Perform acid-base titration calculations using Ma x Va = Mb x Vb. Find the unknown concentration or volume at the equivalence point for monoprotic and polyprotic reactions.
Titration is the classical method of determining the concentration of an unknown solution by reacting it with a known one. Drip a standard solution (the "titrant") from a burette into a measured volume of the unknown solution until a color change or pH indicator marks the "endpoint" — the point where the reactants are stoichiometrically balanced. From the volume added and the concentration of the titrant, the unknown concentration follows directly.
The equation behind titration is just stoichiometric bookkeeping: moles of acid = moles of base at the equivalence point (for monoprotic systems), or generalized to nₐ × Mₐ × Vₐ = n_b × M_b × V_b for polyprotic systems where one acid molecule donates n protons (or one base accepts n protons). This calculator handles both cases — enter what you know, pick what to solve for, and you get the missing variable.
Titration is one of the oldest quantitative chemistry techniques, going back to the 1700s. It remains the standard method for measuring acidity (vinegar, wine, pool water), drug content in pharmaceuticals, water hardness, alkalinity in soils, and many other applications. Modern automated titrators do the burette-and-indicator dance with electrodes and software, but the underlying math is unchanged.
**Scenario:** Standardize a NaOH solution by titrating against 0.5024 g of potassium hydrogen phthalate (KHP, 204.22 g/mol, monoprotic). Endpoint reached at 27.45 mL of NaOH. **Calculation:** Moles KHP = 0.5024 / 204.22 = 0.002460 mol. At equivalence: moles NaOH = 0.002460 mol. NaOH molarity = 0.002460 / 0.02745 L = 0.0896 M. **Result:** NaOH solution is 0.0896 M (compared to nominal 0.10 M target — the solution is slightly less concentrated, possibly due to CO₂ absorption during storage). KHP is the standard "primary standard" because it's easy to obtain pure, stable, non-hygroscopic, and exactly monoprotic.
**Scenario:** Titrate 10.0 mL of household vinegar with 0.10 M NaOH. Phenolphthalein endpoint at 41.7 mL. Acetic acid is monoprotic. What's the acetic acid concentration? **Calculation:** Mₐ = (n_b × M_b × V_b) / (nₐ × Vₐ) = (1 × 0.10 × 41.7) / (1 × 10.0) = 0.417 M. To convert to %: 0.417 mol/L × 60.05 g/mol = 25.0 g/L = 2.5 g per 100 mL ≈ 2.5% (w/v) acetic acid. **Result:** This vinegar is 2.5% acetic acid by volume. Commercial labels typically say "5% acidity" which means weight/volume — this sample is a bit weak, possibly diluted with water or near expiration. Standard vinegar is 5–6%; specialty vinegars range 4–8%.
**Scenario:** Sample 5.0 mL of battery acid (concentrated H₂SO₄), diluted to 250 mL with water. Titrate 25 mL of the diluted sample with 1.0 M NaOH. Endpoint at 39.2 mL. **Calculation:** Diluted H₂SO₄ molarity: nₐ × Mₐ × Vₐ = n_b × M_b × V_b → 2 × Mₐ × 25 = 1 × 1.0 × 39.2 → Mₐ = 39.2 / (2 × 25) = 0.784 M (in diluted sample). Dilution factor: 250/5 = 50×. Original concentration: 0.784 × 50 = 39.2 M H₂SO₄. **Result:** Battery acid is 39.2 M H₂SO₄ (about 95% w/w concentrated sulfuric acid). Consistent with typical lead-acid battery electrolyte (37 M = 33% w/w when discharged, 39 M = 96% w/w when fully charged).
**Use titration for quantitative concentration measurement:**
- **Acid-base titration**: most common; vinegar acidity, antacid neutralization capacity, soil pH, drug content. - **Redox titration**: iodometry for vitamin C, KMnO₄ for iron content, Karl Fischer for water content. - **Precipitation titration**: Mohr method for chloride (AgNO₃), Volhard for back-titration. - **Complexometric titration**: EDTA for water hardness (Ca²⁺, Mg²⁺), drug metal content. - **Pharmaceutical assay**: USP titration methods for drug active content. - **Brewing chemistry**: titratable acidity in wine, beer, kombucha. - **Water analysis**: alkalinity (HCl titration), chloride, dissolved CO₂.
**Choosing an indicator:**
| Reaction type | Endpoint pH | Recommended indicator | |---|---|---| | Strong acid + strong base | 7.0 | Bromothymol blue (6.0–7.6) | | Strong acid + weak base (NH₃) | ~5.0 | Methyl red (4.4–6.2) | | Weak acid (acetic) + strong base | ~8.7 | Phenolphthalein (8.2–10.0) | | Diprotic acid first equivalence | depends | Bromocresol green | | Polyprotic with two endpoints | multiple | Two indicators or pH probe |
**Why use pH electrode instead of color indicator:**
- More accurate (±0.01 pH vs ±0.2 for visual). - No color interference (works in colored solutions like wine, juice, urine). - Records full titration curve, not just endpoint — extracts pKa info. - Automation possible (auto-titrators).
**Calibration and standardization:**
- **Primary standards**: KHP (for bases), Na₂CO₃ (for acids). Stable, non-hygroscopic, high purity. - **Standardize the titrant before use**: small concentration drift happens during storage. - **Use a burette calibrated against gravimetric water deliveries** for highest accuracy. - **Run a blank**: subtract titrant volume used by the buffer/water alone.
**Beyond simple endpoint:**
- **Equivalence point** = stoichiometric balance. - **Endpoint** = where indicator changes (close to but not exactly the equivalence point). - **Half-equivalence point**: pH = pKa of weak acid. Useful for measuring pKa. - **Buffer region**: pH changes slowly during initial titration of weak acid; gives buffer capacity.
Calculate pH from H+ concentration and convert between pH, pOH, [H+], and [OH-].
Calculate molarity (moles per liter) and perform dilution calculations (C1V1 = C2V2).
Calculate dilution using C1V1 = C2V2 equation. Find any missing variable.
Calculate boiling point elevation using ΔTb = Kb x m x i.
Calculate freezing point depression using ΔTf = Kf x m x i.
Calculate Gibbs free energy using ΔG = ΔH - TΔS.
Moles Acid
0.00250 mol
Moles Base
0.00250 mol
Base Molarity
0.1000 M
| Parameter | Value |
|---|---|
| Acid Molarity (Ma) | 0.1000 mol/L |
| Acid Volume (Va) | 25.00 mL |
| Acid Protons (n) | 1 |
| Base Molarity (Mb) | 0.1000 mol/L |
| Base Volume (Vb) | 25.00 mL |
| Base OH Groups (n) | 1 |
| Moles of Acid | 0.002500 mol |
| Moles of Base | 0.002500 mol |
| Equivalents Acid | 0.002500 eq |
| Equivalents Base | 0.002500 eq |