# Question ef831

Dec 26, 2017

$\text{p} {K}_{a} - 0.30$

#### Explanation:

You're dealing with a strong acid-conjugate base buffer here, so right from the start, you know that you can use the Henderson - Hasselbalch equation to find its $\text{pH}$.

"pH" = "p"K_a + log( (["conjugate base"])/(["weak acid"]))

Here

$\text{p} {K}_{a} = - \log \left({K}_{a}\right)$

with ${K}_{a}$ being the acid dissociation constant of the weak acid.

In your case, acetic acid, $\text{CH"_3"COOH}$, is the weak acid and the acetate anion, ${\text{CH"_3"COO}}^{-}$, is its conjugate base. The acetate anions are delivered to the solution by the soluble sodium acetate in a $1 : 1$ mole ratio, so you know that you have

["CH"_3"COO"^(-)] = "0.125 M"

Notice that your solution contains more weak acid than conjugate base. This tells you that the $\text{pH}$ of the solution will be lower than the $\text{p} {K}_{a}$ of the weak acid.

This is the case becase at equal concentrations of weak acid and conjugate base, the $\text{pH}$ of the solution is actually equal to the $\text{p} {K}_{a}$ of the weak acid. So if you have more acid than conjugate, the $\text{pH}$ of the solution will fall below* the $\text{p} {K}_{a}$ of the weak acid.

Plug in your values to find

"pH"= "p"K_a + log (( 0.125 color(red)(cancel(color(black)("M"))))/(0.25color(red)(cancel(color(black)("M")))))#

$\text{pH" = "p} {K}_{a} + \log \left(\frac{1}{2}\right)$

This is equivalent to

$\text{pH" = "p} {K}_{a} + {\overbrace{\log \left(1\right)}}^{\textcolor{b l u e}{= 0}} - \log \left(2\right)$

$\text{pH" = "p} {K}_{a} - \log \left(2\right)$

$\text{pH" = "p} {K}_{a} - 0.30$

Now all you have to do is to use the $\text{p} {K}_{a}$ of acetic acid, which you can find listed here, to find the $\text{pH}$ of the solution. You should round the answer to two decimal places, the number of sig figs you have for the concentration of acetic acid.

Notice that you have

$\text{pH" = "p"K_a - 0.30 " " < " " "p} {K}_{a}$

which is consistent with the fact that the buffer contains more acetic acid than acetate anions.