Finds the pH of a buffer made from a weak acid and its salt, using the Henderson-Hasselbalch equation pH = pKa + log(base ÷ acid). With equal amounts of each, the pH equals the pKa.
A buffer is a solution whose pH barely moves when acid or base is added. It is made by mixing a weak acid with its salt.
This is the Henderson-Hasselbalch equation. What sets the pH is not either concentration but the ratio between them.
Add acid and the conjugate base present in solution absorbs it, turning into the weak acid. Add base and the weak acid hands over a hydrogen ion, turning into the conjugate base. There is a reservoir waiting in each direction.
And it is the ratio that matters. Adding a little acid to a one-to-one buffer might shift it to 1.2 against 0.8, a ratio of 0.67. The logarithm of that is about −0.18, so the pH moves by 0.18 and no more. The logarithm flattens the change.
The default input mixes acetic acid, with a pKa of 4.76, at 0.1 mol/L with its salt sodium acetate at 0.2 mol/L.
The ratio is 2, whose logarithm is about 0.301, so the pH is , about 5.061. The hydrogen ion concentration is about mol/L.
Make the two concentrations equal and the ratio is 1, its logarithm 0, and the pH is exactly the pKa of 4.76. Ten times as much base puts the pH one unit higher, at 5.76.
A buffer works well while the ratio stays between one to ten and ten to one, which is to say within one pH unit of the pKa. Beyond that one component is nearly exhausted, the reservoir is gone, and the pH begins to swing.
Choosing an acid whose pKa sits near the target pH is therefore the first step in preparing a buffer.
Only the ratio appears in the equation, so diluting a buffer with water leaves its pH almost unchanged. What does fall is the buffer capacity, the quantity of acid or base it can absorb. An unchanged pH is not the same as undiminished performance.
Blood is held at pH 7.4 by exactly this mechanism, buffered by carbonic acid and hydrogen carbonate ions.