Following this post, I wanted to follow up with another quick note on the math of buffers as it relates to the new (when will I stop calling it that?), AP chemistry curriculum. If I am honest, this post repeats some of the stuff from the previous post on the subject, but I think it bears repeating from a slightly different perspective.
When one examines the course description carefully, one sees that in EK 6.C.2., there are few more specific references to the math of buffers.
Firstly in EK 6.C.2.a., there is a note that alerts students to the reason that buffers resist changes in pH, namely that in order to change the pH of a buffer by a unit of 1, the ratio of salt:acid has to change by a factor of 10. For example, when using the H-H equation
if we start with the ratio of salt:acid being 1:1*, the log of (1/1) = 0. In order to make the term log([salt]/[acid]) change by a unit of 1, the ratio of salt:acid must become 10:1 (since the log of (10/1) = 1) or 1:10 (since the log (1/10) = -1), i.e., there must be a ten-fold change in the concentration of one of the components. Since such large changes rarely happen quickly, the pH of buffers tends to change slowly, and they are often referred to as ‘resisting’ pH change.
*It’s worth noting that many buffers often do start with a ratio of salt:acid that is 1:1 (or at least close to it), since this affords two advantages. Firstly, with approximately equal amounts of weak acid and salt (conjugate base) present, the ability of the buffer solution to absorb both external base and external acid, is equally good. Secondly, from a practical point of view, one can more easily select an acid for use as part of a buffer solution with a particular pH, by simply assuming that the ratio of salt:acid will/should be 1:1, and therefore know that the pKa of the acid will be equal to the pH.
In EK 6.C.2.d., there is another, subtle reference to salt:acid ratios in buffers. It is important to know some basic math here, i.e., that the log of a number greater than 1 is positive, and that the log of a number less than 1 is negative. Becasue of the H-H equation,
we can deduce that a buffer with a pH that is greater than the pKa, must have a salt:acid ratio larger than 1, and vice-versa. This means that when pH’s start to deviate (in either direction) significantly from the corresponding pKa’s, then there must be significant deviations in the salt:acid ratio from 1, i.e., there must be significant differences in the amount of salt and acid present in the buffer.