Why is my phosphate buffer pH lower than Henderson–Hasselbalch predicts?

Henderson–Hasselbalch uses concentrations, but a pH meter responds to H⁺ activity, and the tabulated pKa applies at zero ionic strength. HPO₄²⁻ carries two negative charges, so its activity coefficient is much smaller than that of H₂PO₄⁻ and the apparent pKa₂ falls from 7.20 to about 6.8–6.9. A 0.1 M, pH 7.4 phosphate buffer made by the ideal equation actually reads about pH 7.0. This tool corrects for this with the Davies equation, log γ = −A z²(√I/(1+√I) − 0.3I), iterated to a self-consistent ionic strength, and shows both results.

How do I make Tris-HCl buffer and how much HCl do I need?

Dissolve Tris base (121.14 g/mol) in about 80% of the final volume, titrate with HCl to the target pH and make up to volume. The HCl needed equals the total Tris times the protonated fraction 1/(1 + 10^(pH − pKa)). At 25 °C Tris has a pKa of 8.07, so for 50 mM at pH 8.0 about 54–58% of the Tris must be protonated — roughly 27–29 mL of 1 M HCl per litre. Tris pKa drops about 0.028 per °C, so set the pH at the temperature of use: pH 8.0 at 25 °C becomes about 8.6 at 4 °C.

What are buffer range and buffer capacity?

Within pKa ± 1 the base-to-acid ratio lies between 1:10 and 10:1 and the buffer resists pH change well; outside that range one form is scarce and small additions of acid or base shift the pH sharply. Buffer capacity β = dC/dpH is the amount of strong acid or base needed to change the pH by one unit; for a single pKa β ≈ 2.303·C·α(1−α), with a maximum of 0.576·C at pH = pKa. Choose a buffer whose pKa is close to the target pH and use an adequate concentration.

What is the recipe for PBS?

Standard 1× PBS contains, per litre, 8 g NaCl, 0.2 g KCl, 1.44 g anhydrous Na₂HPO₄ and 0.24 g KH₂PO₄ — 137 mM NaCl, 2.7 mM KCl, 10 mM phosphate dibasic and 1.8 mM phosphate monobasic — adjusted to pH 7.4 with HCl or NaOH and made up to volume. With Na₂HPO₄·12H₂O use 3.63 g, with Na₂HPO₄·7H₂O 2.72 g. For 10× PBS multiply everything by ten; it may crystallise in the fridge, so warm it before use. The Common recipes tab scales this to any strength and volume.

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🧯Buffer Preparation Calculator - Phosphate, Tris-HCl, HEPES, Acetate & Citrate Recipes

The usual way to make a buffer is to use the Henderson–Hasselbalch equation, pH = pKa + log([base]/[acid]), to get the ratio of acid and base forms and convert it into grams. Tabulated pKa values, however, are thermodynamic values at zero ionic strength, and in a real solution activity coefficients are below 1, so highly charged systems such as phosphate have a noticeably lower apparent pKa: equimolar NaH₂PO₄/Na₂HPO₄ at an ionic strength of about 0.1 M reads about pH 6.88, not 7.20. This calculator covers 13 systems — phosphate, acetate, citrate, Tris, HEPES, MES, MOPS, PIPES, carbonate–bicarbonate, glycine–HCl, glycine–NaOH, boric acid–borax and ammonium chloride–ammonia. It starts from 25 °C thermodynamic pKa values, shifts them to your temperature with dpKa/dT, and iterates the ionic strength and Davies activity coefficients to self-consistency; polyprotic systems such as citrate, with three overlapping pKa values, are solved from the full charge balance. Molar masses are those of the reagents you actually buy, including NaH₂PO₄·H₂O, Na₂HPO₄·7H₂O or ·12H₂O, sodium acetate trihydrate, citric acid monohydrate, trisodium citrate dihydrate and borax, and glacial acetic acid and ammonia solution are converted to millilitres. For example, 1 L of 0.1 M sodium phosphate at pH 7.4 needs 2.77 g NaH₂PO₄·H₂O and 21.43 g Na₂HPO₄·7H₂O; 1 L of 50 mM Tris-HCl at pH 8.0 (25 °C) needs 6.06 g Tris base and about 29 mL of 1 M HCl (27 mL by ideal Henderson–Hasselbalch). You also get the ionic strength, buffer capacity β, a side-by-side comparison of the ideal and activity-corrected recipes, a warning when the pH is outside pKa ± 1, and a step-by-step protocol to copy or print. Standard recipes for PBS, TBS, 50× TAE, 10× TBE, TE and 0.5 M EDTA scale to any strength and volume.

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How to use Buffer Preparation Calculator

1Choose a buffer system and enter the target pH, total buffer concentration, final volume and temperature, or click an example
2Pick a method — weigh acid and base forms, titrate one reagent with HCl/NaOH, or mix two equimolar stocks — and select the exact reagents you have (including hydrates)
3Follow the generated protocol to weigh, dissolve, adjust the pH and make up to volume; copy or print it, then confirm with a calibrated pH meter

FAQ

Why is my phosphate buffer pH lower than Henderson–Hasselbalch predicts?: Henderson–Hasselbalch uses concentrations, but a pH meter responds to H⁺ activity, and the tabulated pKa applies at zero ionic strength. HPO₄²⁻ carries two negative charges, so its activity coefficient is much smaller than that of H₂PO₄⁻ and the apparent pKa₂ falls from 7.20 to about 6.8–6.9. A 0.1 M, pH 7.4 phosphate buffer made by the ideal equation actually reads about pH 7.0. This tool corrects for this with the Davies equation, log γ = −A z²(√I/(1+√I) − 0.3I), iterated to a self-consistent ionic strength, and shows both results.
How do I make Tris-HCl buffer and how much HCl do I need?: Dissolve Tris base (121.14 g/mol) in about 80% of the final volume, titrate with HCl to the target pH and make up to volume. The HCl needed equals the total Tris times the protonated fraction 1/(1 + 10^(pH − pKa)). At 25 °C Tris has a pKa of 8.07, so for 50 mM at pH 8.0 about 54–58% of the Tris must be protonated — roughly 27–29 mL of 1 M HCl per litre. Tris pKa drops about 0.028 per °C, so set the pH at the temperature of use: pH 8.0 at 25 °C becomes about 8.6 at 4 °C.
What are buffer range and buffer capacity?: Within pKa ± 1 the base-to-acid ratio lies between 1:10 and 10:1 and the buffer resists pH change well; outside that range one form is scarce and small additions of acid or base shift the pH sharply. Buffer capacity β = dC/dpH is the amount of strong acid or base needed to change the pH by one unit; for a single pKa β ≈ 2.303·C·α(1−α), with a maximum of 0.576·C at pH = pKa. Choose a buffer whose pKa is close to the target pH and use an adequate concentration.
What is the recipe for PBS?: Standard 1× PBS contains, per litre, 8 g NaCl, 0.2 g KCl, 1.44 g anhydrous Na₂HPO₄ and 0.24 g KH₂PO₄ — 137 mM NaCl, 2.7 mM KCl, 10 mM phosphate dibasic and 1.8 mM phosphate monobasic — adjusted to pH 7.4 with HCl or NaOH and made up to volume. With Na₂HPO₄·12H₂O use 3.63 g, with Na₂HPO₄·7H₂O 2.72 g. For 10× PBS multiply everything by ten; it may crystallise in the fridge, so warm it before use. The Common recipes tab scales this to any strength and volume.

Features

13 common buffers: phosphate, acetate, citrate, Tris, HEPES, MES, MOPS, PIPES, carbonate, glycine, borate and ammonia
Three methods: weigh two salts, titrate one reagent (mL of HCl or NaOH), or mix equimolar stock solutions Sørensen-style
Molar masses of the actual reagent forms, including hydrates, with volumes for liquid reagents
Davies activity correction with self-consistent ionic strength, compared with ideal Henderson–Hasselbalch
Temperature-corrected pKa (e.g. Tris −0.028 per °C) and full charge-balance solution for polyprotic acids
Ionic strength, buffer capacity β and apparent pKa, with a warning outside pKa ± 1
Step-by-step protocol you can copy or print
PBS, TBS, TAE, TBE, TE and EDTA recipes scaled to any strength and volume

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