How this calculation works
The curve changes steeply near stoichiometric equivalence because the excess acid or base becomes very small. Simply taking the logarithm of a zero excess would fail precisely at that point. Including water autoionization keeps the ideal charge-balance calculation defined.
D = signed excess acid concentration; [H+] = (D + sqrt(D² + 4Kw))/2, evaluated stably; pH = −log10[H+]A worked example
Twenty-five millilitres of 0.1 M strong acid require twenty-five millilitres of 0.1 M strong base at equivalence. At pKw fourteen the ideal pH there is exactly seven. At 12.5 mL added base, the excess acid concentration is about 0.03333 M and the ideal pH is about 1.4771. At 37.5 mL the base is in excess and the pH is about 12.3010. These checkpoints explain the two sides of the plotted jump.
Good to know
Ideal full dissociation, additive volumes and a single acid/base equivalent per mole; no activity correction, weak buffer, indicator or real endpoint prediction. This is a calculation exercise, not a laboratory procedure or handling guide. Real titration preparation, chemical compatibility and safety need appropriate supervision and protocols.
Reference: OpenStax — acid-base titration calculations (opens in a new tab) ↗
What this model answers
The curve changes steeply near stoichiometric equivalence because the excess acid or base becomes very small. Simply taking the logarithm of a zero excess would fail precisely at that point. Including water autoionization keeps the ideal charge-balance calculation defined.
This page covers a strong monoprotic acid with a strong monovalent base, or the reverse. A weak-acid buffer region and a polyprotic sequence require different equilibrium equations. They cannot be reproduced by changing only the starting concentration here.
The Molarity calculator converts entered solute amounts and solution volume into concentration. Titration additionally tracks reacting equivalents and dilution as the opposite titrant is added; starting molarity alone does not supply the whole curve. For one weak dissolved species in pure water rather than a strong titration, the Weak acid or base equilibrium with water autoionization calculator retains water autoionization in its charge balance.
Measure the right inputs
Concentrations are moles per litre and volumes are millilitres. Consistent volume units cancel in the excess-concentration ratio, while the final total volume accounts for dilution. Titrant must be the opposite strong species to the solution initially in the vessel.
Water pKw is an explicit input. The default fourteen corresponds to the familiar ideal neutral pH of seven. Changing pKw changes the model’s neutral pH to half that value; the calculator does not infer a temperature or choose a water constant from laboratory conditions.
Read the result in context
Equivalence volume comes from equal reacting amounts, independent of the plotted endpoint. The selected addition can lie outside the graph range; its metric is still calculated, and the table includes it. Widen the graph to see it on the curve.
Near equivalence, a stable quadratic expression avoids subtracting nearly equal floating-point numbers. Far from equivalence, the result approaches the usual excess-strong-acid or excess-strong-base estimate. Concentrated real solutions may differ because ideal activities are an assumption.
Work through the numbers
Twenty-five millilitres of 0.1 M strong acid require twenty-five millilitres of 0.1 M strong base at equivalence. At pKw fourteen the ideal pH there is exactly seven.
At 12.5 mL added base, the excess acid concentration is about 0.03333 M and the ideal pH is about 1.4771. At 37.5 mL the base is in excess and the pH is about 12.3010. These checkpoints explain the two sides of the plotted jump.
Where the model stops
Ideal full dissociation, additive volumes and a single acid/base equivalent per mole; no activity correction, weak buffer, indicator or real endpoint prediction.
This is a calculation exercise, not a laboratory procedure or handling guide. Real titration preparation, chemical compatibility and safety need appropriate supervision and protocols.
A few questions, answered
Why is equivalence not always pH seven here?
Its ideal pH equals pKw/2. Seven follows when the entered pKw is fourteen.
Can I use acetic acid?
No. A weak acid needs its dissociation equilibrium and buffer chemistry, which are outside this strong-species model.