A solution of a weak acid (.025M, 200ml) is mixed with a solution of NaOH ( 0.015M, 150ml). The equilibrium pH is 5.51. What is the Ka of the weak acid?

Use the Henderson-Hasselbalch equation. You SHOULD use M for acid and base BUT you can use a shortcut and save some time by using mols. However, make sure your prof will allow you to do take that shortcut.

mols acid = M x L = 0.025 x 0.2 = ?
mols base = 0.015 x 0.150 = ?

Substitute into the H-H equation and solve for pKa. Convert to Ka.