[professordad]

"Calculate the pH at the equivalence point in the titration of 50.0 mL of 0.100 M HC₂H₃O₂ with 0.100 M NaOH."

("Sample exercise 17.8" in "Chemistry: The Central Science" by "Brown Lemay Bursten".)

(The solution implied that "50.0 mL" NaOH was necessary for titration)
So there are 0.00500 mol acetic acid and 0.00500 mol NaOH.  The reaction of acetic acid and NaOH is
HC₂H₃O₂ + NaOH    H₂O + NaC₂H₃O₂
After the reaction, there should be 0.00500 mol NaC₂H₃O₂, implying 0.00500 mol C₂H₃O₂^-. 

Now I would use HC₂H₃O₂    H⁺ + C₂H₃O₂^-.  But HC₂H₃O₂ has a concentration of 0 M.  So I can't use this equation..

The book said to use the reaction
"C₂H₃O₂^- (aq) + H₂O (l)    HC₂H₃O₂ (aq) + OH^- (aq)"

Later in the solution the author(s) wrote
"K_b = [HC₂H₃O₂^-][OH^-] / [C₂H₃O₂^-] = (x)(x) / (0.0500 - x)"

First, where did they get that reaction and why do they use this one over the one I mentioned?
Also, is the minus sign attached to the acetic acid concentration expression not supposed to be there?  Is it a typo?
Finally, why do you let the concentration of acetic acid be x when you already found that it was 0 M?

Thanks.

[Borek]

You are calculating pOH of the solution of conjugate base.