When it says that the PH = pKa at the half equivalence point, is it saying that the acid species (ie HCl) has that pKa or that the base species (Cl-) has that pKa as well?
It's still pKa for titrating a base when we're dealing with pH. Only if they specify pOH, will it be pKb.
Right. So when you're titrating acetic acid with a strong base, you are doing something like:
CH3COOH + NaOH ---> CH3COO- + H2O
At the half equivalence point, you've used up half of the original acetic acid, and the concentrations of the acetic acid and its conjugate base are equal.
You now have an equilibrium in the solution where Acetic acid and acetate are both reacting with water to create each other.
CH3COOH + H2O <----> CH3COO- + H3O+
The Ka for this equation is [CH3COO-][H3O+]/[CH3COOH].
At the half-equivalance point, [CH3COO-] is equal to [CH3COOH], so they cancel out of the equation and Ka = [H3O+]
take the negative log of both sides and you have pKa = pH.
You could do the exact same problem with pKb, if you REALLY wanted:
If we write our equilibrium as:
CH3COO- + H2O <----> CH3COOH + OH-
then Kb = [CH3COOH][OH-]/[CH3COO-]
again at the half-equivalence point, the concentrations are the same and pKb = pOH.
Understand that the pKa and pKb terms refer to the ratio of both conjugates as well as the H3O+ or OH- concentration. So the pKa isn't a property of ONLY the conjugate acid or base, it's a property shared by both.
Kb just refers to the ratio of products you would find in a solution if you dumped a bunch of conjugate base into water (e.g. NaCH3COO- ) while Ka refers to the ratio of products you would find in a solution if you dumped a bunch of conjugate acid into water (e.g. CH3COOH). They're two sides of the same coin.
If you're titrating a weak base with a strong acid, you might have an equation like:
NH3 + HCl ---> NH4+ + Cl-
So before completion, you have an equilibrium that looks like:
NH3 + H2O <----> NH4+ + OH-
and you can solve this using the pKb....
but you can re-write the equilibrium as:
NH4+ + H2O <----> NH3 + H3O+
and solve it using the pKa. Once again, the pKa and pKb BOTH refer to BOTH the concentrations of NH4+ and NH3.
All that said, if this comes up on the MCAT it will probably be a conceptual question like:
Aqueous ammonia (pKb 4.75) is titrated with HCl. At the half-equivalence point:
A. pH is < 4
B. pH is > 4 and < 7
C. pH is = 7
D. pH is > 7
when the two species are equal in concentration, pH = pKa and pOH = pKb. the answer is D.