H⁺ / Hb (O₂-linked)
Phosphate bufferIntracellular fluid~7.2H₂PO₄⁻ / HPO₄²⁻
Protein bufferAll body fluidsVariousAmino acid side chains

Clinical importance: Blood pH outside 7.0–7.8 is life-threatening. Acidosis (pH < 7.35) and alkalosis (pH > 7.45) require medical intervention.

Bicarbonate Buffer Equation

CO₂ + H₂O ⇌ H₂CO₃ ⇌ H⁺ + HCO₃⁻ pH = 6.1 + log([HCO₃⁻]/(0.03 × PCO₂))

Where:

  • [HCO₃⁻]= Bicarbonate concentration (mEq/L)
  • PCO₂= Partial pressure of CO₂ (mmHg)
  • 6.1= pKa of carbonic acid at body temperature

Buffer Calculation Methods

Several calculation types are common when working with buffers.

To FindGivenFormula/Method
Buffer pHpKa, [A⁻], [HA]pH = pKa + log([A⁻]/[HA])
Ratio needed for target pHpKa, target pH[A⁻]/[HA] = 10^(pH - pKa)
pH after adding acidInitial buffer, mol H⁺ addedNew ratio = (mol A⁻ - mol H⁺)/(mol HA + mol H⁺)
pH after adding baseInitial buffer, mol OH⁻ addedNew ratio = (mol A⁻ + mol OH⁻)/(mol HA - mol OH⁻)
Amounts to mixTotal concentration, target pHUse ratio to split total between A⁻ and HA

Worked Examples

Calculate Buffer pH

Problem:

What is the pH of a buffer containing 0.20 M acetic acid and 0.35 M sodium acetate? (pKa of acetic acid = 4.76)

Solution Steps:

  1. 1Identify: [HA] = 0.20 M (acetic acid), [A⁻] = 0.35 M (acetate), pKa = 4.76
  2. 2Apply Henderson-Hasselbalch: pH = pKa + log([A⁻]/[HA])
  3. 3Substitute: pH = 4.76 + log(0.35/0.20)
  4. 4Calculate: pH = 4.76 + log(1.75) = 4.76 + 0.243 = 5.00

Result:

The buffer pH is 5.00. The higher acetate concentration (base) shifts pH above pKa. This buffer is effective in the range 3.76–5.76 (pKa ± 1).

Prepare Buffer at Target pH

Problem:

How would you prepare 1.0 L of pH 7.40 phosphate buffer with total phosphate concentration of 0.10 M? (pKa₂ = 7.20)

Solution Steps:

  1. 1Find required ratio: [HPO₄²⁻]/[H₂PO₄⁻] = 10^(7.40 - 7.20) = 10^0.20 = 1.58
  2. 2Set up equations: [HPO₄²⁻] + [H₂PO₄⁻] = 0.10 M; [HPO₄²⁻] = 1.58 × [H₂PO₄⁻]
  3. 3Solve: 1.58[H₂PO₄⁻] + [H₂PO₄⁻] = 0.10; [H₂PO₄⁻] = 0.0388 M
  4. 4Calculate: [HPO₄²⁻] = 0.10 - 0.0388 = 0.0612 M
  5. 5For 1 L: Use 0.0388 mol NaH₂PO₄ (5.37 g) + 0.0612 mol Na₂HPO₄ (8.69 g)

Result:

Mix 5.37 g NaH₂PO₄ and 8.69 g Na₂HPO₄ in water, dissolve, and adjust to 1.0 L. Verify pH with a meter and adjust if necessary.

pH Change After Adding Acid

Problem:

A 500 mL buffer contains 0.15 M NH₃ and 0.10 M NH₄⁺ (pKa = 9.25). What is the pH after adding 0.01 mol HCl?

Solution Steps:

  1. 1Initial moles: NH₃ = 0.15 × 0.5 = 0.075 mol; NH₄⁺ = 0.10 × 0.5 = 0.05 mol
  2. 2HCl reacts with NH₃: NH₃ + H⁺ → NH₄⁺
  3. 3New moles: NH₃ = 0.075 - 0.01 = 0.065 mol; NH₄⁺ = 0.05 + 0.01 = 0.06 mol
  4. 4Apply H-H (can use moles directly): pH = pKa + log(0.065/0.06)
  5. 5Calculate: pH = 9.25 + log(1.083) = 9.25 + 0.035 = 9.28

Result:

The pH changes from initial 9.43 to 9.28—a change of only 0.15 pH units despite adding significant acid. This demonstrates the buffer's resistance to pH change.

Tips & Best Practices

  • Choose a buffer with pKa within ±1 of your target pH for optimal buffering capacity.
  • When pH = pKa, the buffer has maximum capacity because [A⁻] = [HA].
  • Higher total concentration means greater buffer capacity—double concentration, double capacity.
  • Prepare buffers at the temperature they'll be used; pKa is temperature-dependent (especially for Tris).
  • For biological work, consider Good's buffers (HEPES, MOPS, MES) that don't interfere with enzymes.
  • Verify buffer pH with a calibrated pH meter; don't rely solely on calculations.
  • Buffer range is approximately pKa ± 1; outside this range, buffering is ineffective.

Frequently Asked Questions

Select a buffer with pKa within ±1 unit of your target pH (ideally pKa ≈ target pH). Consider compatibility with your system: avoid phosphate with Ca²⁺ (precipitates), check if buffer interacts with enzymes or assays. For biological work, Good's buffers (HEPES, MES, MOPS) minimize interference with biochemical reactions.
Buffers require a weak acid/base equilibrium system. Strong acids and bases dissociate completely—there's no equilibrium to shift. When you add HCl to a strong base, the base is consumed with no reserve species to regenerate it. Weak acids, however, have a reservoir of undissociated molecules that can release H⁺ to counteract added base.
When buffer capacity is exhausted (one component runs out), the pH changes rapidly like an unbuffered solution. For example, if all the conjugate base is consumed by added acid, further acid addition causes pH to drop sharply. This is why you should never add more than about 10% of the buffer's moles as strong acid or base.
pKa values change with temperature due to thermodynamic effects on the dissociation equilibrium. Tris buffer is notably temperature-sensitive: pH drops ~0.03 units per °C increase. Phosphate buffer is more stable (~0.003 per °C). Always prepare buffers at the temperature where they'll be used, or apply correction factors.
The equation is only valid for buffer solutions with weak acids/bases. It assumes: (1) the weak acid doesn't fully dissociate, (2) concentrations aren't too dilute (> 0.001 M), (3) pH is within the buffer range (pKa ± 1). For strong acids/bases or very dilute solutions, use the full equilibrium expressions instead.
Buffer strength (or concentration) refers to the total molarity of buffer components. Buffer capacity measures how much acid/base can be neutralized per pH change. Capacity depends on both concentration AND how close the pH is to pKa. A dilute buffer at its pKa might have similar capacity to a concentrated buffer far from its pKa.

Sources & References

Last updated: 2026-01-22