Posted by Chris on Saturday, December 1, 2012 at 3:03pm.
The pH at the halfway point of a weak acid/srong base or weak base/strong acid is pH = pKa.
Look at the Ka expression for a weak acid.
Ka = (H^+)(A^-)/(HA).
Now solve this for H^+.
(H^+) = Ka*[(HA)/(A^-)].
When you are halfway there, the (HA) = (A^-); therefore, Ka = (H^+). If you take the -log of both sides we get
-logKa = -log(H^+).
By definition the left side is pKa and the right side is pH.
For the titration of a strong acid/strong base, there is no Ka and this rules doesn't apply.
For your example,
millimoles HF = 100 mL x 0.1 = 10 mmols initially.
Halfway there is 50 mL NaOH x 0.1 = 5 mmols.
So you have 5 mmols of the salt formed (NaF) and you have 10.0-5.0 = 5.0 millimols HF remaining. Plug those into the equation I had above and you see one is in the numerator and one in the denominator so they cancel and (H^+) = Ka.
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