The Henderson-Hasselbalch Equation

Buffers and The Henderson-Hasselbalch Equation

A buffer solution is one that contains approximately equal amounts of a wead acid and its salt, or a weak base and its salt. For example we could have a buffer solution of acetic acid and sodium acetate, or carbonic acid and sodium carbonate.

Consider the acetic acid and sodium acetate system. Since acetic acid is a weak acid, its Brönsted-Lowry equation is

CH₃COOH	+ H₂O		CH₃COO^-	+ H₃O⁺
Acetic Acid			Acetate ion

If some more H₃O⁺ is added to this system, it will combine with the acetate ion, shifting the equilibrium to the left. Thus there will not be a very great increase in the [H₃O⁺] and the pH. If some OH^- was added to this system it would remove some of the H₃O⁺, but then more acetic acid would dissociate to make moreH₃O⁺to replace that which is removed. Again, there will only be a small change in the[H₃O⁺]. These are good examples of Le Chatelier's principle at work -- an added stress is being minimized.

The Henderson-Hasselbalch equation is used to give a good approximation to the pH of a buffer solution.

This equation can be derived as follows. The general equation for any weak Brönsted-Lowry acid can be written as: HA + H2O

A^- + H₃O⁺ for which the acid equilibrium constant expression is

This equation can be rearranged to the form

which becomes

when you take the negative logarithm of both sides.
Here [HA] and [A^-] are the concentrations at equilibrium. However, making the standard weak acid assumption that these will not change very much from their initial values, because a weak acid barely dissociates, we can assume that this will also apply to the initial values. Therefore, approximately