I'm just thinking out loud a little to give you some ideas.
If we have an acid, and we know the partition coefficient is moles organic phase/moles aqueous phase, when the solution is pH 10 we should have mostly the salt and K should be small. At pH 2 the acid should be in the un-ionized form and K should be large. So you figure how much of each form you have and calculate Ka from that. I've never done that before and don't know if it will work.
If I have a set of data that gives the apparent partition coefficient as a function of pH, over a range of pH 2-10, how do I calculate the Ka of the compound?
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