Buffer problem

Hey chemistry experts, i need help with a problem. This is not homework, this is just for self studying purposes and i even have the solutions but i still cant make it.

Available are 0.10 M solution of HCl, HAc (Acetic acid), NH3 and NAOH. One wants to make a buffer solution with pH = 4.0 and with a pH = 9.0. Neither of these two buffers may be prepared by combining the solutions of acetic acid and NH3.

a) Explain the solutions of the buffer with a pH of 4.0 and calculate the volume ratio of these solutions in order to achieve the goal.

-> CH3COOH + NaOH -> <- NaCH3COO + H2O

K = 0.1 x 55.56 = 555.6

0.1 x 0.1

pK = -log (555.6) = 2.7

CH3COOH + H2O -> <- CH3COO- + H3O+

= [CH3OO-] [H3O+]

[HAc] [H20]

K = [CH3COO-] = 10^-2.7 = 19.95

[CH3O] [HAc] 10^-4

So this is apparently wrong. I think i need pKa but its not given in this problem, but it is written in the solution. The solution says the pKa is 4.74. So i did the following:

10^-4.74 = 0.18

10^-4

I think that is right. But how can i calculate this without the pKa. Here is the what is written in my solution:

pH = 4.0 to make out HAc (with pKa = 4.74) with lye

Kz = [H3O+] [Ac-]/[HAc] so [Ac-]/[HAc] = Kz / [H3O+] = 10^-4,74 / 10^-4 = 0,18

You achieve this by 118 mL mixing liquor with 18 mL (both 0.1M).

Sorry for the long post, thank you very much in advance