# What Is the Hendersonâ€“Hasselbalch Equation?

The Bronsted-Lowry theory defines acids and bases based on their ability to donate, and accept, hydrogen protons. The Henderson-Hasselbalch equation builds off of those definitions to create a formula for finding the pH or concentrations of a buffer solution. Accurate buffer solutions can be used in titration or for industrial uses such as shampoo manufacturing.

According to the Bronsted-Lowry theory, an acid is any molecule capable of donating a hydrogen proton, while a base is a molecule capable of accepting the proton. Dissociation reaction of the acid, HA, results in a H^{+} that is donated and an A^{-}. This A^{-} is then called the conjugate base. The Henderson-Hasselbalch equation is built using this dissociation reaction as reworked for the acid dissociation constant.

An acid dissociation constant, denoted K_{a}, is the equilibrium point for the dissociation reaction. It's represented in the formula K_{a} = ([A^{-}][H^{+}]) / [HA], where A^{-}, H^{+}, and HA represent the respective concentrations in moles per liter. Since the Henderson-Hasselbalch equation solves for pH, the K_{a} equation needs to be reworked.

The conversion operates around the fact that pH = -log[H^{+}], meaning that this should appear in the converted equation. A -log is multiplied to both sides of the K_{a} equation for -logK_{a} = -log([A^{-}][H^{+}]) / [HA] and then logarithmic distribution converts this to -logK = -log[H^{+}] + (-log ([A^{-}] / [HA])). Using the definition of pH, and the fact that pK_{a} = -logK, it can be written pK_{a} = pH - log ([A^{-}] / [HA]). In terms of pH, that becomes pH = pK + log ([A^{-}] / [HA]).

The Henderson-Hasselbalch equation can be used by placing the known concentration of the conjugate base in for A^{-} and the known weak acid concentration in for HA. An example buffer solution might include 0.10 moles acetic acid (HC_{2}H_{3}O_{2}) and 0.45 moles acetate ion (C_{2}H_{3}O_{2}) with a pK value of 1.7 x 10^{-5}. The resulting equation: pH = -log (1.7 x 10^{-5}) + log (0.45 / 0.10) = 5.4.

Solving the Henderson-Hasselbalch equation instead for the concentration of either the acid or base can determine how much to use when creating a buffer solution. Buffers are used in titrations to determine the pH level of other acid-base pairs. They also have industrial uses wherever pH needs to be well-managed. Shampoo is kept from becoming too caustic and beer kept from spoiling due to the addition of well-calculated buffers.

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