# Does pKa affect pH?

Dec 6, 2016

pKa is a measure of how much of the acid will ionize in water creating hydrogen ions. The more hydrogen ions in the water the lower the pH.

Dec 6, 2016

The lower (more negative) the $p {K}_{a}$, the lower (more negative) the $p H$. $p {K}_{a}$ quantifies aqueous acidity.

#### Explanation:

For the generalized acid base reaction in water, we write:

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

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

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

On rearrangement,

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

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

And thus acids with large ${K}_{a}$ values, and negative $p {K}_{a}$ values gives rise to low $p H$ solutions.