Titration Endpoint Formula
The titration formula C₁V₁ = C₂V₂ calculates unknown concentrations by reacting an acid with a base to reach the equivalence point.
The Formula
In a titration, a solution of known concentration (the titrant) is gradually added to a solution of unknown concentration (the analyte) until the reaction is complete. This point is called the equivalence point.
At the equivalence point, the moles of acid equal the moles of base (adjusted for stoichiometry). A color-changing indicator or pH meter signals when this point is reached.
Variables
| Symbol | Meaning |
|---|---|
| n₁ | Stoichiometric coefficient of the acid (number of H⁺ ions per molecule) |
| C₁ | Concentration of the acid (in mol/L) |
| V₁ | Volume of the acid (in liters or mL — must match V₂ units) |
| n₂ | Stoichiometric coefficient of the base (number of OH⁻ ions per molecule) |
| C₂ | Concentration of the base (in mol/L) |
| V₂ | Volume of the base (same units as V₁) |
Simplified Form
For monoprotic acid-base reactions (1:1 stoichiometry like HCl + NaOH), the formula simplifies to:
Example 1
25.0 mL of HCl (unknown concentration) is titrated with 0.100 M NaOH. It takes 31.2 mL of NaOH to reach the endpoint. What is the HCl concentration?
Both are monoprotic (1:1 ratio), so C₁V₁ = C₂V₂
C₁ × 25.0 = 0.100 × 31.2
C₁ = 3.12 / 25.0
C₁ = 0.125 M HCl
Example 2
20.0 mL of 0.150 M H₂SO₄ (diprotic) is titrated with 0.200 M NaOH (monoprotic). How much NaOH is needed?
H₂SO₄ has n₁ = 2 (donates 2 H⁺), NaOH has n₂ = 1
n₁ × C₁ × V₁ = n₂ × C₂ × V₂
2 × 0.150 × 20.0 = 1 × 0.200 × V₂
6.00 = 0.200 × V₂
V₂ = 6.00 / 0.200
V₂ = 30.0 mL of NaOH
When to Use It
Titration is one of the most common analytical techniques in chemistry.
- Determining the concentration of an unknown acid or base
- Quality control in pharmaceutical and food industries
- Water treatment and environmental analysis
- Standardizing laboratory solutions
- Measuring alkalinity or acidity of samples
Always ensure units are consistent between the two sides. If V₁ is in mL, V₂ must also be in mL — the units cancel in the ratio.