# Question 998ab

Jun 4, 2015

The pH of the buffer is equal to 7.34.

You're dealing with a buffer solution that consists of a weak acid, in your case hypochlorous acid, $H C l O$, and its conjugate base, the hypochlorite ion, $C l {O}^{-}$.

Even before doing any calculations, you can predict what the pH of the solution will be relative to the value of the pKa.

You know that, at equal concentrations of weak acid and conjugate base, the pH of the solution is equal to the pKa. Since you have more acid than base present, you can predict that the pH will be smaller than the $p {K}_{a}$.

You'll need to use the Henderson-Hasselbalch equation, which looks like this

pH_"sol" = pK_a + log((["conjugate base"])/(["weak acid"]))

In your case, the pKa will be equal to

$p {K}_{a} = - \log \left({K}_{a}\right) = - \log \left(2.9 \cdot {10}^{- 8}\right) = 7.54$

The pH of your solution will thus be

pH_"sol" = 7.54 + log((0.099cancel("M"))/(0.158cancel("M")))

pH_"sol" = 7.54 - 0.203 = color(green)("7.34")#

Indeed, the pH of the solution is smaller than the $p {K}_{a}$.