Buffer Dilution Calculator

A buffer works because it holds a weak acid together with its conjugate base, and it resists a change in pH because the two interconvert. A little added acid turns some of the base form into the acid form; a little added base does the reverse. How far the mixture moves depends on the proportion of the two forms, and that proportion is a property of the ratio rather than of the total amount present. The net charge and Henderson-Hasselbalch guide works through the same relationship in a different system.

The consequence for dilution is precise and slightly counter-intuitive. A tenfold dilution divides both forms by ten at the same moment, and dividing two quantities by the same number leaves their ratio untouched. So the pH predicted by the acid-base relationship is essentially what it was, which is why it is commonly said that a buffer keeps its pH when it is diluted. What does not survive the dilution is capacity: the reservoir of base able to absorb added acid, and of acid able to absorb added base, shrinks in proportion to the dilution.

Capacity and ratio are two different properties, and conflating them is why buffer dilution is sometimes described as doing nothing at all and sometimes as ruining the buffer. It does neither. The ratio survives because both species are diluted by the same factor, and the capacity falls because there is simply less of each species available to react. A buffer at a tenth of its original concentration has a tenth of the reservoir, so a fixed perturbation moves the ratio ten times further than it did before. A tenth of the reservoir is a real loss even on a day when the pH reading has not moved at all.

There is a limit to that description. The relationship between ratio and pH describes a system in which the buffer species dominate the acid-base behaviour. As a buffer is diluted towards the point where the solvent and its own chemistry start to matter, the simple account stops describing what a pH measurement would actually read, and no volume arithmetic on this page can recover that. The charge against pH calculator shows the same kind of shift in proportion for ionisable groups, which is the general shape of the effect. None of this is visible in a dilution table.

The stock strength is a multiple of working strength, and the calculation rests on every component of the stock being at that same multiple. A tenfold stock diluted tenfold is at working strength for each component together, and that is what makes a single multiplier meaningful for a mixture of salts at all. The assumption holds for a stock that was made to one recipe, and it need not hold for one assembled in stages where the components arrived at different final volumes. This page will compute from a number that does not describe such a stock without any complaint.

The other failure here is reading the multiplier as an absolute concentration. A tenfold stock of a component might be 1 M, and 1 is not 10. The multiplier has no unit, because it is a ratio of one stock to one working solution, which is why it survives being written as a bare number and why reading it as a molarity gives an answer that looks reasonable and is wrong by whatever the working concentration happens to be. The working solution calculator is the same two-volume arithmetic with concentrations in the fields instead of multiples.

The diluent field here means whatever brings the total to the volume you entered, and in the ordinary case that is solvent. Diluting a buffer into a sample or into another solution is a different operation, because the receiving liquid has its own composition and its own pH, and neither is represented by an assumption of pure solvent. The arithmetic still returns two volumes that sum to your final volume, and each buffer component is still at working strength in the mixture, but the pH of the result is now a property of a mixture rather than of a buffer alone. When two solutions genuinely have to be combined, the solution mixing calculator carries both amounts explicitly.

It is worth being clear about the scope of the page. It answers one question, which is how much of a given stock and how much diluent produce the requested final volume at the requested multiple. Everything else about a buffer, including whether the components are compatible in combination, whether working strength suits the application and whether the mixture holds its pH at the temperature it will be used at, sits outside both the inputs and the arithmetic. The concentration after a volume change calculator covers the related single-addition case, where a solution already exists and only the effect of one addition is wanted.