Acid-Base Titrations: Calculations and Interpretation

Acid-Base Titrations

Overview of Acid-Base Titrations

An acid-base titration is a quantitative analytical procedure used to determine the concentration of an acid or base by reacting it with a standard solution of base or acid. The process involves the gradual addition of a titrant to a solution of analyte until the reaction reaches completion, which is often indicated by a color change (endpoint) or a measured pH value.

• Titrant: The solution of known concentration added from a burette.

• Analyte: The solution of unknown concentration being analyzed.

• Equivalence Point: The point at which stoichiometrically equivalent amounts of acid and base have reacted.

• Buffer Region: The range where the solution resists changes in pH, typically before the equivalence point in weak acid/base titrations.

• pH = pKa Point: The point in a weak acid-strong base titration where the concentrations of acid and conjugate base are equal.

Calculating pH During a Titration

The pH of the solution changes as titrant is added. Calculations depend on the type of acid and base involved and the stage of the titration:

1. Initial pH: Before any titrant is added, calculate the pH of the analyte solution.

2. Before Equivalence Point: Calculate the pH after adding a certain volume of titrant but before the equivalence point is reached.

3. At Equivalence Point: Calculate the pH when stoichiometric amounts of acid and base have reacted.

4. After Equivalence Point: Calculate the pH after excess titrant has been added.

Strong Acid–Strong Base Titrations

Key Features

• Both acid and base dissociate completely in water.

• pH changes rapidly near the equivalence point.

• At equivalence, the solution is neutral (pH ≈ 7 at 25°C).

Example Calculation Steps

1. Initial pH: For a strong acid, use $pH = -\log [H^+]$.

2. Before Equivalence: Subtract moles of OH− added from initial moles of H+, then calculate new [H+].

3. At Equivalence: All H+ neutralized; pH = 7.

4. After Equivalence: Excess OH− determines pH: $pOH = -\log [OH^-]$, $pH = 14 - pOH$.

Weak Acid–Strong Base (or Weak Base–Strong Acid) Titrations

Key Features

• Weak acids/bases only partially ionize; equilibrium calculations are required.

• Buffer region exists before equivalence point.

• At equivalence, the solution contains the conjugate base/acid, so pH ≠ 7.

• At the point where $[HA] = [A^-]$, $pH = pK_a$ (for weak acid titration).

Example Calculation Steps

1. Initial pH: Use the weak acid/base equilibrium: $K_a = \frac{[H^+][A^-]}{[HA]}$.

2. Buffer Region (Before Equivalence): Use the Henderson-Hasselbalch equation: $pH = pK_a + \log \left( \frac{[A^-]}{[HA]} \right)$.

3. At Equivalence: All weak acid/base converted to conjugate; calculate pH from hydrolysis of conjugate base/acid.

4. After Equivalence: Excess strong base/acid determines pH.

Polyprotic Acid Titrations

Key Features

• Polyprotic acids can donate more than one proton (e.g., H2SO4, H3PO4).

• Multiple equivalence points, one for each ionizable proton.

• Each equivalence point corresponds to the neutralization of one proton.

Example Calculation Steps

1. First Equivalence Point: Calculate as for a monoprotic acid.

2. Second Equivalence Point: Repeat calculation for the next proton, considering the new acid species formed.

3. Buffer Regions: Exist between equivalence points; use Henderson-Hasselbalch equation for each step.

Summary Table: Titration Features

Type of Titration	Initial pH Calculation	pH at Equivalence	Buffer Region	pH = pKa Point
Strong Acid–Strong Base	$pH = -\log [H^+]$	7 (neutral)	No	Not applicable
Weak Acid–Strong Base	ICE table, $K_a$ expression	>7 (basic)	Yes	Yes, when $[HA] = [A^-]$
Polyprotic Acid	ICE table for first proton	Multiple equivalence points	Yes, between equivalence points	Yes, for each step

Additional info:

• For weak base–strong acid titrations, similar steps apply, but calculations are based on base hydrolysis and $K_b$ values.

• Indicators are chosen based on the expected pH at the equivalence point.