Buffer solution, Henderson-Hasselbalch equation
pH = pKa + log([A⁻]/[AH])
The relation pH = pKa + log([A⁻]/[AH]) in its three bench readings: the pH of a buffer whose concentrations are known, the base/acid ratio to achieve a target pH, and the full preparation, moles of each species for a given volume and concentration. The tool checks that the pH stays inside the pair’s buffer zone, pKa ± 1, and warns when it leaves it: the minority species runs out there at the first drop, and the word buffer no longer means anything. The validity domain of the relation, which is an approximation, is displayed rather than implied.
4.76
- Calculation
- pH = pKa + log([A⁻]/[AH]) = 4.76 + log(1) = 4.76
This buffer has a pH of 4.76.
The buffer zone runs from pKa − 1 to pKa + 1, where the ratio stays between 1:10 and 10:1. Buffering power peaks at pH = pKa, where both forms are equal: that is the selection criterion for a pair: pick the one whose pKa sits closest to the target pH.
Buffer capacity, for its part, depends on the TOTAL concentration: a 1 M buffer absorbs ten times more acid than a 0.1 M buffer at the same pH. The pH says where the buffer holds, the concentration says how much it holds.
The Henderson-Hasselbalch relation assumes the introduced concentrations are the equilibrium ones: it holds when they dominate water autoionisation and the pair’s dissociation, that is concentrations around 0.01 to 1 mol/L and a pH between roughly 3 and 11. Very dilute or far from neutrality, the exact balance of the pH tool does better.
Scientific dossier
What the tool computes, what it assumes, where it stops being valid, and where its data comes from.
Method & formulaspH = pKa + log([A⁻]/[AH])
pH = pKa + log([A⁻]/[AH])
[A⁻]/[AH] = 10^(pH − pKa)
buffer zone: pKa − 1 ≤ pH ≤ pKa + 1
The relation follows from the acidity constant written in logarithms: it ties the pH to the ratio of the two forms of the pair alone, not to their absolute values. At equal ratio, a concentrated and a dilute buffer share the same pH; they do not share the same capacity.
- pKa
- · the pH at which both forms of the pair are equal: acetate 4.76, phosphate 7.21, ammonium 9.25 at 25 °C.
- AH / A⁻
- · the acid form of the pair and its conjugate base.
- Buffer zone
- · pKa ± 1, where the ratio stays between 1:10 and 10:1 and the solution resists additions of acid or base.
- Capacity
- · the amount of acid or base the buffer can absorb: it grows with the total concentration of the pair.
Validity domainThe relation assumes the introduced concentrations are the equilibrium ones: it holds when they largely dominate water autoionisation and the pair’s own dissociation, that is concentrations around 0.
The relation assumes the introduced concentrations are the equilibrium ones: it holds when they largely dominate water autoionisation and the pair’s own dissociation, that is concentrations around 0.01 to 1 mol/L and a pH between roughly 3 and 11. Very dilute, very acidic or very basic, the solution requires the exact balance, that of the pH tool. pKa values depend on temperature and ionic strength: the pKa of Tris loses nearly 0.03 units per degree, which shifts a biological buffer prepared at 25 °C and used at 37 °C.
Reading the resultTwo distinct quantities govern a buffer: the pH, set by the ratio of the forms, and the capacity, set by the total concentration.
Two distinct quantities govern a buffer: the pH, set by the ratio of the forms, and the capacity, set by the total concentration. A 1 M and a 0.01 M buffer at the same ratio show the same pH, but the former absorbs a hundred times more acid. The selection criterion for a pair is its pKa: pick the one closest to the target pH, to work at maximum buffering power.