🧪 Titration Calculator – Acid-Base Chemistry Made Easy
Titration is one of the most fundamental quantitative techniques in analytical chemistry. By carefully adding a reagent of known concentration (the titrant) to a solution of unknown composition (the analyte) until the reaction reaches completion, chemists can determine concentrations, verify purity, and study reaction stoichiometry with remarkable precision. This calculator automates every stage of that process — from finding an unknown concentration to generating a complete pH curve.
What Is a Titration?
In an acid-base titration, an acid and a base react to form water and a salt. The reaction continues until all of one species is consumed — a point called the equivalence point. In practice, a pH indicator or a pH meter signals when the equivalence point has been reached, allowing the experimenter to record the exact volume of titrant used and calculate the unknown concentration.
The fundamental relationship governing all titrations is the neutralisation equation:
C₁ × V₁ × n₁ = C₂ × V₂ × n₂where C is molar concentration (mol/L), V is volume (L), and n is the n-factor (number of replaceable H⁺ or OH⁻ per formula unit). For a simple 1:1 acid-base pair this simplifies to the familiar C₁V₁ = C₂V₂.
The Four Calculation Modes
Mode 1 – Find Unknown Concentration
This is the most common titration task in a teaching laboratory. You know the concentration of the titrant (C₁) and have recorded the volumes V₁ and V₂. The calculator rearranges the neutralisation equation to give:
C₂ = (C₁ × V₁ × n₁) / (V₂ × n₂)Example: 0.1 mol/L NaOH (V₁ = 22.50 mL) neutralises 25.00 mL of HCl. C₂ = (0.1 × 22.50) / 25.00 = 0.090 mol/L HCl.
Mode 2 – Equivalence Point Volume
If you know both concentrations, you can predict exactly how much titrant is required to reach the equivalence point before performing the experiment — useful for planning the experiment and choosing an appropriate burette range:
V_eq = (C₂ × V₂ × n₂) / (C₁ × n₁)Mode 3 – pH at Any Point
The pH of the solution changes continuously as titrant is added. This mode calculates the exact pH at a specified titrant volume. Four situations are handled automatically:
| Region | Strong Acid + Strong Base | Weak Acid + Strong Base |
|---|---|---|
| Before Eq | Excess [H⁺] or [OH⁻] directly | Henderson–Hasselbalch: pH = pKa + log([A⁻]/[HA]) |
| At Eq | pH = 7.00 (25 °C) | Conjugate base hydrolysis: [OH⁻] = √(Kb × C_salt) |
| After Eq | Excess [OH⁻] or [H⁺] | Excess strong base dominates |
| Half-Eq | — | pH = pKa (Henderson–Hasselbalch simplifies) |
Mode 4 – Full Titration Curve
This mode sweeps through 150 data points from 0 mL to 2.2 × V_eq, computing the pH at each step to produce the characteristic S-shaped titration curve. Key landmarks are automatically identified and annotated:
- Start (V₁ = 0) — Initial pH of the pure analyte solution.
- Half-equivalence point — For weak acid/base systems, pH = pKa. This is the point of maximum buffer capacity.
- Equivalence point — The inflection point (steepest part of the S-curve) where all analyte has been neutralised.
The curve for a strong acid + strong base shows a sharp near-vertical jump near pH 7 at the equivalence point. For a weak acid + strong base, the jump is less steep, begins above pH 7 at the equivalence point, and shows a clear buffer plateau in the middle section.
pH Indicators
Common acid-base indicators change colour over a pH transition range that must include the equivalence point of the titration. The indicator overlay on the curve lets you verify whether your chosen indicator is appropriate:
| Indicator | Transition pH Range | Best Used For |
|---|---|---|
| Methyl Orange | 3.1 – 4.4 | Strong base titrating strong acid |
| Methyl Red | 4.4 – 6.2 | Strong base titrating weak acid (low pKa) |
| Bromothymol Blue | 6.0 – 7.6 | Strong acid + strong base |
| Phenolphthalein | 8.2 – 10.0 | Weak acid + strong base |
| Alizarin Yellow | 10.1 – 12.0 | Very weak acid + strong base |
The Henderson–Hasselbalch Equation in Titrations
During a weak acid + strong base titration, the solution becomes a buffer mixture between the original weak acid (HA) and its conjugate base (A⁻) formed by neutralisation. In this buffer region the pH follows:
pH = pKa + log₁₀([A⁻] / [HA])Because volumes cancel in the ratio, this simplifies to pH = pKa + log₁₀(n_base / n_acid_remaining). At the half-equivalence point, equal moles of HA and A⁻ are present, the ratio equals 1, its logarithm is 0, and therefore pH = pKa — a straightforward experimental route to measuring an acid's dissociation constant.
Temperature Effects
Water's ionic product Kw varies significantly with temperature: from approximately 1.1 × 10⁻¹⁵ at 0 °C to 1.0 × 10⁻¹⁴ at 25 °C and ~2.4 × 10⁻¹⁴ at 37 °C. The calculator uses the empirical fit pKw ≈ 14.94 − 0.0135 × T(°C) to adjust all equilibrium calculations accordingly. At 37 °C, the neutral pH is ~6.81, not 7.00.
Accuracy and Limitations
All calculations assume ideal dilute solutions with activity coefficients of 1.0. For highly concentrated solutions (>0.1 mol/L), ionic-strength corrections may be needed. The Henderson–Hasselbalch approximation is most accurate when the [A⁻]/[HA] ratio is between 0.1 and 10 (within ±1 pH unit of pKa). Edge cases such as very dilute solutions (below ~10⁻⁶ mol/L) are handled using the full quadratic expression that includes water's own autoionisation contribution.