The Acid-Base Titration Calculator solves neutralization reactions using n-factor equivalence, correctly handling polyprotic acids and polyhydroxyl bases. Find unknown concentration or volume for any acid-base system — from simple HCl/NaOH to H₃PO₄ and Ca(OH)₂ — with full step-by-step calculation.
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The calculator for acid-base titration applies the n-factor equivalence principle to solve neutralization problems for any acid-base combination — from simple monoprotic systems (HCl/NaOH) through polyprotic acids (H₂SO₄, H₃PO₄) and polyhydroxyl bases (Ca(OH)₂, Al(OH)₃). This generalized approach handles cases where the simple C₁V₁ = C₂V₂ formula fails due to unequal proton stoichiometry.
The fundamental equation governing acid-base titrations is the equivalence of moles of H⁺ and OH⁻:
N₁V₁ = N₂V₂ or equivalently C₁V₁n₁ = C₂V₂n₂
where C is molar concentration, V is volume, and n is the n-factor (number of H⁺ or OH⁻ ions per formula unit). For HCl, n = 1; for H₂SO₄, n = 2; for H₃PO₄, n = 1, 2, or 3 depending on which equivalence point is targeted. For NaOH, n = 1; for Ca(OH)₂, n = 2. Applying the correct n-factor is critical for accurate calculations. The simple titration calculator handles the n = 1 case; this calculator covers all n-factor combinations.
Understanding n-factors for common laboratory acids and bases:
The reaction between H₂SO₄ and NaOH at n = 2: 1 mole H₂SO₄ requires 2 moles NaOH — 0.1 M H₂SO₄ × 25 mL × 2 = 0.1 M NaOH × V_NaOH × 1, giving V_NaOH = 50 mL. Use this online calculator for any combination. The normality calculator converts between molarity and normality using the same n-factor concept.
The pH at the equivalence point determines which indicator produces a sharp color change at the endpoint:
The redox titration calculator, back titration calculator, and analytical chemistry calculators category provide the complete titration toolkit.
At the equivalence point of an acid-base titration, the equivalents of acid equal the equivalents of base:
$$M_{acid} \times V_{acid} \times n_{acid} = M_{base} \times V_{base} \times n_{base}$$
where M is molarity (mol/L), V is volume (mL), and n is the n-factor representing the number of replaceable H⁺ ions (for acids) or OH⁻ ions (for bases) per molecule.
Common n-factors include:
$$\text{Acids: HCl}(n=1), \; H_2SO_4(n=2), \; H_3PO_4(n=3)$$
$$\text{Bases: NaOH}(n=1), \; Ca(OH)_2(n=2), \; Al(OH)_3(n=3)$$
Solving for each unknown:
$$M_{acid} = \frac{M_{base} \times V_{base} \times n_{base}}{V_{acid} \times n_{acid}}$$
$$V_{base} = \frac{M_{acid} \times V_{acid} \times n_{acid}}{M_{base} \times n_{base}}$$
The milliequivalents (meq) at the equivalence point are calculated as M × V × n (when V is in mL), providing a measure of the reactive capacity that is independent of the specific acid or base identity.
The calculated unknown gives the exact value needed to achieve stoichiometric equivalence. The milliequivalents output confirms that acid and base equivalents are equal at the equivalence point. When n-factor > 1, significantly less volume of a polyprotic acid or polyhydroxyl base is needed compared to a monoprotic/monohydroxyl species at the same molarity. For example, 0.1 M H₂SO₄ (n=2) requires only half the volume of 0.1 M NaOH (n=1) compared to 0.1 M HCl (n=1). Always verify that the n-factor matches the actual reaction conditions; phosphoric acid can act with n=1, 2, or 3 depending on the equivalence point being targeted.
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25 mL of 0.05 M H₂SO₄ (n=2) requires exactly 25 mL of 0.1 M NaOH (n=1) because 2.5 meq of acid equivalents = 2.5 meq of base equivalents.
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If 18.5 mL of 0.1 M NaOH neutralizes 20 mL of HCl, the HCl concentration is 0.0925 M.
The n-factor (also called basicity for acids or acidity for bases) represents the number of H⁺ ions an acid can donate or OH⁻ ions a base can accept per molecule in the reaction. HCl has n=1, H₂SO₄ has n=2, H₃PO₄ can have n=1, 2, or 3 depending on the endpoint. NaOH has n=1, Ca(OH)₂ has n=2, and Ba(OH)₂ has n=2.
The simple titration calculator uses C₁V₁ = C₂V₂, which assumes 1:1 stoichiometry. This acid-base calculator includes n-factors (M₁V₁n₁ = M₂V₂n₂), making it correct for polyprotic acids and polyhydroxyl bases. For monoprotic acid + monobasic base (both n=1), both calculators give the same result.
Phosphoric acid is triprotic and can lose 1, 2, or 3 protons depending on which equivalence point is being targeted. Titrating to the first equivalence point (H₂PO₄⁻) uses n=1, to the second (HPO₄²⁻) uses n=2, and to the third (PO₄³⁻) uses n=3. In practice, only the first two equivalence points are clearly observable by titration.
The pH depends on the type of titration: strong acid + strong base → pH 7.0; weak acid + strong base → pH > 7 (due to conjugate base hydrolysis); strong acid + weak base → pH < 7 (due to conjugate acid hydrolysis); weak acid + weak base → depends on relative Ka and Kb values. The pH at equivalence is critical for choosing the correct indicator.
Strong acid-strong base (pH ≈ 7): bromothymol blue or phenolphthalein. Weak acid-strong base (pH 8-10): phenolphthalein. Strong acid-weak base (pH 4-6): methyl orange or methyl red. For polyprotic acid titrations, different indicators are needed for each equivalence point. pH meter titration curves provide the most reliable endpoint detection.
For diprotic acids like H₂SO₄ or oxalic acid, set n=2 to calculate the total neutralization equivalence point. If you want the first equivalence point only (like with H₂CO₃ or H₂S where stepwise titration is needed), use n=1. The calculator assumes complete reaction to the specified n-factor.
Normality (N) = Molarity (M) × n-factor. Normality directly represents the concentration of reactive equivalents, so the equivalence relationship simplifies to N₁V₁ = N₂V₂ regardless of stoichiometry. However, IUPAC has deprecated normality, and modern practice prefers molarity with explicit stoichiometric factors.
This calculator finds the equivalence point, not buffer compositions. For buffer preparation, you need to stop titrating before the equivalence point, creating a mixture of weak acid and its conjugate base. The Henderson-Hasselbalch equation (pH = pKa + log([A⁻]/[HA])) is used for buffer calculations, which requires a different approach.
If the two acids have sufficiently different strengths (pKa difference > 3-4 units), they can be titrated sequentially, showing two distinct equivalence points on the titration curve. The first endpoint gives the amount of the stronger acid, and the total titre gives the sum of both acids. This calculator handles single acid-base pairs; mixtures require stepwise analysis.
Well-performed acid-base titrations achieve accuracies of 0.1-0.2% when using properly calibrated burettes, standardized solutions, and appropriate indicators or pH meters. The main sources of error are titrant standardization accuracy, endpoint detection precision, and volumetric glassware calibration. Class A burettes have a tolerance of ±0.05 mL for a 50 mL burette.
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