Determine the Ph

Question

Determine the pH during the titration of 22.2 mL of 0.363 M acetic acid (K_a = 1.8×10^-5) by 0.329 M NaOH at the following points.

(a) Before the addition of any NaOH 

(b) After the addition of 6.10 mL of NaOH 

(c) At the half-equivalence point (the titration midpoint) 

(d) At the equivalence point 

(e) After the addition of 36.7 mL of NaOH

Answer 1

(a). Before addition of NaOH:

Ka = [H+][Ac-] / [HAc]

1.8x10^-5 = (x)(x) / 0.363 - x and assuming x is small relative to 0.363 M, it can be ignored

1.8x10^-5 = x2 / 0.363

x = [H+] = 2.56x10^-3 M (this is less than 0.7% of 0.363 M so above assumption was valid)

pH = -log [H+] = 2.59

After addition of NaOH, you are creating a BUFFER. HAc + NaOH ==> NaAc + H2O

(b). moles HAc = 22.2 ml x 1 L / 1000 ml x 0.363 mol / L = 8.06x10^-3 mols

moles NaOH added = 6.10 ml x 1 L / 1000 ml x 0.329 mol / L = 2.00x10-3 mols

moles HAc remaining = 8.06x10^-3 mol - 2.00x10^-3 mol = 6.06x10^-3 mols

moles Ac- formed = 2.00x10^-3 mols

Total volume = 22.2 ml + 6.10 ml = 28.3 ml = 0.0283 L

Final [ ]: [HAc] = 6.06x10^-3 mol/0.0283 L = 0.214 M; [Ac-] = 2.00x10^-3 mol/0.0283 L = 0.0707 M

Using Henderson Hasselbalch to find pH: pH = pKa + log [Ac] / HAc] and pKa = -log Ka = 4.74

pH = 4.74 + log (0.0707 / 0.0283) = 474 + 0.3976

pH = 5.14

(c). At 1/2 the equivalence point, pH = pKa

pH = 4.74

(d). At equivalence point, strong base + weak acid, pH will be >7. All HAc has been converted to Ac- + H2O and thus need to look at hydrolysis of Ac-.

Initial mols HAc = 8.06x10^-3 mols

Volume NaOH to reach equivalence: (0.329 mol / L) (x L) = 8.06x10^-3 mol and x = 0.0245 L

Final volume at equivalence = 0.0245 L + 0.0222 L = 0.0467 L

Final mols Ac- = 8.06x10^-3 mols

Final [Ac-] = 8.06x10^-3 mol / 0.0467 L = 0.173 M

Ac- + H2O ==> HAc + OH-

Kb = [HAc][OH-] / [Ac-] and Kb for Ac- = 1x10^-14 / 1.8x10^-5 = 5.56x10^-10

5.56x10^-10 = (x)(x) / 0.173

x = [OH-] = 9.81x10^-6 M

pOH = -log [OH-] = 5.00

pH = 14 - pOH

pH = 8.99 (greater than 7, as predicted)

(e). Try this yourself. I'm tired.