PH of buffer with addition of conjugate base

[Maharg]

Homework Statement

Consider 1L of a solution that is 0.100 M in acetic acid and 0.100 M in sodium acetate. What will the pH be, when 0.0900 mol of sodium acetate are added?
Ignore changes in volume.

acetic acid pka = 1.75 E-5

Homework Equations

HA --> H+ + A-
pH=pka +log A-/HA

The Attempt at a Solution

I had similar questions that I know how to do with strong acids. The difference in this question is that the added acid/base is a weak one. With the strong base addition I can just add it to A- concentration and subtract it from HA and use Henderson-Hasselbach equation.

This one I tried that but the numbers I know are off. I also tried doing ka = H+*(0.1+.009)/0.1

Solving for H+ and then using that to find out concentrations of A- and HA but the H+ number is far too small to make a difference and I'm fairly sure I can't just add the conjugate bases together.

Can someone please help.

 

[Borek]

I also tried doing ka = H+*(0.1+.009)/0.1

0.009? * instead of log? This is a correct approach, just check your math.

 

[Maharg]

0.009? * instead of log? This is a correct approach, just check your math.

Oops I made it a mistake, anyways when I did my math I just did 1.75E-5 = H+(0.19)/0.1

I get 9.2E-6

but I have no idea what to do with this. If I do it the same way as a strong base question I would add it to the A- concentration and subtract it from HA, but this value is too small to make a difference to a 0.1 M.

 

[Borek]

You have added conjugate base - so change only base concentration, acid concentration is untouched. Simply plug numbers into HH equation.