The pKa of Tris is 8.3. How to prepare 1 L of 0.1 M Tris pH 8.0 using
1 M tris
1M HCl
1M NaOH
distilled water
pH = pKa + log (base/acid) = pKa + log b/a
8.0 = 8.3 + log b/a
log b/a = -0.30
b/a = 0.501
b = 0.501*a is one equation. The second one is
a + b = 0.1 and solve these two equations simultaneously.
a = 0.0667 M
b = 0.0333 M
Start with 50 mL of 1 M tris which is 0.05 moles
...............base + H^+ --> acid
I...............0.05........0............0
add........................x.............
C..............-x..........-x...........x
E.............0.05-x........0...........x
We want 0.05-x HCl = 0.0333 moles = base
0.0500-0.0333 = x moles HCl
x moles HCl = 0.0167 = acid
So you add 50 mL of the 1 M tris base to 167 mL of the 1M HCl and dilute to 1000 mL. Can we be sure this will do it. We can calculate what we have.
50 mL x 1 M tris = 500 mmoles tris
add 167 mmoles HCl ==> leaving 500-167 = 333 mmols tris and 167 mmols acid. To add 167 mmoles HCl remember mL x M = millimoles or mL = mmoles/M = 167 mmoles/1M = 167 mL.
pH = 8.3 + log (b/a) = 8.3 + log (333/167) = 8.0 which is what you wanted.
There is another way to do it what involves much fewer calculations. It's done this way. Set i[ a 2 L beaker with a pH meter.Add 50 mL of the 1M tris base. Add some water to make about 300 or so mL of solution. With the pH meter turned on, add 1 M HCl dropwise until the pH meter reads 8.0. Add enough water to make close to 1 L of solution, then add HCl or NaOH or distilled water as need to make the final pH = 8.0. Done.