Monday, September 10, 2007

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Henderson-Hasselbalch equation Henderson-Hasselbalch

The Henderson-Hasselbalch equation is used to calculate the pH of a buffer solution or buffer, from a pK (the acid dissociation constant) and the equilibrium concentrations of acid or base, acid or conjugate base.

pH = pK_a + \log_{10} \left ( \frac{[A^-]}{[AH]} \right )

Derivation

Suppose an acid AH with partial decoupling. The balance is:

AH + H_{2}O \leftrightharpoons A^- + H_{3}O^+

and associated dissociation constant will be:

K_{a} = \frac{[A^-][H_{3}O^+]}{[AH]}

Solving [ H 3 O +] of the constant Dissociation:

[H_{3}O^+] = \frac{K_{a}[AH]}{[A^-]}

Taking logarithms on both sides and applying the property of logarithms to a product we get:

- \log_{10} \left ( [H_{3}O^+] \right ) = - \log_{10} \left ( K_{a} \right ) - \log_{10} \left ( \frac{[AH]}{[A^-]} \right )
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E ratio:

pH = pK_{a} + \log_{10} \left ( \frac{[A^-]}{[AH]} \right )

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