Analyze acid-base titrations, calculate pH, and determine equivalence points
Strong Acid-Strong Base: Sharp equivalence point at pH 7, large pH jump
Weak Acid-Strong Base: Equivalence point > 7, buffer region present, pH = pKa at half-equivalence
Weak Base-Strong Acid: Equivalence point < 7, buffer region present, pOH = pKb at half-equivalence
Buffer Region: Resists pH changes, uses Henderson-Hasselbalch equation
A titration curve is a graphical representation of pH (y-axis) versus volume of titrant added (x-axis) during an acid-base titration. It provides crucial information about the equivalence point, buffer regions, and the nature of the acid-base reaction.
The shape of the titration curve depends on the strength of the acid and base being titrated. Strong acid-strong base titrations show sharp pH changes at the equivalence point, while weak acid or weak base titrations exhibit buffer regions and less dramatic pH transitions.
Example: HCl titrated with NaOH
pH calculation before equivalence: pH = -log[H⁺]
where [H⁺] = (C_a × V_a - C_b × V_b) / (V_a + V_b)
Example: CH₃COOH (acetic acid) titrated with NaOH
Henderson-Hasselbalch equation (buffer region):
pH = pKa + log([A⁻]/[HA])
At half-equivalence: pH = pKa
Example: NH₃ (ammonia) titrated with HCl
Buffer region equation:
pOH = pKb + log([BH⁺]/[B])
pH = 14 - pOH
pH determined solely by the analyte (acid or base being titrated). For weak acids/bases, use equilibrium calculations. For strong acids/bases, pH = -log[H⁺] or pH = 14 + log[OH⁻].
Present only in weak acid/base titrations. Both the weak acid/base and its conjugate form are present, creating a buffer solution that resists pH changes. Use Henderson-Hasselbalch equation.
Occurs when exactly half the titrant needed to reach equivalence has been added. For weak acid titrations: pH = pKa. For weak base titrations: pOH = pKb. This is the point of maximum buffer capacity.
Moles of acid equal moles of base. pH depends on the salt formed: pH = 7 for strong-strong, pH > 7 for weak acid-strong base, pH < 7 for weak base-strong acid. This is where the largest pH change occurs per drop of titrant.
pH determined by excess titrant (strong base or strong acid). The solution is no longer buffered, and pH is calculated from the concentration of excess OH⁻ or H⁺.
The endpoint (indicator color change) should match the equivalence point (stoichiometric point). Indicator selection depends on the pH at equivalence: phenolphthalein for weak acid titrations, methyl orange for weak base titrations.
Calculate the pH when 25.0 mL of 0.100 M NaOH is added to 50.0 mL of 0.100 M acetic acid (CH₃COOH, Ka = 1.8 × 10⁻⁵, pKa = 4.74).
Equivalence volume = (C_acid × V_acid) / C_base = (0.100 × 50.0) / 0.100 = 50.0 mL
Since 25.0 mL is exactly half of 50.0 mL, we are at the half-equivalence point.
Moles CH₃COOH initially = 0.100 M × 0.0500 L = 0.00500 mol
Moles NaOH added = 0.100 M × 0.0250 L = 0.00250 mol
After reaction:
Moles CH₃COOH remaining = 0.00500 - 0.00250 = 0.00250 mol
Moles CH₃COO⁻ formed = 0.00250 mol
At half-equivalence, [HA] = [A⁻], so the log term equals zero.
pH = pKa + log([CH₃COO⁻]/[CH₃COOH])
pH = 4.74 + log(1)
pH = 4.74 + 0
pH = 4.74
This confirms the principle that at half-equivalence, pH = pKa for weak acid titrations.
Determine unknown concentrations through standardization, analyze mixtures of acids or bases, and validate purity of chemical samples. Titration is a fundamental quantitative technique in analytical laboratories.
Design buffer solutions by identifying the buffer region on titration curves. Determine the optimal ratio of weak acid to conjugate base for desired pH and buffer capacity. Critical for biochemical applications.
Determine active ingredient concentrations in drugs, analyze formulation stability, and verify drug purity. Titration curves help optimize drug delivery systems and ensure product quality.
Measure water acidity/alkalinity, analyze soil pH profiles, and monitor industrial waste streams. Titration provides accurate pH data for environmental compliance and ecosystem health assessment.
Determine acidity in beverages, vinegar strength, citric acid content in fruits, and dairy product quality. Titration ensures food safety standards and quality control in production.
Demonstrate acid-base equilibrium principles, teach pH calculations, and explore indicator selection. Titration curves are essential pedagogical tools for understanding chemical equilibria.
Determine if you have strong acid-strong base, weak acid-strong base, or weak base-strong acid. This dictates which equations to use and what pH to expect at equivalence.
Use stoichiometry: V_eq = (C_analyte × V_analyte) / C_titrant. This is the reference point for determining which region of the curve you're in.
Compare volume added to equivalence volume: before (excess analyte), at (stoichiometric), or after (excess titrant). Each region uses different calculation methods.
Buffer region: Henderson-Hasselbalch. Before/after equivalence: excess H⁺ or OH⁻ calculation. At equivalence: hydrolysis of conjugate acid/base (weak) or neutral (strong-strong).
Only true for strong acid-strong base titrations. Weak acid titrations have pH > 7 at equivalence (basic conjugate base). Weak base titrations have pH < 7 (acidic conjugate acid).
✓ Always consider the salt formed at equivalence and whether it hydrolyzes.
Concentrations change as titrant is added because the total volume increases. Always use V_total = V_initial + V_added when calculating concentrations.
✓ Account for dilution: [H⁺] or [OH⁻] = moles / (V_a + V_b).
Henderson-Hasselbalch only applies when both weak acid and conjugate base (or weak base and conjugate acid) are present in significant amounts.
✓ Use H-H equation only in the buffer region (between start and near equivalence).
Half-equivalence (V = V_eq/2) is where pH = pKa for weak acids. Equivalence (V = V_eq) is where moles acid = moles base. These are different points with different pH values.
✓ Half-equivalence: maximum buffer capacity, pH = pKa. Equivalence: all acid converted to conjugate base.