# Henderson Hasselbalch Equation

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The Henderson Hasselbalch equation is a formula that shows the relationship between the pH or pOH of a solution and the pKa or pKb of the acid or base involved in the solution. It also relates the pH or pOH to the ratio of the concentrations of the conjugate acid and base pairs in the solution. The equation can be used to calculate the pH of buffer solutions, which are solutions that resist changes in pH when small amounts of acid or base are added.

The equation was developed independently by two scientists, Lawrence Joseph Henderson and Karl Albert Hasselbalch, in the early 20th century. Henderson derived the equation in 1908 to study the bicarbonate buffer system in blood, while Hasselbalch rewrote it in logarithmic form in 1917 to make it easier to use.

The equation can be written in different ways, depending on whether the solution contains a weak acid and its conjugate base, or a weak base and its conjugate acid. The most common forms are:

$$pH = pKa + \log_{10} \frac{}{}$$

$$pOH = pKb + \log_{10} \frac{}{}$$

where:

• pH is the negative logarithm of the hydrogen ion concentration
• pOH is the negative logarithm of the hydroxide ion concentration
• pKa is the negative logarithm of the acid dissociation constant
• pKb is the negative logarithm of the base dissociation constant
• is the concentration of the conjugate base of the weak acid
• is the concentration of the weak acid
• is the concentration of the conjugate acid of the weak base
• is the concentration of the weak base

The equation can also be written in terms of molarities (M) or moles per liter (mol/L) instead of concentrations.

The Henderson Hasselbalch equation is an approximation that assumes that the concentrations of the acid and its conjugate base (or the base and its conjugate acid) do not change significantly during equilibrium. It also neglects the effect of water dissociation on the pH or pOH of the solution. Therefore, it is most accurate for dilute solutions and weak acids or bases with low dissociation constants.