afterwards said:
I think that some of the problem is that we're talking about the pKa of a buffered solution - So the conjugate base (A-) is DMT, and the acid is DMTHCl. Therefore the pKa is
log[[DMT-][HCl+]/DMTHCl].
If I understand correctly, when 50% (moles) is DMT and 50% (moles) is HCl (neutralized by a base) the Ka [DMT][HCl]/DMTHCl = 1 and logKa = 0 and the pH is 8.68.
No, not exactly.
its 50% DMT to 50% DMT-H+, not HCl, when the pH has been adjusted to 8.68. (Assuming it will all be in solution, which it actually wont be.)
The Henderson-Hasselbalch equation [pH=pKa +log(A-/H)] is modified version of the the Ka equilibrium constant equation. But the
log[[DMT-][HCl+]/DMTHCl]=1
doesn't make sense for a few reasons.
First, DMT never exists in a state with a negative charge, and neither does HCl ever have a positive charge. DMT is a base. The Ka constant equation is for DMT is correctly written as:
Ka= [DMT][H3O+]/[DMTH+]
Understand that pH is inherent into this equation THE->> [H3O+] and from this alone, if 50% of DMTH+ dissociates, it does not equal 1.
In the henderson-hasselbalch, the the log(H+) is taken out and becomes pH on the left hand side. It is used to quickly
estimate the ratio of A- to HA for small tweaking of pH. As in when creating a buffer solution.
So log([A-]/[HA} does
NOT equal Ka. Ka is equal log([H+]) + log([A-]/[HA]) , and log[H+] happens to be pH.
and as pitubo mentioned, DMT is a base, it would make more sense intuitively to calculate the
pKb.
and it should be Kb
= [DMT-H+][OH-]/[DMT] , but in reality it is no more useful to the chemist than the pKa, so for the purposes of simplicity and standardization, the pKa is used regardless unless explicitly necessary.