# Buffer Hermetica

I can never remember how the maths works with buffers and acids and bases and all that stuff. I never even learned the stuff about effective vs thermodynamic pKas. These are my notes on what i've remembered or learned. A lot of this is very basic.

• pX = -log10(X); for example, pH = -log10([H+]), pKa = -log10(Ka). Conversely, X = 10 ^ -pX.
• Where AH <=> A- + H+, Ka = [A-][H+]/[AH]. I am talking only about monoprotic acids for the rest of this page!
• Given the definition of Ka, if we define [A] = [AH] + [A-], then [A-] = [A]/([H+]/Ka + 1).
• Every A- produced means a H+ produced; so ...
• If there are no other players, [H+] = [A-], in which case, [H+] = [A-] = 1/2 . Ka (sqrt(4[A]/Ka + 1) - 1) - i think.
• If this is a buffer, and the pH is set by addition of strong acid or base, then the difference between the actual amount of H+ ([H+]) and the amount of H+ produced by hydrolysis of the acid (equal to [A-]) is [H+] - [A-] = [H+] - [A]/([H+]/Ka + 1). This is the amount of strong acid or base that has been added; positive means acid, negative means base.
• All those [concentrations] should be {activities}, and i have no idea how to work those out.
• The numbers in the tables are (or at least should be) thermodynamic pKas, which are defined at infinite dilution in a zero ionic strength solution; to get effective pKas (known as pKa'), you need to add a correction factor. This factor is known, but is not described in detail online anywhere that i can find; apparently, it's tabulated in "Buffers for pH and Metal lon Control" - D. D. Perrin, B. Dempsey (1974); Chapman and Hall Laboratory Manuals (London), and it ranges from 0 at I = 0, via 0.015 for I = 0.001 M to 0.159 for I = 0.5.
• Ionic strength is half the sum over all ions of the product of that ion's concentration and the square of its charge. Note that for a solution of a salt of singly-charged ions (eg NaCl), the ionic strength is equal to the concentration.

Some common pKas (thanks Sigma and Petrik Laboratories):

AcidpKa (25 C)
Acetic4.76
Boric9.23, 12.74, 13.80
HEPES7.55
Phosphoric2.15, 7.20, 12.33
PIPES3.00, 6.76
Tris8.06