TAHA Engineering Toolsby TAHA Knowledge Lab

Chemical Engineering

Acid-Base Titration Calculator

Unknown analyte concentration, titrant volume needed, or titrant standardisation, from the equivalence point and the balanced equation coefficients.

Inputs

Calculate from
A burette holding titrant above a conical flask holding the analyte, with the equivalence relation n(T)/ν(T) = n(A)/ν(A).Titrant: c(T), V(T)(known concentration)Analyte: c(A), V(A) or mn(T) ÷ ν(T) = n(A) ÷ ν(A)at the equivalence point
Titrant of known concentration is run from the burette into the analyte until the reaction is just complete (equivalence point). Then the amounts are in the ratio of the coefficients of the balanced equation: n(T) ÷ ν(T) = n(A) ÷ ν(A), with n = c × V. Diagram not to scale.

For H₂SO₄ + 2 NaOH → Na₂SO₄ + 2 H₂O with H₂SO₄ as analyte: ν_A = 1, ν_T = 2.

Final burette reading minus initial reading.

Titrant used by a blank without analyte; it is subtracted.

Result

Analyte concentration
0.0938
Amount of titrant at the equivalence point
2.345
Amount of analyte
2.345
Working
n_T = c_T × V_T = 0.1 mol/L × 0.02345 L = 0.002345 mol Equivalence: n_T ÷ ν_T = n_A ÷ ν_A, so n_A = n_T × 1 ÷ 1 (1 : 1) = 0.002345 mol c_A = n_A ÷ V_A = 0.002345 mol ÷ 0.025 L = 0.0938 mol/L

The analyte concentration is 0.0938 mol/L (2.345 mmol in the aliquot).

  • Stoichiometric equivalence only: this uses the amounts at the equivalence point. It does not draw the pH titration curve or choose an indicator; the end point you read should be close to the equivalence point.

Educational estimate — check the assumptions below.

About this calculator

In an acid-base titration, a solution of known concentration (the titrant, usually in a burette) is added to a measured amount of the substance being analysed (the analyte) until the reaction is just complete — the equivalence point. At that point the amounts of titrant and analyte are in the ratio of their coefficients in the balanced equation.

This calculator uses that relationship to find an unknown concentration, the titrant volume needed, or the exact concentration of a titrant (standardisation). Entering the coefficients from the balanced equation handles diprotic and triprotic acids and bases correctly — the common shortcut MaVa = MbVb is only true for 1 : 1 reactions. It is a stoichiometry calculator, not a simulator of the pH titration curve.

Formula

nT ÷ νT = nA ÷ νA    nT = cT × (VT − Vblank)    nA = cA × VA or m × P ÷ M

cA = cT × VT × νA ÷ (νT × VA)    VT = cA × VA × νT ÷ (νA × cT)

n = amount (mol), c = concentration (mol/L), V = volume (L), ν = coefficient in the balanced equation, m = mass of a primary standard, P = purity (fraction), M = molar mass. A = analyte, T = titrant.

Worked example

  • 25.00 mL of hydrochloric acid needs 23.45 mL of 0.1000 mol/L NaOH (HCl + NaOH, 1 : 1): nT = 0.1000 × 0.02345 = 2.345 mmol → cA = 2.345 mmol ÷ 25.00 mL = 0.09380 mol/L.
  • Diprotic: 25.00 mL of sulfuric acid needs 20.00 mL of 0.1000 mol/L NaOH (H₂SO₄ + 2 NaOH, νA = 1, νT = 2): nA = 2.000 mmol ÷ 2 = 1.000 mmol → 0.04000 mol/L (not 0.08000, as the 1 : 1 shortcut would give).
  • Standardising NaOH with 0.5105 g of KHP (204.22 g/mol, 1 : 1) that needs 24.85 mL: n = 0.5105 ÷ 204.22 = 2.4998 mmol → cT = 0.10059 mol/L.

Assumptions and limitations

  • The reaction goes to completion and the end point read (indicator colour change or pH-meter inflection) equals the equivalence point.
  • The coefficients must come from the correctly balanced equation of the reaction that actually occurs at the chosen end point. For a polyprotic acid titrated only to its first end point, use the coefficients of that first step.
  • Volumes are measured at the same temperature as the stated concentrations.
  • This calculator does not model the pH during the titration, buffer regions, indicator choice or weak acid/weak base end-point errors.
  • A calculation tool only, not laboratory safety advice.

References

  • Harris, D. C., Quantitative Chemical Analysis — titration stoichiometry and primary standards (potassium hydrogen phthalate).
  • IUPAC, Compendium of Analytical Nomenclature (the “Orange Book”) — titration, equivalence point and end point.