Titration Calculator
Calculate unknown concentration or volume in acid-base titrations using the formula Ca×Va = Cb×Vb (adjusted for mole ratio). Enter three known values and solve for the fourth. Supports any stoichiometric ratio for polyprotic acids and bases. Essential for analytical chemistry and laboratory work. See also our Buffer pH Calculator and Molarity Calculator.
How to Calculate Titration
Titration is a quantitative analytical technique used to determine the concentration of an unknown solution by reacting it with a solution of known concentration (the titrant or standard solution). The point at which the reaction is complete is called the equivalence point, and it is typically detected using an indicator or pH meter.
The fundamental principle of titration is stoichiometric equivalence: at the equivalence point, the moles of titrant added exactly react with the moles of analyte present. For a 1:1 reaction like NaOH + HCl → NaCl + H₂O, this means moles of NaOH = moles of HCl, or Ca×Va = Cb×Vb. For reactions with different stoichiometry, the mole ratio must be included.
- Identify the titrant (known concentration) and analyte (unknown)
- Write the balanced chemical equation to determine the mole ratio
- Measure the volume of analyte using a pipette
- Add titrant from a burette until the equivalence point is reached
- Use Ca×Va = Cb×Vb (adjusted for mole ratio) to calculate the unknown
Formula
Basic Titration Equation (1:1 stoichiometry):
Ca × Va = Cb × Vb
General Titration Equation (any stoichiometry):
Ca × Va / a = Cb × Vb / b
Or: Ca × Va × b = Cb × Vb × a
Where:
Ca = concentration of analyte (mol/L)
Va = volume of analyte (mL or L)
Cb = concentration of titrant (mol/L)
Vb = volume of titrant at equivalence (mL or L)
a, b = stoichiometric coefficients
Moles at equivalence:
moles(analyte) = Ca × Va (in L)
moles(titrant) = Cb × Vb (in L)
Example Calculation
Problem: 25.0 mL of HCl is titrated with 0.100 M NaOH. The equivalence point is reached after adding 30.0 mL of NaOH. What is the concentration of HCl?
Given: Cb = 0.100 M, Vb = 30.0 mL, Va = 25.0 mL, ratio = 1:1
Solution:
Ca × Va = Cb × Vb
Ca × 25.0 = 0.100 × 30.0
Ca = 3.00 / 25.0 = 0.120 M
Answer: [HCl] = 0.120 M
Problem 2 (2:1 ratio): How much 0.1 M NaOH is needed to neutralize 20 mL of 0.05 M H₂SO₄?
H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O (ratio 2:1)
0.05 × 20 × 2 = 0.1 × Vb × 1
Vb = 2.0 / 0.1 = 20.0 mL NaOH
Common Titration Reference Table
| Titration Type | Titrant | Indicator | Endpoint Color |
|---|---|---|---|
| Strong acid-strong base | NaOH / HCl | Phenolphthalein | Colorless → Pink |
| Weak acid-strong base | NaOH | Phenolphthalein | Colorless → Pink |
| Strong acid-weak base | HCl | Methyl orange | Yellow → Orange |
| Redox (permanganate) | KMnO₄ | Self-indicating | Purple persists |
| Redox (iodometric) | Na₂S₂O₃ | Starch | Blue → Colorless |
| Complexometric (EDTA) | EDTA | Eriochrome Black T | Red → Blue |
| Precipitation (Mohr) | AgNO₃ | K₂CrO₄ | Red precipitate |
| Karl Fischer | KF reagent | Electrometric | Voltage change |
Types of Titration
Acid-base titrations are the most common type, involving the neutralization reaction between an acid and a base. The equivalence point pH depends on the strength of the acid and base: strong acid + strong base gives pH 7, weak acid + strong base gives pH > 7, and strong acid + weak base gives pH < 7. This determines the choice of indicator.
Redox titrations involve electron transfer reactions. Permanganate titrations (using KMnO₄) are self-indicating because the purple color persists once all the reducing agent is consumed. Iodometric titrations use starch indicator to detect the endpoint of reactions involving iodine. These are widely used in food chemistry, water analysis, and pharmaceutical quality control.
Complexometric titrations use chelating agents like EDTA to determine metal ion concentrations. EDTA forms stable 1:1 complexes with most metal ions, making calculations straightforward. These titrations are essential in water hardness testing, clinical chemistry, and environmental analysis.
Back titrations are used when the analyte is insoluble, reacts slowly, or when direct titration is impractical. An excess of reagent is added to the analyte, and the unreacted excess is then titrated with a second standard solution. The amount of analyte is calculated by difference.
Frequently Asked Questions
What is the equivalence point?
The equivalence point is the point in a titration where the moles of titrant added exactly equal the moles of analyte (adjusted for stoichiometry). At this point, the reaction is complete. It is detected by a color change (indicator), pH jump (pH meter), or conductivity change.
What is the difference between endpoint and equivalence point?
The equivalence point is the theoretical point where the reaction is exactly complete. The endpoint is the experimentally observed point where the indicator changes color. Ideally, the endpoint should coincide with the equivalence point, but there is usually a small titration error.
How do I choose the right indicator?
Choose an indicator whose color change range (transition pH) includes the pH at the equivalence point. For strong acid-strong base titrations (equivalence at pH 7), most indicators work. For weak acid-strong base (equivalence at pH 8-10), use phenolphthalein. For strong acid-weak base (equivalence at pH 4-6), use methyl orange.
What is a primary standard?
A primary standard is a highly pure, stable compound used to prepare standard solutions of precisely known concentration. Examples include potassium hydrogen phthalate (KHP) for standardizing NaOH, and sodium carbonate for standardizing HCl. Primary standards must be non-hygroscopic, stable, and have high molar mass.
Why do we use a burette in titrations?
A burette allows precise measurement of the volume of titrant delivered (typically ±0.05 mL). The stopcock provides fine control over the flow rate, enabling drop-by-drop addition near the endpoint. This precision is essential for accurate concentration calculations.
Can I titrate polyprotic acids?
Yes. Polyprotic acids like H₂SO₄, H₃PO₄, and H₂CO₃ can be titrated, but they may show multiple equivalence points. H₂SO₄ is a strong diprotic acid (both protons fully dissociate), so it has one equivalence point with a 2:1 mole ratio. H₃PO₄ shows two distinct equivalence points that can be separately detected.