Titration Curve Calculator

Analyze acid-base titrations, calculate pH, and determine equivalence points

Example Titrations

Understanding Titration Curves

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

What is a Titration Curve?

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.

Types of Titration Curves

1. Strong Acid - Strong Base Titration

Example: HCl titrated with NaOH

  • Initial pH: Very low (typically 1-2 for 0.1 M acid)
  • Before equivalence: Gradual pH increase, excess H⁺ present
  • At equivalence: pH = 7.0 (neutral solution of salt and water)
  • After equivalence: Rapid pH increase, excess OH⁻ present
  • pH jump: Very large (typically pH 3-11 near equivalence point)
  • Buffer region: None - no buffering capacity

pH calculation before equivalence: pH = -log[H⁺]
where [H⁺] = (C_a × V_a - C_b × V_b) / (V_a + V_b)

2. Weak Acid - Strong Base Titration

Example: CH₃COOH (acetic acid) titrated with NaOH

  • Initial pH: Higher than strong acid (typically 2.5-3.5 for 0.1 M)
  • Before equivalence: Buffer region with gradual pH increase
  • Half-equivalence point: pH = pKa (maximum buffer capacity)
  • At equivalence: pH > 7 (basic due to conjugate base hydrolysis)
  • After equivalence: pH dominated by excess strong base
  • Buffer region: Present from start to near equivalence

Henderson-Hasselbalch equation (buffer region):
pH = pKa + log([A⁻]/[HA])
At half-equivalence: pH = pKa

3. Weak Base - Strong Acid Titration

Example: NH₃ (ammonia) titrated with HCl

  • Initial pH: Basic (typically 10.5-11.5 for 0.1 M)
  • Before equivalence: Buffer region with gradual pH decrease
  • Half-equivalence point: pOH = pKb (or pH = 14 - pKb)
  • At equivalence: pH < 7 (acidic due to conjugate acid hydrolysis)
  • After equivalence: pH dominated by excess strong acid
  • Buffer region: Present from start to near equivalence

Buffer region equation:
pOH = pKb + log([BH⁺]/[B])
pH = 14 - pOH

Key Regions of a Titration Curve

Initial Point

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⁻].

Buffer Region

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.

Half-Equivalence Point

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.

Equivalence Point

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.

Beyond Equivalence

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⁺.

Endpoint vs Equivalence

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.

Worked Example: Weak Acid Titration

Problem

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).

Step 1: Determine the Region

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.

Step 2: Apply Henderson-Hasselbalch

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.

Step 3: Calculate pH

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.

Applications of Titration Curves

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Analytical Chemistry

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.

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Buffer Preparation

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.

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Pharmaceutical Analysis

Determine active ingredient concentrations in drugs, analyze formulation stability, and verify drug purity. Titration curves help optimize drug delivery systems and ensure product quality.

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Environmental Monitoring

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.

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Food Chemistry

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.

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Education & Research

Demonstrate acid-base equilibrium principles, teach pH calculations, and explore indicator selection. Titration curves are essential pedagogical tools for understanding chemical equilibria.

Problem-Solving Strategy

1

Identify the Titration Type

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.

2

Calculate Equivalence Volume

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.

3

Determine Current Region

Compare volume added to equivalence volume: before (excess analyte), at (stoichiometric), or after (excess titrant). Each region uses different calculation methods.

4

Apply Appropriate Equation

Buffer region: Henderson-Hasselbalch. Before/after equivalence: excess H⁺ or OH⁻ calculation. At equivalence: hydrolysis of conjugate acid/base (weak) or neutral (strong-strong).

Common Mistakes to Avoid

❌ Assuming Equivalence Point pH = 7

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.

❌ Forgetting to Update Total Volume

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).

❌ Using Wrong Equation for Buffer Region

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).

❌ Confusing Half-Equivalence with 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.

Quick Reference Guide

Strong Acid-Strong Base

  • • Equivalence pH = 7.0
  • • Large pH jump at equivalence
  • • No buffer region
  • • Indicators: wide range works

Weak Acid-Strong Base

  • • Equivalence pH > 7
  • • Buffer region present
  • • pH = pKa at half-equivalence
  • • Indicators: phenolphthalein

Weak Base-Strong Acid

  • • Equivalence pH < 7
  • • Buffer region present
  • • pOH = pKb at half-equivalence
  • • Indicators: methyl orange

Key Equations

  • • V_eq = C_a×V_a / C_b
  • • pH = pKa + log([A⁻]/[HA])
  • • pH + pOH = 14
  • • Ka × Kb = 1.0×10⁻¹⁴