i need help with finding the ph of a buffer solution initially consisting of 0.0400 moles NH3 and 0.025 moles NH4^+ and 20 ml 0.75 NaOH.

Question

ka of NH+4 = 5.6 ×10^-10

Answer 1

Use the Henderson-Hasselbalch equation.

Construct an ICE chart. Add 20 mL of 0.75M (I guess that's M but you omitted the symbol) NaOH = 15 millimoles NaOH = 0.015 mols.
(Note: I simply assume the NaOH was not present initially and it was added later. That doesn't change the problem.)
..........NH4^+ + OH^- ==> NH3
initial.0.025......0.....0.0400
add..............0.015................
change..-0.015..-0.015.....+0.015
equil...0.010.....0.........0.015

Plug these numbers into the HH equation and solve for pH.