Question

Write Henderson - Hasselbalch equation?

Answer 1

The Henderson–Hasselbach equation describes the derivation of $pH$ as a measure of acidity (using $pKa$, the negative log of the acid dissociation constant) in biological and chemical systems.

Derivation of henderson-hasselbalch equation:-

In general, the equilibrium established in a solution by a weak acid $HA$ is

$HA\left(aq\right)\to H^{+}\left(aq\right)+A^{-}$

According to the law of dissociation, Ka, which is the acid dissociation constant, is given by

$Ka=\frac{[H+(aq\left)\right][A-]}{\left[HA\right]}$

where:

$\left[A^{-}\right]$ is molar concentration of the conjugate base.

$\left[HA\right]$ is molar concentration of the acid.If we rearrange the equation to make $H^{+}$ the subject of the equation, that gives us

$\left[H^{+}\right]=\frac{Ka\left[HA\right]}{[A-]}$

If we take the negative logarithm on both sides:

$-log[H+]=\frac{-logKa\left[HA\right]}{[A-]}$

You should also remember that $pH=-log[H+]$ and that $pKa=-logKa$. Substituting those in gives us:

$pH=pKa-\frac{log\left[HA\right]}{[A-]}$

We flip the acid/conjugate base to get rid of the negative sign:

$pH=pKa+\frac{log[A-]}{\left[HA\right]}$ or

$pH=pKa+\frac{log[conjugate-base]}{\left[acid\right]}$ or

$pH=pKa+\frac{log\left[salt\right]}{\left[acid\right]}$ [Henderson-Hasselbalch equation]