pH and titration combine several simple concepts. Together the concepts are more complex because failure to fully grasp any one of them prevents comprehension. Logarithms, equilibrium and acid-base theory are essential.
Logarithmic relationships are mathematical functions. Students are often familiar with, but not fluent in logarithms (especially if they're not fluent with mathematical functions in general). The pH scale is logarithmic because hydrogen ion concentrations vary over about 15 orders of magnitude. In buffered regions pH changes slowly with addition of acid or base and in unbuffered regions pH changes dramatically as acid or base are added. The best way to gain fluency is to plot titration curves with a spreadsheet.
Acids and bases
The Bronsted concept of acids and bases is appropriate for biochemists. A Bronsted acid (e.g. acetic acid) can donate a proton. A Bronsted base (e.g. acetate) can accept a proton. A buffer consists of a Bronsted acid and its complementary Bronsted base. Edsall and Wyman (Biophysical Chemistry, Academic Pr, 1958) point out that acetic acid can be protonated (serve as a base) in concentrated sulfuric acid. (see superacids)
Why are acids, bases and pH important in biology
The pH of physiological fluids is about 7, where buffering capacity of water is minimal. Protein stability and enzymatic activity depend on acidic and basic groups which titrate as pH changes.
Acid-base properties of water
Water is both an acid and a base. It's a Bronsted base when it accepts a proton to form H3O+ with a pKa of about -1.3, and a Bronsted acid when it donates a hydrogen ion to form OH- with a pKa of about 15.3.
Buffering capacity is DpH/Dc, where "c" is the concentration of acid or base. Buffering capacity (resistance to pH change) is highest where acids or bases are titrating (maximal where [acid] = [base].)
The Henderson-Hasselbalch equation
The equation pH = pKa + log [A-]/[HA], is readily derived by taking the negative log of the simple equilibrium relationship, Ka = [H+][A-]/[HA]. It's often written pH = pKa + log [salt]/[acid]. This is an artifact of an earlier age when most buffers were acids. There are now common basic buffers such as Tris. The equation is more general as pH = pKa = log [base]/[acid].
How to think about buffers
One should think both logarithmically (what's the pH and where are we on the titration curve) and also in terms of ratios (what's the ratio of basic to acidic forms of the buffer. Note that the ratio [base]/[acid] precisely determines the pH and that adjusting this ratio produces buffers more precisely and reproducibly than using a pH meter. See spreadsheet titration.
Does pKa change with salt concentration?
Yes, and the change is particularly pronounced with multivalent salts. For more precise titration curves,corrections for ionic strength are essential.
Should I adjust the pH of my buffer if the temperature changes?
For small changes it's not important. Keep in mind that temperature affects pKas of both buffers (especially amino groups) and proteins so that simply adjusting the pH of the buffer to that of the original temperature may put you in a different place on a protein's titration curve.
How important are buffer effects?
"Buffer effects" arise from interactions of buffers with system components. These aren't easily predicted. It's good practice to try several buffers. It never hurts to look at the chemical structure of a buffer to see if it resembles a detergent of a sugar.
How concentrated should my buffer be?
Strong enough so the the pH at the end of the reaction is the same as at the beginning.
What pH should I use?
My rule of thumb is to make a spreadsheet table for the recommended buffer. I begin by making recipe buffers at the recommended pH as well as 0.2 units above and 0.2 units below the recommended pH. I then do the assay (procedure) with all three buffers. If the above or below outperforms the recommended, I explore further. If the above and below are similar to the recommended I proceed with the assurance that my procedure will be reproducible.