First, you transposed 3.16E-5 to 3.61E-5 to come up with pKa = 4.44. It won't change that much but pKa is 4.5 using 3.16E-5 for Ka.
Then working with millimoles, x/(107-x) = 0.347 and x = about 27.5 millimols. That isn't that far from you 30.4 but probably far enough that the key counted it wrong. I think all you need to do is to adjust the pKa value.
Strong base is dissolved in 535 mL of 0.200 M weak acid (Ka = 3.16 × 10-5) to make a buffer with a pH of 4.04. Assume that the volume remains constant when the base is added.
HA (aq)+ OH^-(aq) -> H2O(l) + A^-(aq)
Calculate the pKa value of the acid and determine the number of moles of acid initially present.
When the reaction is complete, what is the concentration ratio of conjugate base to acid?
How many moles of strong base were initially added?
For the first question, I got:
pKa: 4.44
mol HA: 0.107
Which the system says is ok, but for the second and third question I got:
[A^-]/[HA]= 0.3981
mol OH^-: 0.03046
I don't know what is wrong, I am doing this:
pH = pKa + log ([A^-]/[HA])
4.04 = 4.44 + log ([A^-]/[HA])
-0.4 = log ([A^-]/[HA])
inv log (-.4) = ([A^-]/[HA])
0.39810 = ([A^-]/[HA])
And then
0.39810 = ([A^-]/[HA])
x / (0.107 - x) = 0.39810
x= 0.0304
3 answers
Many thanks for showing your work. It makes it easy to catch mistakes like this.
Thanks you!!