The Henderson-Hasselbalch equation - alternate form

A colleague found an interesting article on the development of the H-H Equation. Inside this linked pdf, you will find a link to the article as well as same brief comments on the H-H Equation.

The Henderson-Hasselbalch Equation is: (1) a rearrangement of the Ka expression followed by (2) the use of negative logarithms.

It is:

 [A¯] pH = pKa + log ––––– [HA]

The alternate form starts from the ionization equation for a generic base called B:

B + H2O ⇌ HB+ + OH¯

By the way, here is an example of the above generic equation, using ammonia:

NH3 + H2O ⇌ NH4+ + OH¯

The B simply represents the entire base and HB+ represents the substances with an additional H+.

Next, we write the Kb expression for this reaction:

 [HB+] [OH¯] Kb = –––––––––– [B]

Next, we isolate the [OH¯] on the left-hand side of the equation:

 [B] [OH¯] = Kb · ––––– [HB+]

We negative log each of the three terms of the above equation to give pOH, pKb and we flip the third term so as to make it an addition, not a subtraction. Why make it an addition? Not sure, probably because that was the way Henderson & Hasselbalch did it. I really don't know.

Here is the alternate form of the Henderson-Hasselbalch Equation, expressed in terms of pOH and pKb:

 [HB+] pOH = pKb + log ––––– [B]

Using the words base and acid gives us this:

 [acid] pOH = pKb + log ––––– [base]