[SpontaneousRxn]

So I have to solve a problem dealing with NaOH of known concentration and a weak acid.  The problem reads as follows:
You are given a sample of a pure, solid, water-soluble weak acid, known NaOH concentration solution, buret and other glassware, a balance, water, pH paper and standard solutions of pH indicators(by the way, I need to choose an indicator).
 You are to devise an experiment to estimate its approximate pKa, without using a pH meter.  There are two kinds of pH paper available - one covering the pH range 2-7 and one covering the pH range 7-13. This paper changes colors based on pH differences of one pH unit. For example, the paper that covers the lower pH range may be pink at pH 2, red at pH 3, purple at pH 4, blue at pH 5, etc.

[Borek]

How would you determine pKa USING a pH meter?

[SpontaneousRxn]

I am not sure, that was the prompt we were asked to answer

[Borek]

What is pH at 50% titration?

[SpontaneousRxn]

At the equiv point you mean?
Ma = Mb

At 1/2 equiv point
pH = pKa

[Borek]

At 1/2 equiv point
pH = pKa

That's your starting point, build experiment around this information.