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Titration Calculator

Ready to calculate
C₁V₁n₁ = C₂V₂n₂.
4-way solver.
pH estimate + excess.
100% Free.
No Data Stored.

How it Works

01Pick Neutralization Mode

Yes (at equivalence — solve for missing C or V); No / Not sure (compute current pH from full inputs).

02Enter Acid & Base Panels

Strength (strong/weak/unknown); concentration (M/mM/µM/N); volume (mL/L/µL); H+/OH- equivalents per molecule.

03Apply C₁V₁n₁ = C₂V₂n₂

Equivalence relation: total acid equivalents = total base equivalents at the endpoint.

04Get pH + Excess + Solved Value

Final pH (strong/strong = 7; weak/strong shifts up/down); excess equivalents and ion concentrations.

What is a Titration Calculator?

Acid-base titration is the most-taught and most-used quantitative analytical technique in chemistry — a known volume of titrant (standard acid or base) is added to a sample until the equivalence point is reached, allowing precise determination of concentration via the relation C_acid × V_acid × n_H = C_base × V_base × n_OH. It's used to standardize reagents, analyze water alkalinity, determine antacid potency, measure free fatty acids in oils, quantify drug active ingredients, and a thousand other practical applications. Our Titration Calculator implements the full workflow with two operating modes — "Yes" (neutralized at equivalence) and "No / Not sure" (compute current state) — plus pH estimation based on acid/base strength categories.

Yes mode (4-way solver): enter 3 of the 4 fields (acid concentration, acid volume, base concentration, base volume) and the calculator solves for the 4th. Strength options for each side (strong / weak / unknown) classify the pH at equivalence: strong+strong = 7; weak acid + strong base ≈ 8-10 (basic salt hydrolysis); strong acid + weak base ≈ 4-6 (acidic salt hydrolysis); weak+weak depends on relative Ka/Kb. No / Not sure mode: enter all 4 fields; the calculator computes excess (acid or base), the excess concentration in the total mixture volume, and the resulting pH from the strong-electrolyte limit (use Henderson-Hasselbalch for weak components).

Polyprotic acid support via the "H⁺ donated per molecule" field: HCl n=1, H₂SO₄ n=2, H₃PO₄ n=3, H₂CO₃ n=2; same for OH⁻ on the base side: NaOH n=1, Ca(OH)₂ n=2, Al(OH)₃ n=3. Multi-unit input: concentration in M / mM / µM / N (normality, where N = M × n already); volume in mL / L / µL. Output: equivalence-point pH or excess pH; ion concentrations [H⁺] / [OH⁻]; pOH; classification (acidic / basic / neutral); per-side equivalents and total mixture volume; full transparent calculation breakdown. Designed for general chemistry / AP Chemistry / IB Chemistry coursework, analytical-chemistry labs standardizing solutions, water-quality analysts measuring alkalinity, food chemists titrating fatty acids, pharma QC labs verifying drug potency — runs entirely in your browser, no account, no data stored.

Pro Tip: Pair this with our Molarity Calculator for solution preparation, our % to Molarity Calculator for concentrated reagent conversion, our Dilution Factor Calculator for serial dilution prep, or our Molality Calculator for colligative-property work.

How to Use the Titration Calculator?

Pick the Neutralization Mode: Yes if you want to find what concentration / volume is needed to reach equivalence (4-way solver, leave one field blank). No / Not sure if you want to compute the current state (all 4 fields entered) — find excess and resulting pH.
Set Acid Strength: Strong = fully ionizes (HCl, HBr, HI, HNO₃, H₂SO₄ first H, HClO₄). Weak = partial ionization (HF, acetic acid, carbonic, phosphoric, H₂S, HCN, organic acids). Unknown = treat as strong for math, with caveat in output.
Set Base Strength: Strong = fully ionizes (NaOH, KOH, LiOH, Ca(OH)₂, Sr(OH)₂, Ba(OH)₂). Weak = partial ionization (NH₃ / NH₄OH, methylamine, pyridine, soluble carbonate / bicarbonate salts).
Enter Concentration and Volume for Both Sides: M / mM / µM / N for concentration; mL / L / µL for volume. In Yes mode, leave one of the 4 fields blank for the calculator to solve. In No mode, fill all four.
Enter "H⁺ donated" and "OH⁻ donated": Number of equivalents per molecule. Acids: HCl=1, HNO₃=1, acetic=1, H₂SO₄=2, H₂CO₃=2, H₃PO₄=3, citric=3. Bases: NaOH=1, KOH=1, NH₃=1, Ca(OH)₂=2, Mg(OH)₂=2, Al(OH)₃=3.
Apply C_acid × V_acid × n_H = C_base × V_base × n_OH: the equivalence relation that holds at the endpoint regardless of strength. The calculator handles unit conversion automatically.
Read pH at Equivalence (Yes mode): strong+strong = 7.0; weak acid + strong base ≈ 8-10 (basic salt — conjugate base of weak acid hydrolyzes); strong acid + weak base ≈ 4-6 (acidic salt — conjugate acid of weak base hydrolyzes); weak+weak depends on relative Ka and Kb (can be 7, > 7, or < 7).
For "No / Not sure" Mode — Compute Excess: if eq_acid > eq_base, acid is in excess; pH from [H⁺] = excess_eq / V_total; pH = −log[H⁺]. If eq_base > eq_acid, base is in excess; pH from pOH = −log[OH⁻], pH = 14 − pOH. The calculator handles both cases automatically.
For Exact pH Near Equivalence with Weak Components: use Henderson-Hasselbalch with the appropriate Ka or Kb. The calculator gives qualitative ranges; for research-grade exact pH (within 0.1 unit), apply the buffer equation manually.

How is acid-base titration calculated?

Acid-base titration is one of the foundational topics in analytical chemistry — derived from stoichiometric equivalence between protons and hydroxide ions, the math is simple but the variations (polyprotic, weak, mixed) require careful bookkeeping. The calculator handles the arithmetic; the chemistry intuition (which species are present, what hydrolyzes the salt) remains the user's responsibility.

References: Skoog, West, Holler & Crouch — Fundamentals of Analytical Chemistry (10th ed., 2022); APHA Standard Methods for the Examination of Water and Wastewater (24th ed.); Atkins' Physical Chemistry (12th ed.); IUPAC Compendium of Chemical Terminology (Gold Book).

Core Equation — Equivalence Point

C_acid × V_acid × n_H = C_base × V_base × n_OH

Where C is molar concentration, V is volume, n_H is the number of H⁺ released per acid molecule (HCl=1, H₂SO₄=2, H₃PO₄=3), and n_OH is the number of OH⁻ released per base molecule (NaOH=1, Ca(OH)₂=2). When normality (N = M × n) is used, the relation simplifies to N_acid × V_acid = N_base × V_base.

pH at Equivalence — Four Cases

  • Strong acid + strong base (HCl + NaOH): salt is neutral; pH = 7.0 exactly.
  • Weak acid + strong base (CH₃COOH + NaOH): salt is basic (conjugate base hydrolyzes); pH = ½(pKw + pKa + log C) where C is salt concentration. Typical range 8-10.
  • Strong acid + weak base (HCl + NH₃): salt is acidic (conjugate acid hydrolyzes); pH = ½(pKw − pKb − log C). Typical range 4-6.
  • Weak acid + weak base (CH₃COOH + NH₃): pH = ½(pKw + pKa − pKb), independent of concentration. Can be 7 (if pKa = pKb), > 7 (if pKa > pKb), or < 7 (if pKa < pKb).

Excess (Pre- or Post-Equivalence)

If eq_acid > eq_base: excess acid; pH = −log([excess H⁺]) where [H⁺] = (eq_acid − eq_base) / V_total.

If eq_base > eq_acid: excess base; pH = 14 − pOH; pOH = −log([excess OH⁻]) where [OH⁻] = (eq_base − eq_acid) / V_total.

For weak excess, apply Henderson-Hasselbalch instead: pH = pKa + log([A⁻]/) for weak-acid + conjugate-base buffer.

Worked Example — Standardize NaOH with KHP

Weigh 0.4084 g of KHP (potassium hydrogen phthalate, MW 204.22, monoprotic acid n=1) into a flask, dissolve in water, titrate with unknown NaOH solution. Endpoint at 19.85 mL.

  • Moles KHP = 0.4084 / 204.22 = 2.000 × 10⁻³ mol = 2.00 mmol.
  • At equivalence: moles NaOH = moles KHP = 2.00 mmol (both n = 1).
  • NaOH concentration = 2.00 mmol / 19.85 mL = 0.1008 M = 100.8 mM.
  • NaOH solution is now standardized to 4 significant figures — ready for analytical titrations.

Worked Example — Pre-Equivalence pH (Excess Acid)

Mix 50 mL of 0.10 M HCl (strong acid, n = 1) with 30 mL of 0.10 M NaOH (strong base, n = 1).

  • eq_acid = 0.10 × 50 × 1 = 5.0 mmol H⁺.
  • eq_base = 0.10 × 30 × 1 = 3.0 mmol OH⁻.
  • Excess acid = 5.0 − 3.0 = 2.0 mmol H⁺.
  • Total volume = 50 + 30 = 80 mL = 0.080 L.
  • [H⁺] = 2.0 × 10⁻³ / 0.080 = 0.025 M.
  • pH = −log(0.025) = 1.60. Strongly acidic — typical pre-equivalence titration curve point.

Common Acids and Bases — Strength Reference

  • Strong acids: HCl, HBr, HI, HNO₃, H₂SO₄ (1st H), HClO₄, HClO₃. Fully ionize.
  • Strong bases: LiOH, NaOH, KOH, RbOH, CsOH, Ca(OH)₂, Sr(OH)₂, Ba(OH)₂. Fully ionize.
  • Weak acids: HF (Ka 6.6×10⁻⁴); HC₂H₃O₂ acetic (Ka 1.8×10⁻⁵); H₃PO₄ (Ka₁ 7.5×10⁻³); H₂CO₃ (Ka₁ 4.3×10⁻⁷); H₂S (Ka₁ 8.9×10⁻⁸); HCN (Ka 6.2×10⁻¹⁰).
  • Weak bases: NH₃ (Kb 1.8×10⁻⁵); CH₃NH₂ (Kb 4.4×10⁻⁴); pyridine (Kb 1.7×10⁻⁹); aniline (Kb 4×10⁻¹⁰).

Indicator Selection (Visual Endpoint Detection)

  • Methyl orange (3.1-4.4): use for strong acid + weak base (acidic equivalence pH ≈ 5).
  • Bromothymol blue (6.0-7.6): use for strong acid + strong base (neutral equivalence pH = 7).
  • Phenolphthalein (8.2-10.0): use for strong base + weak acid (basic equivalence pH ≈ 9).
  • Phenol red (6.4-8.2): general-purpose, adequate for most strong-strong titrations.
  • Litmus (4.5-8.3): coarse-resolution; rarely used quantitatively.
Real-World Example

Worked Example — Find Acid Concentration via Strong-Strong Titration

Question: 25.00 mL of an unknown HCl solution requires 32.45 mL of 0.1024 M NaOH to reach the phenolphthalein endpoint. What is the HCl concentration?

Step 1 — Identify the System.

  • Acid: HCl (strong, monoprotic, n_H = 1).
  • Base: NaOH (strong, monobasic, n_OH = 1).
  • Mode: "Yes" (at equivalence — solving for unknown acid concentration).

Step 2 — Apply the Equivalence Equation.

  • C_acid × V_acid × n_H = C_base × V_base × n_OH.
  • C_HCl × 25.00 × 1 = 0.1024 × 32.45 × 1.
  • C_HCl = (0.1024 × 32.45) / 25.00 = 3.323 / 25.00 = 0.1329 M HCl.

Step 3 — Verify Equivalence-Point pH.

  • Strong acid + strong base → salt is NaCl (neutral).
  • pH at equivalence = 7.0 (exactly, ignoring water autoionization corrections).
  • Indicator choice: phenolphthalein (8.2-10.0) is slightly mismatched; the endpoint will appear at ~pH 8 (slightly past true equivalence). Use bromothymol blue (6.0-7.6) for tighter centering.

Step 4 — Sanity Check.

  • Acid concentration 0.1329 M = ~1.5% w/w HCl (by mass; 0.1329 × 36.46 / (1.001 × 1000) × 100). Diluted from a stock; consistent with typical lab HCl solutions.
  • Equivalents check: 0.1329 × 25.00 = 3.323 mmol H⁺; 0.1024 × 32.45 = 3.323 mmol OH⁻. Match ✓.
  • Total mixture volume after titration: 25.00 + 32.45 = 57.45 mL. Salt concentration: 3.323 mmol / 57.45 mL = 0.0578 M NaCl.

Step 5 — Reporting the Result.

  • Report HCl concentration as 0.1329 M (4 significant figures, matching the precision of the burette readings ±0.05 mL on 32.45).
  • For analytical use, repeat 3-5 times and report mean ± standard deviation; aim for ±0.1% RSD on standardization.
  • For traceable concentration, standardize against a primary standard (KHP for bases; sodium carbonate for acids; both via single-use mass + volumetric flask, no propagated error from another titration).

Who Should Use the Titration Calculator?

1
Standard early-curriculum topic. Calculator handles equivalence math; students focus on conceptual understanding (strength, hydrolysis, indicator selection).
2
Standardize NaOH against KHP, HCl against Na₂CO₃, KMnO₄ against Na₂C₂O₄ (oxalate). Required first step for any titrimetric analysis where ±0.1% accuracy matters.
3
Standard Methods 2320 titrates water alkalinity with H₂SO₄ to pH 4.5 endpoint (total alkalinity) or 8.3 (phenolphthalein alkalinity). Output in mg/L CaCO₃.
4
Titratable acidity in juices, wines, dairy products via NaOH titration to phenolphthalein endpoint. Free fatty acids in cooking oils via similar protocol.
5
USP / EP titrations to verify drug potency in tablets, IV solutions, injectables. Aspirin, salicylates, antacids (Ca/Mg/Al hydroxides), antibiotics — all routinely titrated.
6
Soil pH buffer capacity measured by titrating soil suspension with strong acid or base; informs lime/sulfur application rates for pH adjustment.
7
Generate problem sets with varying difficulty (strong-strong simple, polyprotic medium, weak-weak advanced); calculator verifies student answers and explains common errors.

Technical Reference

Equivalence Point vs Endpoint. The equivalence point is the theoretical exact moles-equal point of titration. The endpoint is the experimentally observed point (color change, pH meter inflection, conductometric break) used to estimate the equivalence point. Indicator choice introduces a small offset (typically < 0.1% for well-matched indicator + system); pH meter and automatic-titrator endpoints can be within 0.001-0.01 of true equivalence. For high-precision work, use derivative-based endpoint detection (find dpH/dV maximum from continuous pH measurements).

Strong vs Weak Acids and Bases.

  • Strong acids (Ka >> 1, fully ionize): HCl, HBr, HI (hydrohalic acids except HF), HNO₃, H₂SO₄ (first H only; Ka₂ ≈ 0.012 is moderately weak), HClO₄, HClO₃, H₂SeO₄, HMnO₄.
  • Strong bases (Kb >> 1, fully ionize): Group I hydroxides (LiOH, NaOH, KOH, RbOH, CsOH); heavier Group II hydroxides (Ca(OH)₂, Sr(OH)₂, Ba(OH)₂). Mg(OH)₂ is generally insoluble.
  • Weak acids: HF (Ka 6.61×10⁻⁴), HC₂H₃O₂ (Ka 1.76×10⁻⁵), H₂CO₃ (Ka₁ 4.3×10⁻⁷), H₃PO₄ (Ka₁ 7.5×10⁻³), H₂S (Ka₁ 8.9×10⁻⁸), HCN (Ka 6.2×10⁻¹⁰), most carboxylic acids (Ka 10⁻³ to 10⁻⁵), most phenols (Ka 10⁻¹⁰).
  • Weak bases: NH₃ (Kb 1.78×10⁻⁵), most amines (Kb 10⁻³ to 10⁻⁶), pyridines (Kb 10⁻⁹), aniline (Kb 4×10⁻¹⁰), nitrogen-heterocycles.

Polyprotic Acids — Equivalence Points.

  • H₂SO₄: Ka₁ >> 1 (strong), Ka₂ = 1.2×10⁻². Both H⁺ titrate together as one equivalence point (the buffer region of Ka₂ is too weak to resolve in simple titration).
  • H₂CO₃: Ka₁ = 4.3×10⁻⁷, Ka₂ = 5.6×10⁻¹¹. Two distinct equivalence points but the second is weak (low buffer); typically only one is used for water alkalinity titration to phenolphthalein endpoint.
  • H₃PO₄: Ka₁ = 7.5×10⁻³, Ka₂ = 6.2×10⁻⁸, Ka₃ = 4.4×10⁻¹³. Three equivalence points at pH ~ 4.7, ~9.7, and ~13. Third is very weak (need high-concentration NaOH; typically not titratable in dilute solution).
  • Citric acid (H₃Cit): three Ka close together (3.1, 4.7, 6.4); equivalence points overlap, giving one apparent inflection rather than three distinct endpoints.
  • EDTA (H₄Y): four Ka spanning 2-10; used for metal-cation chelation titrations, not acid-base.

Henderson-Hasselbalch — Buffer Region. Between equivalence points (or in the buffer region of a weak-acid + conjugate-base mixture): pH = pKa + log([A⁻]/). Practical use: at half-equivalence (50% titrated), [A⁻] = , so pH = pKa. This is the most accurate way to determine pKa experimentally — titrate the weak acid with strong base, find half-equivalence-point pH = pKa. Same logic for weak base + strong acid: half-equivalence pH = pKa of conjugate acid = 14 − pKb.

Equivalence-Point pH Calculations (Detail).

  • Strong acid + strong base: salt is from strong-acid conjugate-base + strong-base conjugate-acid; neither hydrolyzes appreciably; pH = 7 (ignoring autoionization corrections at very dilute concentrations).
  • Weak acid + strong base: at equivalence the solution contains the salt A⁻ (conjugate base of HA); A⁻ undergoes hydrolysis: A⁻ + H₂O ⇌ HA + OH⁻ with Kb = Kw/Ka. pH = ½(pKw + pKa + log C_salt). For 0.05 M sodium acetate (Ka_HOAc = 1.76×10⁻⁵, pKa = 4.75): pH = ½(14 + 4.75 + log 0.05) = ½(14 + 4.75 − 1.30) = 8.73.
  • Strong acid + weak base: at equivalence the salt is BH⁺ (conjugate acid of B); hydrolyzes BH⁺ + H₂O ⇌ B + H₃O⁺ with Ka = Kw/Kb. pH = ½(pKw − pKb − log C_salt). For 0.05 M NH₄Cl (Kb_NH₃ = 1.76×10⁻⁵, pKb = 4.75): pH = ½(14 − 4.75 − (−1.30)) = ½(14 − 4.75 + 1.30) = 5.27.
  • Weak acid + weak base: pH = ½(pKw + pKa − pKb), independent of concentration. For acetic + ammonia (pKa = 4.75, pKb = 4.75): pH = ½(14 + 4.75 − 4.75) = 7.0 (coincidence; typically off-7).

Volumetric Glassware Precision. For analytical-grade titrations: Class A volumetric flasks (±0.06% tolerance, e.g. 100 mL ± 0.08 mL); Class A burettes (±0.02 mL on 50 mL = ±0.04%); Class A pipettes (±0.02 mL on 10 mL pipette = ±0.2%). For research-grade work use Class A glassware AND temperature control (calibrate at 20 °C; thermal expansion of water 0.04% per °C). For ultra-precision work (NIST-traceable, < 0.05% RSD), use gravimetric titration (mass-based) instead of volumetric.

Modern Titration Methods. Beyond visual endpoint detection: (1) Potentiometric titration — pH electrode tracks pH continuously; endpoint at maximum dpH/dV. Standard for weak/multi-endpoint systems. (2) Conductometric titration — conductivity changes track ion concentrations; equivalence at sharp inflection. Useful for weak-acid + weak-base where pH change is small. (3) Spectrophotometric titration — color change of an absorbing species; works for colored systems. (4) Automatic titrators (Mettler-Toledo Karl-Fischer style) — programmable burette, electrode, software endpoint detection. Standard in modern analytical labs; ±0.01% repeatability achievable. References: Skoog, West, Holler & Crouch (10th ed., 2022); Harris, Quantitative Chemical Analysis (10th ed., 2020); APHA Standard Methods 2320; IUPAC Compendium of Chemical Terminology.

Conclusion

Acid-base titration is the workhorse of analytical chemistry — one stoichiometric relation (C_acid × V_acid × n_H = C_base × V_base × n_OH) that handles 95% of routine quantitative work in water labs, food labs, pharma QC, and undergraduate teaching labs. The math is straightforward; the chemistry intuition (which species hydrolyzes, which indicator to use, which equivalence point of a polyprotic acid you're seeing) is what general-chemistry courses are really testing.

Three operational reminders: (1) Strength matters at equivalence. Strong+strong = pH 7; weak acid + strong base ≈ 8-10 (basic salt); strong acid + weak base ≈ 4-6 (acidic salt). Choose your indicator to match: phenolphthalein for basic equivalence, bromothymol blue for neutral, methyl orange for acidic. (2) Polyprotic acids have multiple equivalence points. H₂SO₄ has 2 (only the second is detectable as a separate endpoint because Ka₂ is moderately weak, ~10⁻²); H₃PO₄ has 3 distinct ones (pKa₁ 2.1, pKa₂ 7.2, pKa₃ 12.3); be specific about which one you're measuring. (3) Standardize your titrant against a primary standard (KHP for NaOH, Na₂CO₃ for HCl, oxalic acid for KMnO₄) before any analytical titration — propagated errors from titrant-on-titrant standardization compound rapidly.

Frequently Asked Questions

What is the Titration Calculator?
It implements the standard acid-base equivalence relation C_acid × V_acid × n_H = C_base × V_base × n_OH as a 4-way solver, with pH estimation based on acid/base strength categories. Two modes: Yes (at equivalence — solve for missing C or V); No / Not sure (compute current state and pH from all 4 inputs). Strong/weak/unknown options for both acid and base classify the equivalence-point pH. Polyprotic support via H⁺ and OH⁻ donated per molecule.

Pro Tip: Pair this with our Molarity Calculator.

What is acid-base titration?
The quantitative analytical technique of adding a known concentration of titrant (acid or base) to a sample until the equivalence point is reached — the moment when moles of acid equivalents equal moles of base equivalents. Visual endpoint detection uses pH indicators (color change at known pH); electronic detection uses pH meters (potentiometric titration). Used to standardize reagents, measure water alkalinity, determine antacid potency, quantify food acidity, and a thousand other practical applications.
What's the formula for titration?
C_acid × V_acid × n_H = C_base × V_base × n_OH at equivalence, where C is concentration, V is volume, and n_H/n_OH are equivalents per molecule (HCl=1, H₂SO₄=2, H₃PO₄=3 for H⁺; NaOH=1, Ca(OH)₂=2 for OH⁻). Equivalent normality form: N_acid × V_acid = N_base × V_base, where N = M × n. Example: 25 mL of unknown HCl titrated with 32.45 mL of 0.1024 M NaOH → C_HCl = 0.1024 × 32.45 / 25 = 0.1329 M.
What is the equivalence point?
The exact moment in titration when moles of acid equivalents equal moles of base equivalents. At equivalence, neither species is in excess. The pH at equivalence depends on strength: strong+strong = 7 (neutral salt); weak acid + strong base ≈ 8-10 (basic salt — conjugate base hydrolyzes); strong acid + weak base ≈ 4-6 (acidic salt — conjugate acid hydrolyzes); weak+weak depends on relative Ka and Kb. The equivalence point is theoretical; the experimentally-observed endpoint (indicator color change or pH-meter inflection) approximates it within 0.01-0.1% for well-matched detection.
How do I find the unknown concentration in a titration?
Use the equivalence relation: C_unknown = (C_known × V_known × n_known) / (V_unknown × n_unknown). Worked example: 25.00 mL HCl titrated with 32.45 mL of 0.1024 M NaOH (both n = 1): C_HCl = 0.1024 × 32.45 / 25.00 = 0.1329 M. The calculator handles this automatically when you pick "Yes" mode and leave the unknown field blank.
What's the difference between strong and weak acids/bases?
Strong electrolytes fully ionize in water (~100%); weak electrolytes partially ionize (typically < 5% at 0.1 M). Strong acids: HCl, HBr, HI, HNO₃, H₂SO₄ (1st H), HClO₄. Strong bases: NaOH, KOH, LiOH, RbOH, CsOH, Ca(OH)₂, Sr(OH)₂, Ba(OH)₂. Weak acids: HF (Ka 6.6×10⁻⁴), acetic acid (Ka 1.8×10⁻⁵), carbonic, phosphoric, H₂S, HCN. Weak bases: NH₃ (Kb 1.8×10⁻⁵), amines, pyridines. The strength affects the equivalence-point pH but NOT the equivalence relation itself.
What is a polyprotic acid and how do I handle it?
An acid that releases multiple H⁺ per molecule. H₂SO₄ donates 2 H⁺ (n=2) — both ionize together as one equivalence point because Ka₂ ≈ 0.01 is too weak to resolve separately. H₃PO₄ donates 3 H⁺ (n=3) — three distinct equivalence points at pH ~4.7, ~9.7, ~13 corresponding to its three pKa values (2.1, 7.2, 12.3). Citric acid (H₃Cit) donates 3 H⁺ but the pKa values are close (3.1, 4.7, 6.4) so the equivalence points merge into one apparent inflection. Set the n field to the appropriate equivalents-per-molecule when titrating polyprotic acids.
How do I calculate pH at equivalence?
Four cases. Strong acid + strong base: pH = 7 (neutral salt). Weak acid + strong base: pH = ½(pKw + pKa + log C_salt) — basic, typically 8-10. Strong acid + weak base: pH = ½(pKw − pKb − log C_salt) — acidic, typically 4-6. Weak acid + weak base: pH = ½(pKw + pKa − pKb), independent of concentration. The calculator gives qualitative pH ranges for each strength combination; for exact pH use the appropriate formula with measured Ka/Kb values.
What indicator should I use?
Match the indicator's color-change pH range to the equivalence-point pH. Methyl orange (3.1-4.4): for strong acid + weak base (acidic equivalence pH ~5). Bromothymol blue (6.0-7.6): for strong acid + strong base (neutral equivalence pH = 7). Phenolphthalein (8.2-10.0): for strong base + weak acid (basic equivalence pH ~9). Phenol red (6.4-8.2): general-purpose. Mismatched indicator introduces a small (0.05-0.5%) systematic error; for best precision use a pH-meter endpoint detection instead of visual.
What's the difference between equivalence point and endpoint?
The EQUIVALENCE point is theoretical; the moment when moles of acid equivalents exactly equal moles of base equivalents. The ENDPOINT is experimental; the moment when the indicator color changes or the pH meter shows the maximum slope (dpH/dV peak) — used to estimate the equivalence point. Difference: indicator endpoint typically < 0.1% offset from true equivalence; pH-meter endpoints within 0.001-0.01%; gravimetric titration achieves < 0.05% with proper calibration. For analytical work, match indicator pKa to equivalence pH within ±1 unit.
How do I standardize a NaOH solution?
Titrate against a primary standard like potassium hydrogen phthalate (KHP, MW 204.22, monoprotic acid). Workflow: (1) dry KHP at 110 °C for 1 hour, cool in desiccator. (2) Weigh ~0.4 g KHP into Erlenmeyer flask (record mass to ±0.0001 g). (3) Dissolve in 50 mL distilled water, add 2-3 drops phenolphthalein. (4) Titrate with NaOH from a clean burette to pink endpoint that persists 30 seconds. (5) Compute: C_NaOH = (mass_KHP / 204.22) / V_NaOH. (6) Repeat 3-5 times; average for ±0.1% precision. The calculator handles step (5) when you select "Yes" mode and leave NaOH concentration blank.

Author Spotlight

The ToolsACE Team - ToolsACE.io Team

The ToolsACE Team

Our ToolsACE chemistry team built this calculator to handle every common variation of <strong>acid-base titration</strong> math. The defining identity at equivalence is <strong>C_acid × V_acid × n_H = C_base × V_base × n_OH</strong>, where n_H and n_OH are the equivalents per molecule (HCl n=1, H₂SO₄ n=2, H₃PO₄ n=3 for H⁺; NaOH n=1, Ca(OH)₂ n=2 for OH⁻). The calculator works in two modes: <strong>(1) Yes (neutralized at equivalence)</strong> — enter 3 of 4 fields (acid C, acid V, base C, base V) and the calculator solves for the 4th. <strong>(2) No / Not sure</strong> — enter all 4 fields and the calculator computes excess (acid or base), excess concentration in the total mixture volume, and the resulting pH. Strength options for both acid and base (strong / weak / unknown) modify the qualitative pH at equivalence: strong+strong = 7; weak acid + strong base ≈ 8-10 (basic salt hydrolysis); strong acid + weak base ≈ 4-6 (acidic salt hydrolysis). Multi-unit input: concentration in M / mM / µM / N (normality); volume in mL / L / µL.

Standard analytical chemistry references; APHA Standard MethodsIUPAC Compendium of Chemical Terminology (Gold Book)Skoog, West, Holler & Crouch — Fundamentals of Analytical Chemistry (10th ed.)

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Acid-base titration calculations assume fast equilibrium and complete reaction — accurate for strong-strong systems, approximate for weak. For weak acids/bases, the calculator provides qualitative pH ranges based on strength category; for exact pH use Henderson-Hasselbalch with the appropriate Ka or Kb. Polyprotic acids (H₂SO₄ n=2, H₃PO₄ n=3) have multiple equivalence points each requiring separate analysis. Indicator selection: match indicator pKa to equivalence pH within ±1 unit (methyl orange for acidic, bromothymol blue for neutral, phenolphthalein for basic). For research-grade titration use a pH meter, automatic titrator, or gravimetric protocol. References: Skoog, West, Holler & Crouch — Fundamentals of Analytical Chemistry (10th ed., 2022); APHA Standard Methods (24th ed.); IUPAC Compendium of Chemical Terminology.