Acid Base Titration Equation Explained

The acid-base titration equation is the stoichiometric relationship used to find the unknown concentration of an acid or base from the volume of a standard solution needed to reach the equivalence point. In the simplest case of a monoprotic acid and a monoprotic base, the equation is M�V� = M₂V₂, where M is molarity (mol/L) and V is volume (L) of the acid (1) and base (2). This page includes a calculator that applies this equation to any acid-base titration, taking your known concentration and volume plus the volume of the unknown solution, and returns the unknown molarity.

Formula

The core equation for a 1:1 acid-base reaction (e.g., HCl + NaOH → NaCl + H₂O) is:

M�V� = M₂V₂

Where:

• Mâ‚� = molarity of the titrant (the solution of known concentration), in mol/L
• Vâ‚� = volume of titrant used to reach the equivalence point, in L (or mL, as long as both volumes use the same unit)
• Mâ‚‚ = molarity of the analyte (the solution being analyzed), in mol/L
• Vâ‚‚ = volume of the analyte sample, in L (or mL)

For reactions where the acid and base react in a different ratio (e.g., Hâ‚‚SOâ‚„ with 2 moles of NaOH), you must include the stoichiometric coefficients. The general form is:

n� × M� × V� = n_b × M_b × V_b

where n� and n_b are the moles of H� (for acid) and OH� (for base) per mole of compound. For H₂SO₄, n� = 2; for NaOH, n_b = 1.

Worked Example

Using the calculator defaults: you have 25.0 mL of 0.100 mol/L HCl (titrant) and 50.0 mL of NaOH solution (analyte). At the equivalence point, the moles of acid equal the moles of base.

1. Calculate moles of titrant: 0.0250 L × 0.100 mol/L = 0.00250 mol
2. Apply M�V� = M₂V₂: (0.100 mol/L)(0.0250 L) = M₂(0.0500 L)
3. Solve for M₂: M₂ = (0.100 × 0.0250) / 0.0500 = 0.0500 mol/L

The calculator returns 0.050 mol/L (rounded to 3 decimals). This matches the step-by-step result.

When to Use This Equation

The M�V� = M₂V₂ equation is valid only for titrations where the reaction goes to completion and the stoichiometry is known. It is used in:

• Standardizing a solution of unknown concentration (e.g., finding the molarity of a NaOH solution by titrating with a known HCl solution)
• Determining the concentration of an acid or base in a commercial product (vinegar, antacids, etc.)
• Educational labs to teach volumetric analysis

It works for strong acid–strong base, strong acid–weak base, and weak acid–strong base titrations, as long as you use the correct stoichiometric ratio. For weak acid–weak base, the equivalence point may be less sharp, but the stoichiometry still holds.

How to Read the Result

The calculated molarity (mol/L) is the concentration of the analyte solution. For example, if you get 0.050 mol/L for NaOH, that means each liter of that solution contains 0.050 moles of NaOH. If you need the concentration in g/L, multiply by the molar mass (for NaOH, 40.00 g/mol → 2.00 g/L).

Remember that the equation gives the concentration at the equivalence point, not the endpoint. The endpoint is the point where the indicator changes color, which should be as close as possible to the equivalence point. A small difference (titration error) is normal.

Common Mistakes and How to Avoid Them

• Unit mismatch: Both volumes must be in the same unit (both mL or both L). If you mix them, the result will be off by a factor of 1000.
• Forgetting stoichiometry: For diprotic acids (like Hâ‚‚SOâ‚„) or diacidic bases (like Ca(OH)â‚‚), you must multiply by the number of Hâ�º or OHâ�» ions. Ignoring this leads to a factor-of-2 error.
• Using the wrong volume: The volume of titrant is the volume added to reach the endpoint, not the total volume of the flask.
• Rounding too early: Keep extra digits during intermediate steps and round only at the final answer.

Limitations of the Equation

The M�V� = M₂V₂ equation assumes:

• Complete reaction with no side reactions
• Known stoichiometry
• No volume change upon mixing (volume additivity) – this is acceptable for dilute solutions
• That the equivalence point is detectable with an indicator or pH meter

It does not apply to titrations involving complexation, redox, or precipitation reactions, which have different stoichiometric relationships. For those, you would use the specific reaction equation.

Frequently Asked Questions

What is the difference between endpoint and equivalence point?

The equivalence point is the exact point where the moles of H� and OH� are stoichiometrically equal. The endpoint is the point where the indicator changes color. Ideally they are the same, but in practice the endpoint is slightly past the equivalence point. The difference is called the titration error.

Can I use this equation for weak acids or weak bases?

Yes, the stoichiometry is the same. For example, titrating acetic acid (CH₃COOH) with NaOH uses the same M�V� = M₂V₂ equation because one mole of acetic acid reacts with one mole of NaOH. The pH curve is different, but the moles at equivalence are still equal.

What if the acid and base react in a 2:1 ratio?

Then you must include the stoichiometric coefficient. For H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O, the equation becomes 2 × M� × V� = 1 × M_b × V_b (or equivalently M� × V� = (1/2) × M_b × V_b). The calculator above assumes a 1:1 ratio; for other ratios, adjust the result by the appropriate factor.

Why do I need to use a burette for titration?

A burette allows you to add the titrant in a controlled, measurable way. You need to know the exact volume added to use the equation. Burettes are calibrated to deliver accurate volumes, typically to ±0.05 mL.

How do I choose an indicator?

Choose an indicator whose color-change range overlaps the steep part of the pH curve at the equivalence point. For strong acid–strong base, phenolphthalein (pH 8.2–10.0) or methyl orange (pH 3.1–4.4) work. For weak acid–strong base, phenolphthalein is suitable; for strong acid–weak base, methyl orange is better.

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in t | Volume of titrant (known) | mL | 25.0 | 0
in c | Concentration of titrant | mol/L | 0.100 | 0
in v | Volume of analyte (unknown) | mL | 50.0 | 0
out m | Concentration of analyte | mol/L | (t * c) / v | 3
out moles_titrant | Moles of titrant used | mmol | t * c | 2