Question

Derive the Henderson Haselbach equation.

Answer 1

Take the ionization reaction of a weak acid (HA):

The dissociation constant Ka of the above reaction will be:

Then from the equation (2) take out the [H⁺] to the left side (solve for H⁺): ...

Substitute the pH and pKa in the equation (4):

Take the ionization reaction of a weak acid (HA):

ionization of acid

The dissociation constant Ka of the above reaction will be:

proton donor and proton acceptor

Dissociation constant is the ratio of the concentration of products by the concentration of reactants. The square brackets, [ ], denote ‘concentration’.

Then from the equation (2) take out the [H⁺] to the left side (solve for H⁺):

ph pka and buffer action

Then take the negative logarithm of both sides:

titration curve of weak acid

We know that the – log [H⁺] is pH and the – log Ka is pKa.

Substitute the pH and pKa in the equation (4):

what is pKa and ka

Now invert the -log [HA]/[A¯], which involves changing its sign to obtain the Henderson-Hasselbalch equation.

buffer action

[A¯] is the concentration of proton acceptor (it can accept the proton in a buffer)

[HA] is the concentration of proton donor (it can donate a proton in the buffer)

Thus the equation (6) can be better stated as:

Hasselbalch equation

The above equation is called the Henderson-Hasselbalch equation.