Posted by Zell on .
Suppose that 30.0 mL of 0.20 M C6H5COOH(aq) is titrated with 0.30 M KOH(aq)
(a) What is the initial pH of the 0.20 M C6H5COOH(aq)?
(b) What is the pH after the addition of 15.0 mL of 0.30 M KOH(aq)?
(c) What volume of 0.30 M KOH(aq) is required to reach halfway to the stoichiometric point?
(d) Calculate the pH at the halfway point.
(e) What volume of 0.30 M KOH(aq) is required to reach the stoichiometric point?
(f) Calculate the pH at the stoichiometric point.
attempted solutions:
C6H5COOH + H2O ==> C6H5COO^ + H3O^+
.2*.3
x +x +x
[x^2]/[.6x] = 6.5E5
.000000396.5E5xx^2=0
x=.000593 moles
30 mL = .003L
[H+] = x/.003
pH=log[H+]=0.704
Is this right? It seems really low...
b)
.20M * .03L = .006 mol C6H5COOH
.30 * .015L = .0045 mol KOH
.0045.006 = .0015 excess
pKa C6H5COOH = 4.19
.03 + .015 = .045 L total volume
pH = pka + log([base]/[acid]) =
4.19 + log( (.0045/.045)/(.006/.045)) =
4.06
Is this right?
I haven't gotten to the other parts of the problem yet.

Chemistry 
DrBob222,
Suppose that 30.0 mL of 0.20 M C6H5COOH(aq) is titrated with 0.30 M KOH(aq)
(a) What is the initial pH of the 0.20 M C6H5COOH(aq)?
(b) What is the pH after the addition of 15.0 mL of 0.30 M KOH(aq)?
(c) What volume of 0.30 M KOH(aq) is required to reach halfway to the stoichiometric point?
(d) Calculate the pH at the halfway point.
(e) What volume of 0.30 M KOH(aq) is required to reach the stoichiometric point?
(f) Calculate the pH at the stoichiometric point.
attempted solutions:
C6H5COOH + H2O ==> C6H5COO^ + H3O^+
.2*.3
x +x +x
[x^2]/[.6x] = 6.5E5
.000000396.5E5xx^2=0
x=.000593 moles
30 mL = .003L
[H+] = x/.003
pH=log[H+]=0.704
Is this right? It seems really low...
....C6H5COOH ==> C6H5COO^ + H3O^+
I.......0.20..........0..........0
C........x............x.........x
E.......0.2x.........x..........x
Ka = (H3O^+)(C6H5COO^)/(C6H5COOH)
6.5E5 = (x)(x)/(0.2x)
x = 0.00361 and pH = 2.44.
b)
.20M * .03L = .006 mol C6H5COOH
.30 * .015L = .0045 mol KOH
.0045.006 = .0015 excess
pKa C6H5COOH = 4.19
.03 + .015 = .045 L total volume
pH = pka + log([base]/[acid]) =
OK to here
4.19 + log( (.0045/.045)/(.006/.045)) =
4.06
Is this right?
What you have labeled as excess is the benzoic acid. That's (acid) = 0.0015/0.045. The salt formed (base) = 0.0045/0.045. The volumes cancel so can plug into the HH equation as
4.19 + log (0.0045/0.0015) = about 4.66 
Chemistry 
Zell,
Thanks! I see what I did wrong. I used moles instead of molarity for part a... although I am still uncertain why I should use benzoic acid as the acid in part b? I thought the reaction was C6H5COOH + KOH ==> C6H5COO + K + H2O ... and that I should use the acid and base (C6H5COOH + KOH )of the reactants for the HH equation? Am I supposed to use the base and its conjugate acid (KOH + C6H5COO)? Does this hold for all cases of the HH equation? maybe I've been doing it wrong...
Thanks again!