pKa = pH for strong acid — strong base?

I have learnt that for a *weak acid — strong base* titration, $\mathrm{p}K\_\mathrm{a} = \mathrm{pH}$ at the half equivalence point.


However, the same conclusion is not drawn when discussing *strong acid — strong base* titrations. Why does the above only hold for weak acid — strong base and not strong acid — strong base?


Similarly, why is $\mathrm{pOH} = \mathrm{p}K\_\mathrm{b}$ at half-equivalence point only true for strong acid weak base and not for strong acid strong base?




The reason is that strong acids have $\mathrm{p}K\_\mathrm{a}$ values that are poorly known. These $\mathrm{p}K\_\mathrm{a}$s cannot be determined directly, because the exact concentration of the ions is difficult to know with precision: the electrodes do not react with the concentration of $\ce{H^+}$ or $\ce{H3O^+}$ ions. They react with the activity of $\ce{H+}$ or $\ce{H3O+}$, which may be quite different from the concentration in concentrated solutions.


So, the $\mathrm{p}K\_\mathrm{a}$ values of strong acids can only be determined indirectly, for example by extrapolation of values obtained in organic solvents, and mixtures of organic solvents plus water. This extrapolation is never precise enough.


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