Titration Simulator — Acid-Base Curve, Indicators & Calculator

A note on units: concentrations are labelled M in the compact controls and written as mol dm⁻³ in the worked equations. They are the same unit — 1 M = 1 mol dm⁻³ = 1 mol L⁻¹. Volumes are in mL throughout and converted to litres inside every calculation.

This simulator performs a complete acid–base titration. You choose what sits in the conical flask (the analyte), what sits in the burette (the titrant), their concentrations, the analyte volume and the indicator. As titrant is delivered, the flask colour changes according to the real transition range of the chosen indicator and the pH curve is plotted live beside the apparatus.

The pH is not interpolated from a stored curve. At every volume the simulator solves the full charge-balance equation of the mixture numerically, so buffer regions, dilution, weak-acid and weak-base behaviour and diprotic systems all emerge from the chemistry rather than being hard-coded. Four modes are available: Simulate, Explore, Practice and Quiz.

The two setup bars sit directly below the apparatus so the bench is the first thing you see, and they mirror a real one:

1. In the flask — pick the analyte, then set its concentration (0.01–1.00 M) and volume (5–50 mL). This is the solution being analysed.
2. In the burette — pick the titrant and its concentration. The titrant list filters automatically: choose an acid analyte and you are offered bases, and vice versa.
3. Indicator — choose from six indicators, or select None to see the uncoloured solution and rely on the curve alone.

Each quantity has a slider for quick exploration and a numeric box for exact values. Type a decimal straight into the box — a standardised solution of 0.1035 M, or a pipetted 23.75 mL aliquot, is entered exactly as written and is used at full precision in every calculation. The − and + buttons nudge by 0.01 M or 1 mL without losing the digits you typed, and the arrow keys do the same (hold Shift for a ten-fold step). Out-of-range entries are clamped to the slider limits.

Changing any setup control resets the burette to zero and clears the curve, exactly as refilling the burette would.

The control bar along the bottom of the canvas delivers titrant:

• Drop — delivers a single 0.05 mL drop. Use this near the end point, where one drop can swing the pH by several units.
• +1 mL — delivers 1.00 mL at once, for covering ground early in the titration.
• Hold either button instead of tapping repeatedly — the tap stays open and the flow speeds up the longer you hold, exactly like easing a real stopcock. Release, or slide your finger off the button, to close it instantly.
• Run — opens the stopcock and delivers continuously, slowing as the curve steepens, and closes the tap by itself at the colour change with a small random overshoot for reaction time. That makes it a genuine rough titration: near the right answer, but never the same twice. If the indicator never reaches its transition range, Run stops at the burette limit instead. Press again to pause early.
• Record titre — adds the current run to the Results Table below the canvas and refills the burette for the next run.
• Report — builds a printable A4 test report from your recorded titres and opens it for your browser’s Save-as-PDF. The same button also sits at the bottom of the Results Table. It stays greyed out until you have actually run something — either titrant delivered or at least one titre recorded — because there is nothing to certify before that.
• Reset — empties the flask, refills the burette and clears the plotted curve.
• Calculations — opens a step-by-step working of the current state, with the mole arithmetic set out in full.

A real titration takes dozens of drops near the end point, so hold rather than tap: press +1 mL to run quickly to within a millilitre of the expected titre, then hold Drop and watch for the first permanent colour change.

Right-clicking the canvas offers Export PNG, Export CSV (the full volume–pH dataset) and Reset.

The Display panel at the top-right of the canvas toggles graph layers and bench equipment. It starts collapsed so it never covers the curve — click the eye to open it.

• Grid — graph gridlines.
• Equivalence — a vertical marker at the calculated equivalence volume and a horizontal marker at the pH there.
• Indicator band — shades the pH range over which the chosen indicator changes colour. This is the single most useful layer: if the band crosses the steep section, the indicator is suitable.
• dpH/dV — overlays the first derivative. Its peak sits at the equivalence point, which is how the point is located when no indicator is used.
• Half-equiv. — marks the half-equivalence volume. For a weak acid the pH there equals the pK_a, which is how pK_a is measured experimentally.
• Labels — axis numbers and point annotations.
• Stirrer — swaps the white tile for a magnetic stirrer plate and stir bar. Off by default: the standard school method is to swirl the conical flask by hand over a white tile, which is why the flask is conical and why the tile is there. Magnetic stirring is the norm in potentiometric and automated titrations, where both hands are needed and the mixing rate must be reproducible.
• Sound — mutes the drip and end-point tones.

A real burette is filled to near zero, not exactly zero, so every run starts from a different initial reading and the titre is a subtraction: titre = final reading − initial reading. Both are recorded to two decimal places, the second decimal being an estimate between the 0.1 mL graduations.

Press Record titre on the canvas to add the current run to the Results Table. The table applies the standard rules automatically: the first run is marked rough and never averaged; runs agreeing within 0.10 mL are marked concordant; anything outside that cluster is marked discard. The mean is taken over the concordant set only.

Each reading carries an uncertainty of ±0.05 mL, and because a titre is the difference of two readings the absolute uncertainty on the titre is ±0.10 mL. The table converts that to a percentage, which is why titres are designed to land in the 20–30 mL range — the same ±0.10 mL is 0.4% of 25 mL but 2% of 5 mL.

A titration exists to measure something you do not know. With the concentration sitting on a slider the exercise is circular, so the Unknown sample button beside the indicator selector hides it.

Set everything up first — analyte, titrant, its concentration, your aliquot volume — then switch Unknown on. Sealing the sample locks all of those, because changing any of them would invalidate the concealed concentration and push the titre outside the burette. The indicator stays free to choose, since it cannot affect the sample. A banner under the reagent bar explains the locked state while it is active.

Switching it on picks a concealed concentration that gives a sensible 15–40 mL titre, locks the setup, and blanks every readout derived from it — equivalence volume, equivalence pH, indicator end point and titration error all show ?, and the equivalence markers disappear from the curve. What remains is exactly what an experimenter can observe: the burette reading, the titre and the colour change.

While a sample is sealed the Results Table moves directly beneath the canvas, so you can record a titre, check concordance and enter your answer without scrolling past setup controls you can no longer change. It returns to its usual place below the readouts when you unseal.

Work as you would at the bench: run a rough titration, then repeat until three titres agree within 0.10 mL. Once the Results Table has a concordant set, an answer box appears. Compute the concentration from the mean titre and enter it. Your answer is graded against the true value: within 1% is the precision a careful titration delivers, within 5% suggests a slip in the mean or the mole ratio, and anything larger usually means the mole ratio was wrong or millilitres were never converted to litres.

Four solvers, each showing full working with units: Unknown concentration from a titre, Titre required to plan a titration, Percentage purity of an impure solid, and Back titration for samples that are insoluble or slow to react.

Set the mole ratio from your balanced equation — 1:1 for HCl and NaOH, 1:2 for H₂SO₄ against NaOH or Na₂CO₃ against HCl. Getting this ratio wrong is the single most common error in titration calculations. Back titration needs two ratios: sample to excess reagent, and excess reagent to back-titrant, and the second box appears only in that mode.

Six cards sit under the canvas. Volume added and pH track the current state. Equivalence at and pH at equivalence are calculated from the setup and do not depend on how far you have titrated.

Indicator end point is the volume at which the chosen indicator reaches the midpoint of its colour change — what you would actually record. Titration error is the percentage difference between that end point and the true equivalence volume, colour-coded green below 0.5%, amber below 2% and red above. This is the quantitative version of “is this the right indicator?”

All four of these show — until you have delivered some titrant, and the equivalence markers and the ghosted future curve stay off the graph until then. Otherwise the equivalence volume is sitting on screen before you start, and the exercise becomes “titrate to 25 mL” rather than “watch for the colour change”. Reset clears them again.

Five categories of concept cards: Basics (what a titration is, apparatus, the four curve types), Curves (shape, steep section, buffer region, half-equivalence), Indicators (transition ranges, why phenolphthalein suits weak acids, the double end point of carbonate), Calculations (mole ratios, back-titration, the Henderson–Hasselbalch equation) and Technique & Errors (rinsing, parallax, the rough-then-accurate method, concordant titres). Every card with a formula carries a worked example.

Practice mode generates randomised problems across eight types: unknown concentration, equivalence volume, pH at a stated volume, pK_a from half-equivalence, indicator selection, mole ratio, percentage purity and titre calculation. Answer by typing a number or picking an option, then click Check. Show Solution lays out the full working.

Quiz mode presents 5 randomly drawn multiple-choice questions. After the fifth you get a score, a 1–5 star rating and a per-question breakdown with explanations.

Report on the canvas dock, or Export Test Report at the foot of the Results Table, builds a printable A4 certificate and opens it for your browser’s Save-as-PDF (Ctrl/Cmd + P). Both buttons stay greyed until you have actually run something.

The report carries six sections: method and reagents with strengths and pK_a values; every burette reading with its run tagged rough, concordant or discarded; the results, including mean titre, absolute and percentage uncertainty and the calculated concentration; the mole working set out line by line; the titration curve redrawn on a light background so it prints legibly; and an indicator assessment graded against the 0.5% limit, with the model’s assumptions and a signature block.

If no titres are recorded it falls back to the run currently on the bench. In unknown-sample mode it deliberately omits the equivalence markers and the nominal concentration, so exporting cannot leak the answer.

• The equivalence point of a weak acid + strong base titration is not pH 7 — it is basic, because the salt formed hydrolyses. Set up ethanoic acid against NaOH and read the value.
• Likewise a weak base + strong acid equivalence point is acidic. Only strong + strong gives exactly 7.
• At the half-equivalence point of a weak acid, pH = pK_a. Turn on the Half-equiv. layer and check it against the reagent's quoted pK_a.
• A weak acid titrated with a weak base has no steep section worth the name — no indicator works, which is why it is never done in practice. Try ethanoic acid against ammonia to see why.
• Diluting both solutions equally does not move the equivalence volume, but it does flatten the steep section and shrink the range of usable indicators.
• Sodium carbonate against HCl gives two end points — phenolphthalein catches the first, methyl orange the second, and the second volume is double the first.
• Use Drop rather than +1 mL within a millilitre of the end point. Overshooting is the single most common practical error.
• On a diprotic analyte the indicator decides which end point you find. Sodium carbonate against HCl gives about 23.5 mL with phenolphthalein but about 50 mL with methyl orange — roughly double. Titres differing by a factor of two across runs almost always mean the indicator, not the technique.