Titration Calculator

Frequently Asked Questions

What is the formula for acid-base titration calculations?

At the equivalence point: (C1 × V1) / n1 = (C2 × V2) / n2, where C is concentration, V is volume, and n is the stoichiometric coefficient (number of H+ or OH− ions per formula unit). For a simple 1:1 reaction like HCl + NaOH: C1 × V1 = C2 × V2. Rearrange to find the unknown.

What is the equivalence point in a titration?

The equivalence point is where moles of titrant exactly equal moles of analyte in the stoichiometric ratio. For strong acid-strong base, pH = 7.00 at the equivalence point. For weak acid-strong base, pH > 7 because the conjugate base undergoes hydrolysis, reacting with water to release OH− ions. The end point is where the indicator changes color, ideally matching the equivalence point.

Why is the mole ratio important in titrations?

Not all reactions are 1:1. H2SO4 has 2 acidic protons, so 1 mol H2SO4 requires 2 mol NaOH. H3PO4 can donate 1, 2, or 3 protons depending on the pH. Using the wrong mole ratio gives a concentration that is off by a factor of 2 or 3. Always write the balanced equation first to determine the ratio.

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How This Calculator Works

Titration determines the concentration of an unknown solution (the analyte) by reacting it with a solution of known concentration (the titrant) until the equivalence point is reached. At equivalence, moles of titrant times stoichiometric ratio equals moles of analyte. The formula used is:

(C1 × V1) / n1 = (C2 × V2) / n2

Where C is concentration in molarity, V is volume in mL, and n is the stoichiometric coefficient. Solving for C2 gives the analyte concentration.

What Is Titration

Titration is a quantitative analytical technique where a reagent of known concentration (titrant) is added slowly to a solution of unknown concentration (analyte) until the reaction is complete. The completion point, called the equivalence point, is detected by a color change from an indicator, a pH meter reading, or a potentiometric probe. Knowing the exact volume of titrant used at equivalence allows calculation of the analyte concentration.

Strong vs. Weak Acid Titrations

Strong acid-strong base titrations (e.g. HCl vs. NaOH) show a sharp equivalence point at pH 7. Weak acid-strong base titrations (e.g. acetic acid vs. NaOH) have an equivalence point above pH 7 because the conjugate base of the weak acid is itself basic. The buffer region before equivalence makes the pH change gradual, and the slope at equivalence is less steep than in strong acid titrations.

The Equivalence Point vs. End Point

The equivalence point is the theoretical point where stoichiometric amounts of acid and base have reacted. The end point is where the indicator changes color. A well-chosen indicator changes color very close to the equivalence point, but the two are rarely identical. The difference between end point and equivalence point is called the titration error. Phenolphthalein transitions at pH 8.2 to 10, making it suitable for strong acid-strong base and weak acid-strong base titrations. Methyl orange transitions at pH 3.1 to 4.4, suitable for strong acid-weak base titrations.

Worked Titration Example

Problem: 25.00 mL of HCl is titrated with 0.100 M NaOH. The equivalence point is reached after adding 32.50 mL of NaOH. What is the HCl concentration?

Mole ratio is 1:1 (HCl + NaOH produces NaCl + H₂O). C2 = (0.100 × 32.50 × 1) / (25.00 × 1) = 0.130 M. Moles of HCl = 0.130 × 25.00 / 1000 = 0.00325 mol.

Worked Example: A Diprotic Acid (H2SO4)

Problem: 20.00 mL of sulfuric acid (H₂SO₄) is titrated with 0.150 M NaOH, reaching the equivalence point after 28.00 mL. Sulfuric acid is diprotic, so the balanced reaction is H₂SO₄ + 2 NaOH produces Na₂SO₄ + 2 H₂O, giving n = 1 for the acid and n = 2 for the base.

Apply (C1 × V1) / n1 = (C2 × V2) / n2 with the acid as the unknown C1: C1 = (0.150 × 28.00 / 2) / 20.00 = 2.10 / 20.00 = 0.105 M. The factor of 2 is the key step: because each H₂SO₄ molecule supplies two protons, it takes twice as many moles of NaOH to reach equivalence. Treating the reaction as 1:1 would overstate the acid concentration by a factor of 2.

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