Buffer Preparation Calculator – Recipes That Hit the pH You Asked For
A protocol says "1 L of 100 mM sodium phosphate, pH 7.40". This buffer preparation calculator turns that line into a bench recipe: which compounds to weigh, how much acid or base to add, and when to make up to volume. It also works the other way round. Enter a recipe someone hands you and it predicts the pH. Unlike a plain Henderson–Hasselbalch calculator, it corrects the pKa for temperature and for everything else dissolved in the solution, so the first pH reading lands close to the target.
Why the textbook pKa gives the wrong pH
A buffer's pH is set by the ratio of its base and acid forms around an apparent pKa, written pKa′. Tables list the thermodynamic value pKa°, defined at 25 °C and zero ionic strength. Real buffers are salty. Ions shield each other, so the activity of a charged species is lower than its concentration, and the effective pKa moves. The Davies equation estimates that shift:
pKa′ = pKa(T) + (2·z_acid − 1) · A · (√I/(1 + √I) − 0.3·I)For H₂PO₄⁻ (z = −1) the factor is −3, so phosphate is hit hard. At 100 mM and pH 7.4 the ionic strength is about 0.26 M, and pKa₂ falls from 7.20 to 6.80. Mix the salts in the textbook ratio and the solution reads pH 7.01, almost 0.4 units low. Neutral acids such as acetic acid and HEPES shift less. Cationic acids such as TrisH⁺ shift slightly upward.
Temperature: set the pH where you will use it
Every pKa also moves with temperature, in proportion to the buffer's ionisation enthalpy ΔH°. Phosphate barely notices (about −0.003 pH per °C). Tris loses about 0.028 pH per °C. A Tris buffer made to pH 8.00 at 25 °C reads about 8.63 in the cold room and 7.68 at 37 °C. Adjust the pH at the temperature of use. If your pH meter sits at room temperature, tick the adjust-temperature box: the tool tells you the reading to aim for there, for example "adjust at 22 °C to pH 7.58; it will be 7.40 at 37 °C".
Choosing a buffer
A buffer works best within about ±1 unit of its pKa′. The ladder chart draws that band for every buffer in the library at your temperature and ionic strength. Rows whose band covers your target stay solid. For biological work, Good's buffers (MES, MOPS, HEPES, CHES, CAPS) were chosen to bind few metals, absorb little UV and cross membranes poorly. Check each system's note for incompatibilities: phosphate precipitates calcium, citrate chelates it, borate binds sugars, and carbonate trades CO₂ with the air.
Buffer capacity at the bench
Buffer capacity β is the amount of strong acid or base that moves the pH by one unit. It grows with concentration and peaks at pKa′, where acid and base forms are equal. The 100 mM phosphate example has β ≈ 37 mM/pH. Adding 1 mM of HCl therefore moves it by about 0.027 pH. A buffer used 1.5 units from its pKa′ has a fraction of that capacity, which is why the tool warns about weak buffering.
Two salts, or one form plus titrant
You can weigh both forms (NaH₂PO₄ + Na₂HPO₄, Tris·HCl + Tris base). You can weigh one form and titrate it with NaOH or HCl. Or you can mix two stock solutions, as in the classic Gomori tables. All three give the same final composition. Check the hydrate on the bottle: Na₂HPO₄·7H₂O weighs almost twice as much per mole as the anhydrous salt. Dissolve in about 80 % of the volume, adjust the pH, then make up to volume. Adding water after the pH adjustment changes the pH only slightly; adding salt after it changes the pH much more.
Polyprotic buffers
Phosphate, citrate, glycine and carbonate have several ionisable steps. The calculator solves the full proton balance rather than one Henderson–Hasselbalch step, so any pair of forms works. Citric acid + trisodium citrate spans pH 3–6.2 because three overlapping pKa values sit between them.