Calculating hydrogen ion concentration after a pH change in a buffer solution.?

I'm trying to do this homework problem, but am confused on what steps to take. I know I need the Henderson-Hasselbalch equation at some point, but don't know what steps to take to get there:

The first two parts I have done:

A) What is the pH of a 2.0 molar solution of acetic acid? Ka = 1.8 x 10^-5

I found that to be 2.22 (checked it and it's right)

B) A buffer solution is prepared by adding 0.10 liter of 2.0 molar acetic acid solution to 0.1 liter of a 1.0 molar sodium hydroxide solution. Compute the hydrogen ion concentration of the buffer solution.

I got that and it's 1.8 x 10^-5, the same value as Ka. Checked it and it's right.

Here's the part I'm stuck on:

C) Suppose that a 0.10 liter of 0.50 molar hydrochloric acid is added to 0.040 liter of the buffer prepared in B). Comput the hydrogen ion concentration of the resulting solution.

?Where do I start? I thought maybe with NaOH + H+ = H20 + Na+ but I'm not sure...

Any good chemists know? Thanks.

Answer:
Look at the ions present in the solution when you add the HCl. There are those Na(+) ions, OH(-) ions, H(+) ions and acetate ions.

The OH(-) will come and react with H(+), this is neutralization as if acetic acid wasn't there. This is because HCl is a much stronger acid than acetic acid.

Conc of NaOH in new solution : 0.02 moles
Conc of HCl in new solution : 0.05 moles

So HCl will neutralize NaOH completely and 0.03 moles of it will be left over. This will ionize completely in the 0.140 L solution.

(H+) concentration will be around 0.21Molar approximately. Again, as I have said, in presence of HCl, acetic acid won't have a much role to play.

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