Acid-Base Titration Notes

Acid-Base Titrations

• A titration is a method of quantitative analysis based on a reaction of known stoichiometry.
• It involves determining the volume of a solution needed to react exactly with a known amount of another substance (acid or base).

Methodology of Acid-Base Titrations

• Titration Defined: A process to find the volume of a solution containing an amount of acid (or base) that reacts exactly with a known amount of base (or acid).
• Example Reaction: Determining the mass of oxalic acid ($H<em>2C</em>2O_4$) in an impure sample by titration with a strong base.
  • Reaction: $H<em>2C</em>2O<em>4(aq) + 2OH^-(aq) \rightarrow C</em>2O<em>4^{2-}(aq) + 2H</em>2O(l)$

Determining Mass of Oxalic Acid

• Procedure:
  • Accurately measure the mass of the impure oxalic acid sample.
  • Dissolve the sample in water.
  • Add small increments of a sodium hydroxide (NaOH) solution of known concentration.
• Equivalence Point: The point at which the amount of added NaOH solution is just enough to react with all the oxalic acid present.
  • $H<em>2C</em>2O<em>4(aq) + 2OH^-(aq) \rightarrow C</em>2O<em>4^{2-}(aq) + 2H</em>2O(l)$

The Equivalence Point

• Definition: Occurs when acid or base has been titrated with an equivalent amount of the corresponding species.
• Strong Acid and Base Titration:
  • Results in a neutral solution at a pH of 7.0.
• Other Combinations:
  • The pH at equivalence is not always 7.
  • Strong acid + weak base: pH < 7.
  • Strong base + weak acid: pH > 7.
• Importance of Titration:
  • One of the most important ways of determining the concentration of acid or base in a solution.

Strong Acid - Strong Base Titration (HCl with NaOH)

• Initial State:
  • Solution is 0.1 M HCl, so pH = 1.
• As NaOH is Added:
  • The amount of HCl decreases.
  • The remaining HCl is in an ever-increasing volume.
  • The pH slowly increases.
• Just Before Equivalence Point:
  • The solution is still quite acidic (e.g., at 49 mL, pH = 3).
• Equivalence Point:
  • The midpoint of the vertical section of the titration curve.
  • The pH rises very rapidly around this point (e.g., 8 pH units between 49 and 50 mL).

Equivalence Point in Strong Acid-Strong Base Titration

• pH at Equivalence Point:
  • pH = 7.0 in titration of a strong acid with a strong base.
• pH Before Equivalence Point:
  • Calculated from the amount of unreacted acid.
• Immediately After Equivalence Point:
  • Addition of a small amount of base causes a dramatic increase in pH.
  • Essentially adding a strong base to water.
• After More Base Added:
  • The rate of increase decreases.
• Reason for Rapid Change at Equivalence Point:
  • At the equivalence point, the pH is neutral.
  • Adding a relatively concentrated base increases the base concentration by orders of magnitude, causing sharp increases in pH.
  • After a few drops, the curve levels out because the ion concentration is only doubling or adding to the existing magnitude instead of changing the order of magnitude.

Weak Acid - Strong Base Titration (CH3COOH with NaOH)

• Initial pH:
  • Found from the acid concentration and the acid $pK_a$.
• At the Equivalence Point:
  • Acetic acid and NaOH have been consumed.
  • The pH is controlled by the acetate ion (conjugate base).
• At Half Equivalence Point:
  • Half of the acid has been neutralized.
  • $[CH<em>3COOH] = [CH</em>3COO^-]$ ($CH_3COO^-Na^+$ 100% dissociates).
  • $pH = pK_a$.
  • $pK_a$ of the acid can be determined.
• Slow pH Change (0-90 mL):
  • The solution is buffered (buffer region).
• Above Equivalence Point:
  • pH rises sharply.
  • pH > 7 at the equivalence point for a weak acid with a strong base.
  • The pH can be calculated using $K_b$ of the conjugate base.
  • $K<em>a = \frac{[H</em>3O^+][conjugate \ base]}{[acid]}$
• $K<em>b = \frac{K</em>w}{K_a}$

Titration of Polyprotic Weak Acids with Strong Base (H2C2O4 with NaOH)

• Initial pH:
  • Comes from the acid concentration and $pK_{a1}$.
• First Rise (around 100 mL):
  • The first H has been titrated.
  • $HC<em>2O</em>4^-$ controls the pH (conjugate base).
• Second Rise:
  • When the 2nd H is titrated, the pH rises more sharply.
  • $C<em>2O</em>4^{2-}$ controls the pH (conjugate base).
  • $C<em>2O</em>4^{2-} + H<em>2O \rightarrow HC</em>2O_4^- + OH^-$
  • $K_b = 1.6 \times 10^{-10}$
  • pH = 8.5 ($K<em>{a1} = 5.9 \times 10^{-2}$, $K</em>{a2} = 5.9 \times 10^{-5}$).

Titration of Diprotic Weak Acids

• If $K<em>{a1} >> K</em>{a2}$, the most acidic proton is removed from nearly all molecules before the second one is removed.
• Prior to the first equivalence point, the solution is a buffer solution, and when the volume of NaOH solution is exactly half that needed to reach the first equivalence point, $pH = pK_{a1}$.
• Between the first and second equivalence points, the solution is a buffer solution, and when the volume added is midway between the first and second equivalence points, $pH = pK_{a2}$.

Weak Base - Strong Acid Titration (NH3 + HCl)

• Initial pH:
  • A function of the base concentration and its $pK<em>a$ (or $pK</em>b$).
• At the Half Equivalence Point:
  • Half of the $NH<em>3$ has been converted to $NH</em>4^+Cl^-$.
  • $[NH<em>4^+] = [NH</em>4^+Cl^-]$.
  • $pH = pK_a$.
• As More HCl Is Added:
  • The pH falls slowly due to the buffer effect.
• At the Equivalence Point:
  • pH of the solution is due to the weakly acidic $NH_4^+(aq)$ ions, and the pH is about 5.
• As More HCl Is Added:
  • $NH<em>4^+Cl^-$ is formed, and the pH falls due to the dissociation of $NH</em>4^+$.
  • $K<em>a = \frac{[H</em>3O^+][conjugate \ base]}{[acid]}$

Biochemical Acid-Base Speciation

• Importance of pH Maintenance:
  • Maintaining pH in cellular fluids of living organisms is vital because enzyme activity is influenced by pH.
• Protection Against pH Changes:
  • The main protection against harmful pH changes in cells is provided by buffers.
• pH Range:
  • In most cells, the pH is maintained between 6.9 and 7.4 through the action of phosphate ($H<em>2PO</em>4^-/HPO<em>4^{2-}$) and carbonate ($H</em>2CO<em>3/HCO</em>3^-$) buffers.
• Effect of CO2:
  • Just as increasing $CO<em>2(g)$ in the atmosphere causes acidification of seawater, increased $CO</em>2(g)$ concentration in the lungs can affect blood pH.