Chemistry · Lesson

Acid-base titration curves and indicators

Use titrant amounts to locate stoichiometric equivalence. Read a complete strong-acid/base model curve and distinguish an observed endpoint from chemical equivalence.

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By the end, you can

Calculate equivalence from moles and stoichiometry.
State why equivalence pH depends on the acid/base system.
Choose an endpoint signal suited to the actual curve and uncertainty.

Equivalence is a stoichiometric condition

A titration adds measured increments of a reacting solution to a sample and follows a specified signal. The equivalence point is where the titrant amount matches the reaction’s stoichiometric requirement. The detected endpoint is an observation, such as a selected color or instrument response, intended to locate that stage.

Our original ideal aqueous model uses 25.00 mL of 0.1000 mol L⁻¹ fully ionized monoprotic acid and 0.1000 mol L⁻¹ strong-base titrant at 25 °C. It assumes additive volumes and the ordinary water approximation K_w = 1.00 × 10⁻¹⁴ with c° = 1 mol L⁻¹. Initial acid is 0.002500 mol, so the 1:1 equivalence volume is 25.00 mL.

Keep water and charge balance across equivalence

The calculated strong/strong curve includes water throughout. Define dimensionless d = (n_acid − n_base)/(V_totalc°), h = [H⁺]/c° and o = [OH⁻]/c°, with c° = 1 mol L⁻¹. Charge balance gives h − o = d, and the chosen ideal water model gives h×o = K_w° = 10⁻¹⁴. The positive solution is h = (d + √(d² + 4K_w°))/2.

The curve therefore passes smoothly through the dilute neutral point at equivalence rather than stitching incompatible zero-water formulas at the boundary. The displayed model pH is −log₁₀h, and the physical hydrogen-ion concentration is hc°. Outside a very narrow equivalence region, excess-acid or excess-base approximations give similar values. This ideal curve is calculated, not measured.

A strong-acid/base model includes water across equivalence

Calculated ideal-model pH

Added strong-base volume / mL

Selected calculated curve values
— Charge and water balance model

Underlying data

Added strong-base volume / mL	Calculated ideal-model pH
20	1.954242509404147 · Selected calculated curve values
25	7 · Selected calculated curve values
30	11.958607314894325 · Selected calculated curve values

Original calculated ideal aqueous model: 25.00 mL × 0.1000 mol L⁻¹ strong monoprotic acid, 0.1000 mol L⁻¹ strong-base titrant, 25 °C, additive volumes, c° = 1 mol L⁻¹ and teaching K_w° = 1.00 × 10⁻¹⁴. The curve solves charge plus water balance at every dose, with a stable positive-root calculation after equivalence. Markers at 20, 25 and 30 mL show calculated values; this is not a measured titration or a weak-acid curve.

A weak system has a different equivalence mixture

For a separate hypothetical weak-acid/strong-base titration with the same initial amounts, K_a° = 1.00 × 10⁻⁵ and the same 25 °C water approximation, equivalence contains formal conjugate-base concentration 0.05000 mol L⁻¹. K_b° = K_w°/K_a° = 1.00 × 10⁻⁹ gives a reduced hydrolysis estimate pH ≈ 8.85. Equivalence is therefore not universally pH 7.

At half-equivalence in the appropriate weak-acid buffer regime, formal HA and A⁻ amounts are equal and pH ≈ pK_a ≈ 5.00. That shortcut assumes the relevant equilibrium and activity corrections are small. The separate weak example is not the strong/strong curve drawn here.

A finite indicator transition is an observed signal

A suitable acid–base indicator changes its observed form ratio over a range near the useful part of the titration curve. In an original hypothetical indicator model with pK_a≈7.00, activity ratios a_In⁻/a_HIn from 0.1 to 10 correspond to approximate pH 6–8. These are supplied illustrative visibility thresholds, not a verified named-indicator range.

An endpoint may differ from equivalence because of the indicator range, chosen signal, mixing, volume resolution and other uncertainties. Choose the detection method for the actual acid/base curve and required accuracy; weak/weak systems may lack a sharp pH jump. A universal instant color change or one fixed equivalence pH is not an adequate model.

Worked examples

Locate equivalence and a pre-equivalence point

Use the original strong/strong model. Find the equivalence volume and approximate pH after 20.00 mL of titrant.

Initial acid = 0.02500 L × 0.1000 mol L⁻¹ = 0.002500 mol.
For 1:1 reaction, equivalence needs 0.002500/0.1000 L = 25.00 mL base.
At 20.00 mL base, 0.002000 mol is added, leaving 0.000500 mol acid excess.
Total additive volume is 45.00 mL, giving excess-acid concentration about 0.0111111 mol L⁻¹.
Water is negligible at this point; normalized pH is approximately 1.954.

Equivalence volume: 25.00 mL. At 20.00 mL, pH ≈ 1.954 under the ideal model; at strong/strong equivalence its dilute neutral estimate is about 7.00 at 25 °C.

Explain a basic weak-acid equivalence mixture

For the separate hypothetical weak HA titration, use K_a°=1.00×10⁻⁵, approximate K_w°=1.00×10⁻¹⁴ and equivalence conjugate-base formal concentration 0.05000 mol L⁻¹.

K_b° = K_w°/K_a° = 1.00×10⁻⁹.
In the stated reduced ideal hydrolysis model, let y=[OH⁻]/c° and solve y²/(0.05000−y)=1.00×10⁻⁹.
The nonnegative root gives [OH⁻]≈7.07057×10⁻⁶ mol L⁻¹ and pOH≈5.15055.
Using approximate pK_w=14.00 gives pH≈8.85.

The conjugate base hydrolyses, producing a basic equivalence estimate pH≈8.85 in this separate reduced model. Stoichiometric equivalence does not require neutral pH.

Try it yourself

What defines chemical equivalence in a titration?
Show the answer and reasoning
The stoichiometrically matching titrant amount.
It follows the reaction and sample inventory rather than a universally fixed pH.
Is an observed color endpoint necessarily identical to equivalence?
Show the answer and reasoning
No.
The finite indicator response and measurement uncertainties can shift the detected stage.
Why is the hypothetical weak-acid/strong-base equivalence mixture basic?
Show the answer and reasoning
Its conjugate base reacts with water to produce OH⁻.
The resulting equilibrium differs from the strong/strong neutral model.
When does half-equivalence give pH≈pK_a for a weak acid?
Show the answer and reasoning
In the relevant conjugate-pair regime with appropriate activity and equilibrium approximations.
Equal formal amounts support the shortcut only when they adequately represent the equilibrium ratio.

What to carry forward

Find stoichiometric equivalence from moles, volume and the written reaction.
Keep observed endpoints distinct from chemical equivalence.
Retain water and charge balance when drawing a curve across equivalence.
Equivalence pH and indicator choice depend on the actual system.

References

Teaching resources and reference material supporting this lesson’s explanations and examples.