Buffer henderson-hasselbalch equation. How do i solve if given everything except the base or acid?

Question

example: ph=3.77, pka= 3.85, acid [.10]. what will the concentration be for the base?

P.S. I can solve it without this henderson equation but I want to know how to manipulate this equation.

Answer 1

We have :
pH = pKa + log [Salt] / [ Acid]
3.77 = 3.85 + log [Salt] / 0.10
- 0.08 = log [ Salt] / 0.10
10^ -08 = [ Salt ] / 0.10
0.831 = [ Salt] / 0.10
[ Salt ] = 0.0831 M

Answer 2

The H-H equation is just the log form of the equilibrium relation. Assume a monobasic weak acid HZ and NaOH, where the conc of
NaOH<.10 M. Then, we can write:
[H+][Z-]/[HZ] = Ka.
In this situation [Z-] will equal the inital conc of the base, since it reacts with the acid to form an ionic salt. [HZ] will equal 0.1-[Z-],

Then you can solve to find out what Z- is, since
[Z-]/[0.1-Z] = Ka/[H+] or do the H-H equivalent.
Note that pH is nearly pKa, so [Z-] is about 0.5.