Titration Calculator

pH curve: 25 mL 0.100 M HCl titrated with 0.100 M NaOH

Titration Calculator: Complete Guide

Acid-base titration adds a solution of known concentration (titrant) to one of unknown concentration (analyte) until the equivalence point where all analyte has reacted. This calculator handles three core calculations: equivalence point volume, titrant volume from C1V1=C2V2, and pH at any point in a strong acid-strong base titration.

The equivalence point and titration equation

At equivalence, moles of titrant equal moles of analyte (adjusted for stoichiometry). For 1:1 reactions: C_a x V_a = C_b x V_b. For H2SO4 with NaOH (diprotic, 1:2 ratio): 2 x C_a x V_a = C_b x V_b. Worked example: 25.00 mL of 0.100 M HCl with 0.100 M NaOH. V_NaOH = 0.100 x 25.00 / 0.100 = 25.00 mL. Using 0.050 M NaOH instead: V_NaOH = 0.100 x 25.00 / 0.050 = 50.00 mL. The halved titrant concentration doubles the required volume. Rearranging for unknown concentration: C_a = C_b x V_b / V_a -- this is how titration determines an unknown concentration.

pH curve for strong acid-strong base titration

Three calculation regions: Before equivalence (excess acid): [H+] = (mol_acid - mol_base) / V_total; pH = -log[H+]. At equivalence: pH = 7.00 at 25 degrees C. After equivalence (excess base): [OH-] = (mol_base - mol_acid) / V_total; pOH = -log[OH-]; pH = 14 - pOH. Example for 25 mL 0.1 M HCl with 0.1 M NaOH: at 10 mL NaOH, excess HCl = 1.5 mmol in 35 mL, pH = 1.37. At 24 mL: excess HCl = 0.1 mmol in 49 mL, pH = 2.69. At 25 mL equivalence: pH = 7.00. At 26 mL: excess NaOH = 0.1 mmol in 51 mL, pOH = 2.71, pH = 11.29. The steep pH jump from approximately 4 to 10 near equivalence is the basis for indicator endpoint detection.

Indicator selection

Indicators change colour over pKa_indicator plus or minus 1. For strong acid-strong base (equivalence at pH 7, jump from 4 to 10): both phenolphthalein (8.2-10.0) and methyl orange (3.1-4.4) work. For weak acid-strong base (equivalence pH 8-10, conjugate base hydrolyses): only phenolphthalein is suitable. For strong acid-weak base (equivalence pH 4-6, conjugate acid formed): only methyl orange or methyl red (4.4-6.2). Never use phenolphthalein for strong acid-weak base -- the colour change occurs too late. The universal rule: indicator pKa must fall within the steep pH jump near the equivalence point.

Standardisation and primary standards

Titrant concentration must be standardised against primary standards: substances of high purity (greater than 99.9%), high molar mass (to minimise weighing error), and long-term stability. Common primary standards include anhydrous sodium carbonate (M_r = 105.99, for standardising HCl) and potassium hydrogen phthalate KHC8H4O4 (M_r = 204.22, for standardising NaOH). Procedure: weigh accurately on an analytical balance; dissolve quantitatively in a small volume; transfer to a conical flask; titrate with working solution; calculate exact concentration from C = n / V_equivalence. Standardisation must be repeated if the titrant has been stored more than a few days, especially for NaOH (absorbs CO2) and HCl (volatile at high concentration).

Back titration method

A back titration adds a known excess of reagent to the analyte, reacts to completion, then titrates the unreacted excess. Used when direct titration is slow, the analyte is insoluble, or the direct endpoint is indistinct. Example: determine CaCO3 content in limestone. Add 50.00 mL of 0.100 M HCl (5.00 mmol, excess). Reaction: CaCO3 + 2HCl -> CaCl2 + CO2 + H2O. Boil to remove CO2. Titrate remaining HCl with 0.100 M NaOH: 28.40 mL used (2.84 mmol). Moles HCl reacted = 5.00 - 2.84 = 2.16 mmol. Moles CaCO3 = 2.16 / 2 = 1.08 mmol. Mass CaCO3 = 1.08 x 100.09 = 108.1 mg. Other back titration applications include Kjeldahl nitrogen (total organic N in food and fertilisers), protein content (formal titration of amino groups), and determination of tablet coating thickness in pharmaceutics.

Exam tips and lab applications

All calculations run in your browser with no data leaving your device. Results copy with one click. The formula is always displayed for verification and citation. The full mixtures and solutions suite covers pH, concentration, dilution, buffer, titration and serial dilution -- the complete quantitative acid-base toolkit for A-level, IB, AP Chemistry and undergraduate analytical chemistry. Key exam connections: C1V1=C2V2 is both the dilution equation and the titration equation at equivalence; pH at any titration point uses [H+] = excess moles / total volume; indicator selection depends on the equivalence point pH and the steep portion of the pH jump near it.

Five solution chemistry formulas that connect everything

These five relationships cover virtually all solution chemistry calculations: (1) c = n/V -- molarity definition. (2) C1V1 = C2V2 -- dilution and titration at equivalence. (3) pH = -log[H+] -- definition of pH. (4) pH = pKa + log([A-]/[HA]) -- Henderson-Hasselbalch. (5) beta = 2.303 x C x Ka x [H+] / (Ka+[H+])^2 -- Van Slyke buffer capacity. All five derive from the same Ka = [H+][A-]/[HA] expression via rearrangement and differentiation. Mastering their interconnections covers the vast majority of acid-base and solution chemistry calculations at A-level through undergraduate level.

Titration in analytical and industrial chemistry

Titrimetric analysis remains one of the most accurate and cost-effective quantitative methods available. In the pharmaceutical industry, assay of active pharmaceutical ingredients by acid-base titration (potentiometric or indicator) is a standard release test in USP and EP monographs. Water hardness (calcium and magnesium carbonate) is determined by complexometric titration with EDTA. Total acidity in wine and juice is measured by titration with NaOH to pH 8.2 (phenolphthalein endpoint). Free fatty acid content in oils and fats is determined by titration with KOH in ethanol. Chloride content in water and food is measured by Mohr or Volhard argentometric titration. Dissolved oxygen (Winkler method) uses iodometric back titration. Biochemical oxygen demand (BOD) in wastewater is measured by titrating the remaining dissolved oxygen after 5-day incubation. In all these applications, accurate titrant standardisation, correct indicator selection, and precise equivalence point detection are critical for valid results.

Potentiometric titration as an alternative to indicators

When the equivalence point colour change is indistinct (highly coloured solutions, turbid samples, non-aqueous solvents) or needs to be determined precisely, a pH meter replaces the indicator. The potentiometric titration curve (pH vs volume of titrant) is plotted in real time. The equivalence point is identified as the inflection point of the curve, where the second derivative d2pH/dV2 = 0, or more practically, where the first derivative dpH/dV is at its maximum. Automated titrators (autotitrators) deliver titrant at controlled rates, detect the equivalence point electronically, and report the result directly. They are standard equipment in pharmaceutical QC laboratories, environmental testing labs, and food analysis facilities. The mathematical relationship between the pH curve shape and the pKa of the analyte acid or base allows pKa determination from a single potentiometric titration -- an important method in drug discovery for characterising new chemical entities.

Common errors and how to avoid them

The most frequent mistakes in solution chemistry calculations are: (1) Using the wrong molar mass -- always check whether you have the anhydrous or hydrated form (e.g. CuSO4 vs CuSO4.5H2O). (2) Mixing up volume of solution and volume of solvent -- molarity uses volume of solution, not just volume of solvent added. (3) Unit mismatch -- concentrations in mol/L and volumes in mL must be converted: n = c x V/1000 when V is in mL. (4) Stoichiometric ratio errors -- for diprotic H2SO4, two moles of NaOH react per mole of acid. (5) Forgetting to account for the dilution during titration -- the total volume increases as titrant is added, affecting the denominator in [H+] and [OH-] calculations. (6) Carry-over in serial dilutions -- always change pipette tips between transfer steps. Catching these errors before submission saves significant time in laboratory practicals and examination contexts.

How this calculator connects to the rest of the solution chemistry suite

The LazyTools mixtures and solutions suite is designed so each calculator complements the others. Titration builds on molarity (c = n/V) and dilution (C1V1=C2V2). pH calculations use the same Ka and pKa values that appear in buffer design. Buffer capacity (Van Slyke) is derived from the Henderson-Hasselbalch equation that governs buffer pH. Serial dilutions use the same dilution factor relationship as the single-step dilution calculator. Understanding how these equations interconnect -- all deriving ultimately from Ka = [H+][A-]/[HA] and the conservation of moles -- gives a unified framework for all quantitative acid-base and solution chemistry rather than a disconnected set of formulas to memorise. Use the related tools section to move between calculators in a logical sequence for multi-step problems.

Frequently asked questions