# What is the function of a buffer?

Sep 16, 2017

To maintain the $p H$ of a solution around a given value.....

#### Explanation:

And a buffer thus acts to RESIST gross changes in $p H$.

Now typically, a buffer consists of a weak acid, and its conjugate base in APPRECIABLE concentrations. And we can represent the acid-base behaviour by the following equilibrium:

$H A \left(a q\right) + {H}_{2} O \left(l\right) r i g h t \le f t h a r p \infty n s {H}_{3} {O}^{+} + {A}^{-}$

And as always, we can represent this by the equilibrium equation.....

${K}_{a} = \frac{\left[{H}_{3} {O}^{+}\right] \left[{A}^{-}\right]}{\left[H A \left(a q\right)\right]}$, and ${K}_{a}$ is typically measured and defined under standard conditions of $298 \cdot K$ and near one atmosphere.

And as for any equation, we can manipulate the equation by dividing, multiplying, adding to, subtracting from, provided that we do the SAME thing to BOTH sides of the equality. One thing we can do is to take ${\log}_{10}$ of BOTH sides......

And so......

${\log}_{10} {K}_{a} = {\log}_{10} \left[{H}_{3} {O}^{+}\right] + {\log}_{10} \left\{\frac{\left[{A}^{-}\right]}{\left[H A \left(a q\right)\right]}\right\}$

And on rearrangement......

${\underbrace{- {\log}_{10} \left[{H}_{3} {O}^{+}\right]}}_{p H} = {\underbrace{- {\log}_{10} {K}_{a}}}_{p {K}_{a}} + {\log}_{10} \left\{\frac{\left[{A}^{-}\right]}{\left[H A \left(a q\right)\right]}\right\}$

And thus....$p H = p {K}_{a} + {\log}_{10} \left\{\frac{\left[{A}^{-}\right]}{\left[H A\right]}\right\}$

This is a form of the buffer equation, which you will have to be able to use effectively. And this says that when $\left[{A}^{-}\right] \equiv \left[H A\right]$, $p H = p {K}_{a}$ because ${\log}_{10} \left\{\frac{\left[{A}^{-}\right]}{\left[H A\right]}\right\} = {\log}_{10} \left(1\right) = 0$.

And thus addition of LESS than stoichiometric quantities of acid or base to the solution, does not dramatically alter solution $p H$.... Biological systems are extensively buffered.