Here is the hint I received on how to solve those tough pH problems I posted earlier:

Question

Both of these can be solved using the H-H and doing the algebra. The math
itself is hard to type out, but in Q1 the values of [NaA] and [HA] are
0.04805 and 0.15195.
In Q2 you will have to set up two eqn's and 2 unknowns. For eqn 1 set up the
H-H for a pH of 7.45, and for eqn 2 set up the H-H for 7.35 with moles base
= initial moles base - 0.005 and moles acid = initial moles acid + 0.005.
You will then sub your eqn 1 value for one of the unknowns into your second
expression.
I have tried to solve the question using this formula but it is clear that I have not gotten far enough. Could anyone out there please try solving this for me?

(1) You wish to make a 0.200 mol/L PIPES buffer (PIPES:
1,4-Piperazine-N,N'-bis(2-ethane-sulfonic acid), C8H18N2O6S2, pKa = 6.80) at

a
pH of 6.300. Available to you is the disodium salt of PIPES
(Na2C8H16N2O6S2),
and a 2.00 F solution of HCl. Calculate

i)the mass of the disodium salt of PIPES,

ii) the volume of HCl,

that must be added to make 500.0 mL of this buffer.

I tried to initally use the Henderson Hasselbach equation to solve for the
ratio of weak base and its conjuate acid that would be needed to make the
buffer with the desired pH but this only gets me so far. I also set up a
second equation [A-] + [HA] = .200. I have then tried to set up a balanced
equation HA + H20 in equilibrium with A- + H3O+. However, I am stuck from
there and cannot seem to figure out the changes in moles.

2.
A chemist is following a hydrolysis reaction with an enzyme. The enzyme has
an
optimal working pH range of 7.40±0.05. It is known that H+ is evolved during
the hydrolysis reaction. The chemist does a quick calculation and determines
that the reaction she is following could generate up to 0.001 moles of H+
per
100.0 mL of solution. Describe how to make up 500.0 mL of the HEPES buffer
(HEPES: 4-(2-Hydroxyethyl)piperazine-1-ethanesulfonic acid, C8H18N2O4S, pKa
=
7.55) such that the reaction mixture will maintain a pH that is within the
optimal working range of the enzyme. Among the reagents in the lab are HEPES

as
the free acid form, and a 5.695 F solution of NaOH. What mass of HEPES and
what volume of NaOH should you use?
Note: while several solutions are possible, here you are asked to calculate
the
minimum amount of HEPES that could still maintain the pH within the desired
limits.