Say I have a solution of ammonia. To the solution I add some HCl.

From the example calculations in my book they say that all the HCl will react completely with the ammonia, leaving only residual ammonia and ammonium. Then to find the pH of the solution they go through a calculation using the Henderson-Hasselbalch equation.

Are all the protons actually consumed or is this just a way of modeling the problem mathematically? I don't get why all the protons would be consumed and subsequently replenished by the partial dissociation of ammonium.

Then I tried to prove that all the H+ would be consumed if I added some HCl to an NH3 solution. I set up an equilibrium expression and using concentrations of H+ and NH3 as well as the Ka tried to prove all the H+ would be converted to NH4+. It didn't work out at all..

I am only confusing myself more. Any help is appreciated.