### The Henderson-Hasselbalch equation - alternate form

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

It is:

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

B + H_{2}O ⇌ HB^{+} + OH¯

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

NH_{3} + H_{2}O ⇌ NH_{4}^{+} + OH¯

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

Next, we write the K_{b} expression for this reaction:

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

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 pK_{b}:

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