A Buffer Holds Its pH by a Ratio, So Dilution Changes Nothing

Why the lungs move blood pH in seconds

The acid half of this particular buffer is a gas. Dissolved carbon dioxide is in equilibrium with the carbon dioxide in the lungs, so changing how fast and deeply you breathe changes the denominator of the ratio directly and within a breath or two — doubling it from 1.2 to 2.4 mM drops the calculated pH from 7.40 to 7.10. The kidney adjusts the other half, the bicarbonate, and takes hours to days to do it. That split is the whole architecture of acid-base regulation: a fast lever with a small range and a slow lever with a large one, working on the numerator and denominator of the same fraction.

Capacity is what dilution does destroy

The pH of a tenfold-diluted buffer is unchanged, but its ability to hold that pH is not. Buffer capacity scales with the absolute concentrations, so the diluted solution absorbs a tenth as much added acid before its ratio — and therefore its pH — starts to move. That is why a recipe specifies both the pH and the molarity of a buffer, and why the second number is not decoration. It also explains why a buffer works best near its own pKa: at a ratio close to 1:1 there is plenty of both partners to consume whatever arrives, whereas at 20:1 one of them is nearly gone and the solution resists acid far better than base.

Frequently asked questions

Why does the equation use a logarithm?

Because pH is already one. The pH scale is the negative base-ten logarithm of the hydrogen-ion concentration, so a solution at pH 5 has ten times the concentration of one at pH 6 and a hundred times one at pH 7. Working in logarithms turns the multiplication of concentrations into the addition of small numbers, which is the only reason the arithmetic is doable in your head. It also means small-looking pH changes are large chemical ones: the shift from 7.40 to 7.10 in the table is a doubling of hydrogen-ion concentration, not a three per cent change.

Where does the equation stop being accurate?

At the edges of the ratio and in concentrated solutions. Beyond roughly ten to one in either direction the approximation behind it starts to fail, which is the practical basis for the rule that a buffer works within about one pH unit of its pKa. It also assumes that concentrations behave ideally, which stops being true as solutions get crowded — real work at high ionic strength uses activities rather than concentrations, and the pKa itself shifts with temperature and with what else is dissolved. For a laboratory buffer near 1:1 at ordinary concentrations, none of that matters; for anything measured to two decimals, all of it does.