You are asked to make 50 mM Tris-HCl pH 7.5. The pK of Tris is 8.1.

Question

What is the concentration of the components (Tris and Tris-H+) in the
final buffer solution?

Answer 1

Use the Henderson-Hasselbalch equation. That is equation 1.
7.5 = 8.1 + log (tris)/(tris-HCl)

equation 2 is:
tris + tris-HCl = 50 mM

Solve the two equations simultaneously to determine tris and trish-H^+