Titration Calculator
Calculate titration values. M1V1/n1 = M2V2/n2 at equivalence point
Titration: M1V1/n1 = M2V2/n2
Titrant (Known Solution)
Analyte (Unknown Solution)
Result
0.100000 M
Moles Titrant
0.002500 mol
Moles Analyte
0.002500 mol
Total Volume at Equivalence
0.0500 L
Formula:
(M1 x V1) / n1 = (M2 x V2) / n2
n = stoichiometric coefficient from balanced equation
What is Titration?
Titration is a quantitative analytical technique where a solution of known concentration (titrant) is added to a solution of unknown concentration (analyte) until the reaction reaches completion (equivalence point). The stoichiometric coefficients account for reactions where the mole ratio is not 1:1.
What Is Titration?
Titration is an analytical technique used to determine the concentration of an unknown solution by reacting it with a solution of known concentration (the titrant). At the equivalence point, the moles of titrant equal the moles of analyte (for 1:1 reactions), allowing precise calculation of unknown concentrations.
| Term | Definition | Example |
|---|---|---|
| Titrant | Solution of known concentration added from burette | 0.1000 M NaOH |
| Analyte | Solution of unknown concentration being analyzed | HCl of unknown concentration |
| Equivalence point | Stoichiometric completion of reaction | mol acid = mol base |
| Endpoint | Point where indicator changes color | Phenolphthalein turns pink |
| Indicator | Substance that changes color at specific pH | Phenolphthalein, methyl orange |
| Standardization | Determining exact titrant concentration | Titrating NaOH against KHP |
Basic Titration Formula
Where:
- M₁= Molarity of solution 1 (titrant)
- V₁= Volume of solution 1 (titrant)
- M₂= Molarity of solution 2 (analyte)
- V₂= Volume of solution 2 (analyte)
Types of Titrations
Different types of titrations are used depending on the reaction chemistry involved.
| Titration Type | Reaction | Indicator/Detection | Example |
|---|---|---|---|
| Acid-base | H⁺ + OH⁻ → H₂O | pH indicators | HCl + NaOH |
| Redox | Electron transfer | Color change or potentiometric | Fe²⁺ with KMnO₄ |
| Complexometric | Metal-ligand complex | Metallochromic indicators | Ca²⁺ with EDTA |
| Precipitation | Precipitate formation | Color or turbidity | Cl⁻ with AgNO₃ (Mohr method) |
| Back titration | Excess titrant + second titrant | Various | Antacid analysis |
Most common: Acid-base titrations are used for routine analysis of acids, bases, and buffer solutions in laboratories worldwide.
Understanding Titration Curves
A titration curve plots pH versus volume of titrant added. The shape reveals important information about the analyte and helps select appropriate indicators.
| Titration | Initial pH | Equivalence pH | Curve Shape | Suitable Indicator |
|---|---|---|---|---|
| Strong acid + strong base | 1–3 | 7.0 | Sharp vertical at equiv. | Any (wide range works) |
| Weak acid + strong base | 3–5 | 8–10 | Buffer region, then sharp | Phenolphthalein (8.2–10) |
| Strong acid + weak base | 11–13 | 4–6 | Sharp, then buffer | Methyl orange (3.1–4.4) |
| Weak acid + weak base | Varies | ~7 (varies) | Gradual change | Difficult; use pH meter |
| Polyprotic acid | Varies | Multiple | Multiple inflections | Depends on which H⁺ |
Buffer region: The relatively flat portion of a weak acid titration curve where pH changes slowly—this is where buffering occurs.
Choosing the Right Indicator
An indicator should change color at a pH close to the equivalence point. The indicator's pKa determines its transition range.
| Indicator | pH Range | Acid Color | Base Color | Best For |
|---|---|---|---|---|
| Thymol blue (1st) | 1.2–2.8 | Red | Yellow | Strong acid titrations |
| Methyl orange | 3.1–4.4 | Red | Yellow | Strong acid with weak base |
| Methyl red | 4.4–6.2 | Red | Yellow | Weak base titrations |
| Bromothymol blue | 6.0–7.6 | Yellow | Blue | Near-neutral equivalence |
| Phenolphthalein | 8.2–10.0 | Colorless | Pink | Weak acid with strong base |
| Thymolphthalein | 9.3–10.5 | Colorless | Blue | High pH equivalence |
Rule of thumb: Choose an indicator whose color change range includes the equivalence point pH. For strong acid-strong base (equiv. pH 7), almost any indicator works due to the sharp pH change.
Titration Calculations and Stoichiometry
The basic calculation depends on the mole ratio from the balanced equation.
| Reaction Ratio | Equation | Example |
|---|---|---|
| 1:1 | M₁V₁ = M₂V₂ | HCl + NaOH → NaCl + H₂O |
| 2:1 | 2M₁V₁ = M₂V₂ | H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O |
| 1:2 | M₁V₁ = 2M₂V₂ | 2HCl + Ba(OH)₂ → BaCl₂ + 2H₂O |
| General a:b | aM₁V₁ = bM₂V₂ | Any stoichiometry |
General formula: At equivalence, mol of acid × acid coefficient = mol of base × base coefficient. Convert using n = MV to get the working equation.
General Titration Equation
Where:
- n₁, n₂= Moles of reactants
- a, b= Stoichiometric coefficients
- M, V= Molarity and volume
Proper Titration Technique
Accurate titrations require careful technique to minimize errors.
| Step | Best Practice | Why |
|---|---|---|
| Burette preparation | Rinse with titrant solution, not water | Prevents dilution of titrant |
| Reading volume | Eye level at meniscus bottom | Avoids parallax error |
| Adding titrant | Slow near endpoint, swirl continuously | Prevents overshoot |
| Detecting endpoint | Look for persistent color change (30 sec) | Transient color isn't endpoint |
| Multiple trials | Perform at least 3 titrations | Improves precision |
| Calculating result | Average concordant results only | Discard outliers |
Tip: Do a rough titration first to find approximate endpoint, then do careful titrations adding dropwise near the endpoint.
Standardizing Solutions
Standardization determines the exact concentration of a titrant using a primary standard—a highly pure, stable compound with known stoichiometry.
| Primary Standard | Formula | MW (g/mol) | Used to Standardize |
|---|---|---|---|
| Potassium hydrogen phthalate (KHP) | KHC₈H₄O₄ | 204.22 | NaOH, KOH solutions |
| Sodium carbonate | Na₂CO₃ | 105.99 | HCl, H₂SO₄ solutions |
| Potassium dichromate | K₂Cr₂O₇ | 294.18 | Sodium thiosulfate |
| Oxalic acid dihydrate | H₂C₂O₄·2H₂O | 126.07 | KMnO₄ solutions |
| EDTA disodium salt | Na₂H₂Y·2H₂O | 372.24 | Metal ion standards |
Primary standard requirements: High purity (>99.9%), stable to air and moisture, high molecular weight (reduces weighing error), reacts stoichiometrically, non-hygroscopic.
Worked Examples
Find Unknown Acid Concentration
Problem:
25.00 mL of HCl is titrated with 0.1025 M NaOH. The endpoint is reached after adding 23.45 mL of NaOH. What is the HCl concentration?
Solution Steps:
- 1Identify reaction: HCl + NaOH → NaCl + H₂O (1:1 ratio)
- 2At equivalence: mol HCl = mol NaOH
- 3Calculate mol NaOH: n = M × V = 0.1025 × 0.02345 = 0.002404 mol
- 4mol HCl = 0.002404 mol (same as NaOH)
- 5Calculate [HCl]: M = n/V = 0.002404/0.02500 = 0.09614 M
Result:
[HCl] = 0.09614 M (or 0.0961 M to 3 significant figures). The precision depends on your measurement precision.
Diprotic Acid Titration
Problem:
30.00 mL of H₂SO₄ requires 48.50 mL of 0.1000 M NaOH to reach the second equivalence point. What is the concentration of H₂SO₄?
Solution Steps:
- 1Reaction: H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O (1:2 ratio)
- 2At equivalence: mol H₂SO₄ × 2 = mol NaOH
- 3Calculate mol NaOH: n = 0.1000 × 0.04850 = 0.00485 mol
- 4mol H₂SO₄ = 0.00485/2 = 0.002425 mol
- 5[H₂SO₄] = 0.002425/0.03000 = 0.08083 M
Result:
[H₂SO₄] = 0.0808 M. Note: For diprotic acids, you must account for the 2:1 stoichiometry—each H₂SO₄ molecule requires two OH⁻ ions for complete neutralization.
Standardization of NaOH
Problem:
0.4892 g of KHP (MW = 204.22 g/mol) is dissolved in water and titrated with NaOH. The endpoint is reached at 23.86 mL. What is the NaOH concentration?
Solution Steps:
- 1KHP reacts 1:1 with NaOH: KHP + NaOH → KNaP + H₂O
- 2Calculate mol KHP: n = mass/MW = 0.4892/204.22 = 0.002395 mol
- 3mol NaOH = mol KHP = 0.002395 mol
- 4[NaOH] = n/V = 0.002395/0.02386 = 0.1004 M
Result:
[NaOH] = 0.1004 M. This standardized NaOH solution can now be used as the titrant for analyzing unknown acid samples.
Tips & Best Practices
- ✓Always rinse the burette with titrant solution (not water) before filling to avoid dilution.
- ✓Add titrant slowly near the endpoint—one drop at a time while swirling the flask.
- ✓The endpoint color should persist for at least 30 seconds; transient color isn't the endpoint.
- ✓Perform at least 3 titrations and average the concordant results (within 0.1-0.2 mL of each other).
- ✓For accurate work, standardize your titrant against a primary standard on the same day.
- ✓Read the burette at eye level from the bottom of the meniscus to avoid parallax error.
- ✓Choose an indicator whose color change pH includes the equivalence point pH.
Frequently Asked Questions
Sources & References
Last updated: 2026-01-22