Titration & pH curves [17.3]

Titration A known concentration of base (or acid) is slowly added to a solution of acid (or base).

Titration A pH meter or indicators are used to determine when the solution has reached the equivalence point, at which the stoichiometric amount of acid equals that of base.

Titration of a Strong Acid with a Strong Base From the start of the titration to near the equivalence point, the pH goes up slowly.

Titration of a Strong Acid with a Strong Base Just before and after the equivalence point, the pH increases rapidly. At the equivalence point, moles acid = moles base, and the solution contains only water and the salt from the cation of the base and the anion of the acid.

Titration of a Strong Acid with a Strong Base As more base is added, the increase in pH again levels off.

Titration of a Weak Acid with a Strong Base Unlike in the previous case, the conjugate base of the acid affects the pH when it is formed. The pH at the equivalence point will be >7. Phenolphthalein is commonly used as an indicator in these titrations.

Titration of a Weak Acid with a Strong Base At each point below the equivalence point, the pH of the solution during titration is determined from the amounts of the acid and its conjugate base present at that particular time.

Titration Problem Solving

1. Stoichiometry problems; then 2. equilibrium problems to find pH Consider titration of 100.0 mL of 0.200 M acetic acid (Ka = 1.8 x 10-5) by 0.100 M KOH. Calculate pH after KOH has been added: 0.0 mL b. 50.0 mL c. 100.0 mL d. 150.0 mL e. 200.0 mL f. 250.0 mL Only a weak acid is present… HC2H3O2 ↔ H+ + C2H3O2 - I .200M ≈ 0 C -x +x E 0.200 –x x

b. Added OH- will react completely with the best acid present: HC2H3O2 1.8 x 10-5 = x2 0.200 x = [H+] = 1.9 x 10-3 M pH = 2.72 b. Added OH- will react completely with the best acid present: HC2H3O2 HC2H3O2 + OH- ↔ C2H3O2- + H2O I .200 M x .1000L = o.0200 moles 0.100 M x 0.050 L = 0.00500 moles ---- C -0.00500 +0.00500 E 0.0150 mols 0.00500 mols

After reaction we have a buffer solution pH = -log (1.8 x 10-5) + log (0.00500/0.150L) (0.0150 /0.150L) pH = 4.74 + (-0.477) = 4.26 c. HC2H3O2 + OH- ↔ C2H3O2- + H2O I 0.200 M x 0.1000L = 0.0200 mols 0.100 M x 0.1000L = 0.0100 moles C -0.0100 +0.0100 E 0.0100 mols pH = -log (1.8 x 10-5) + log (0.0100/0.200L) (0.0100 /0.200L) pH = 4.74

d. HC2H3O2 + OH- ↔ C2H3O2- + H2O pH = 4.74 + log (0.0150/0.0050) = 5.22 I 0.02000 0.100M x 0.150 L = 0.0150 mols C -0.0150 +0.0150 E 0.0050 0.0150

Moles of acid = moles of base pH determined by conjugate base HC2H3O2 + OH- ↔ C2H3O2 - + H2O **equivalence point Moles of acid = moles of base pH determined by conjugate base Kb = Kw/Ka Kb = 5.6 x 10-10 I 0.0200 0.100 M x 0.200 L = 0.0200 C -0.0200 +0.0200 E 0.0200 mols

C2H3O2- + H2O ↔ HC2H3O2 + OH- 5.6 x 10-10 = x2 0.0667 X= [OH-] = 6.1 x 10-6M pOH = 5.21; pH = 8.79 I 0.0200/0.300 L = 0.0667 M C -x +x E 0.0667-x x

HC2H3O2 + OH- ↔ C2H3O2 - + H2O I 0.0200 0.0250 C -0.0200 +0.0200 E 0.0050 [OH-] = 0.0050/0.350 L = 0.014 M pOH = 1.85 pH = 12.15 LR Excess reactant Since [OH-] is strong, pH is determined by excess, conjugate base effect is negligible

Titration of a Weak Acid with a Strong Base With weaker acids, the initial pH is higher and pH changes near the equivalence point are more subtle.

Titration of a Weak Base with a Strong Acid The pH at the equivalence point in these titrations is < 7. Methyl red is the indicator of choice.

Buffers Buffer exists at ½ way titration point pH is stable Buffer @ pKa value Figure: 17-08 Title: Adding a strong acid to a strong base. Caption: The shape of a pH curve for titration of a strong base with a strong acid. The pH starts out at a high value characteristic of the base and then decreases as acid is added, dropping rapidly at the equivalence point. Buffers

Weak vs. strong Buffer @ ½ way titration Equivalence point

Titrations of Polyprotic Acids In these cases there is an equivalence point for each dissociation. Also buffering at each ½ titration point.