Analyse titration curves for strong-strong, strong-weak and weak-strong combinations to identify the equivalence point, distinguish it from the end point, and justify indicator selection

What this dot point is asking

NESA wants you to recognise and sketch the four titration curve shapes (strong-strong, strong-weak, weak-strong, weak-weak), identify the equivalence point on each, calculate or estimate the pH at equivalence, distinguish equivalence point from end point, and choose an indicator whose colour-change range falls on the steep portion of the curve. This consolidates the chemistry from reactions of acids, strong vs weak acids and bases, and conjugate acid-base pairs, and links directly to the Module 5 dot point on titrations and indicators.

The answer

Equivalence point vs end point

• The equivalence point is the point at which stoichiometrically equivalent amounts of acid and base have been combined. It is a property of the chemistry.
• The end point is the point at which the indicator changes colour. It is a property of the indicator chosen.

A good indicator has an end point that coincides (within experimental tolerance) with the equivalence point. Indicator selection is the art of matching colour-change range to equivalence pH.

The four curves at a glance

For a 0.100 mol/L analyte titrated with 0.100 mol/L titrant from a burette, with 25.0 mL of analyte:

Strong acid + strong base

Example: 0.100 mol/L $HCl$ titrated with 0.100 mol/L $NaOH$.

• Start: $[H^+] = 0.100$, $pH = 1.00$.
• Pre-equivalence: pH rises slowly as excess $H^+$ is consumed.
• Near equivalence: pH jumps almost vertically from about 4 to about 10 within one drop of titrant.
• Equivalence: pH = 7.00. Only $Na^+$ and $Cl^-$ remain (both spectators).
• Post-equivalence: pH rises gradually, approaching the pH of the excess strong base.

The very wide vertical section (about 6 pH units) tolerates almost any common indicator with a range between 4 and 10.

Weak acid + strong base

Example: 0.100 mol/L $CH_3COOH$ titrated with 0.100 mol/L $NaOH$.

• Start: weak acid alone, $pH \approx 2.87$ (from $\sqrt{K_a c}$).
• After a small addition of $NaOH$, a buffer forms ($CH_3COOH$ + $CH_3COO^-$). pH rises slowly through the buffer plateau.
• Half-equivalence point (half the titrant volume to equivalence): $[CH_3COOH] = [CH_3COO^-]$, so $pH = pK_a = 4.74$. This is the most reliable way to read $pK_a$ off a curve.
• Equivalence: all weak acid has been converted to its conjugate base. The conjugate base hydrolyses water, giving $pH \approx 8.5$ to 9 (basic).
• Post-equivalence: pH approaches that of the excess strong base.

The steep section here spans roughly pH 7 to pH 11, so phenolphthalein (8.3 to 10.0) is the standard choice. Methyl orange would change too early.

Strong acid + weak base

Example: 0.100 mol/L $HCl$ titrated with 0.100 mol/L $NH_3$.

• Start: $pH = 1.00$.
• Pre-equivalence: $H^+$ is consumed; pH rises gradually.
• Equivalence: all $H^+$ has reacted to form $NH_4^+$ at about 0.050 mol/L. The conjugate acid hydrolyses, giving $pH \approx 5.1$ (acidic). Calculation: $K_a(NH_4^+) = K_w / K_b = 5.56 \times 10^{-10}$, $[H^+] = \sqrt{K_a c} = 5.3 \times 10^{-6}$, $pH = 5.28$.
• Post-equivalence: buffer of $NH_4^+$/$NH_3$ forms; pH rises to a plateau near $pK_a(NH_4^+) = 9.26$ at the half-past-equivalence point if you continue adding base. (Most HSC questions stop at equivalence.)

The steep section spans roughly pH 3 to pH 7. Methyl orange (3.1 to 4.4) or methyl red (4.4 to 6.2) work. Phenolphthalein would change too late.

Weak acid + weak base

The steep section is short or absent because both sides resist pH change. The equivalence pH depends on the relative $K_a$ of the cation and $K_b$ of the anion: if $K_a > K_b$, slightly acidic; if $K_b > K_a$, slightly basic; if equal, exactly 7.

For accuracy, do not use indicators here. Use a pH probe and read the inflection point off the curve.

Why indicator choice matters

An indicator is itself a weak acid: $HIn \rightleftharpoons H^+ + In^-$, with the two forms different colours. Its colour change ($HIn$ to $In^-$) is half-complete at $pH = pK_{a,HIn}$ and effectively complete over $\pm 1$ unit. For a sharp end point, this range must lie within the steep vertical portion of the titration curve. Outside that portion, the colour change is gradual and the end point is imprecise.

Worked example

A 25.0 mL portion of 0.100 mol/L formic acid ($HCOOH$, $K_a = 1.8 \times 10^{-4}$) is titrated with 0.100 mol/L $NaOH$. Calculate the pH (a) at the start, (b) at the half-equivalence point, (c) at equivalence, and (d) recommend an indicator.

(a) Start. Weak acid alone. $[H^+] \approx \sqrt{K_a c} = \sqrt{1.8 \times 10^{-5}} = 4.24 \times 10^{-3}$ mol/L, $pH = 2.37$.

(b) Half-equivalence. $[HCOOH] = [HCOO^-]$, so $pH = pK_a = -\log_{10}(1.8 \times 10^{-4}) = 3.74$.

(c) Equivalence. All acid converted to $HCOO^-$, total volume 50.0 mL, so $c(HCOO^-) = 0.0500$ mol/L. $K_b = K_w/K_a = 5.56 \times 10^{-11}$. $[OH^-] \approx \sqrt{K_b c} = 1.67 \times 10^{-6}$, $pOH = 5.78$, $pH = 8.22$.

(d) Indicator. Equivalence pH 8.22 lies just inside the phenolphthalein range (8.3 to 10.0). Phenolphthalein is acceptable; thymol blue (8.0 to 9.6) would also work and might give a slightly sharper transition.

Common traps

Equating equivalence point with pH 7. True only for strong-strong. Weak acid plus strong base equivalence is basic; weak base plus strong acid equivalence is acidic.

Mixing up equivalence point and end point. They should coincide, but they are conceptually distinct. Equivalence is set by stoichiometry; end point is set by the indicator.

Using phenolphthalein on a strong acid plus weak base titration. The equivalence pH is around 5; phenolphthalein would change at pH 8 to 10, far past equivalence. Use methyl orange or methyl red.

Forgetting the dilution at equivalence. When 25.0 mL of acid is neutralised by 25.0 mL of base, the total volume is 50.0 mL. The conjugate ion concentration is half the original acid concentration.

Calling the buffer plateau "flat". It is gradually rising, not flat. The buffer resists pH change but does not freeze it.

Trying to titrate a weak acid against a weak base. No sharp jump means no reliable indicator end point. Use a pH probe.

In one sentence

A titration curve plots pH against titrant volume; the steep vertical region brackets the equivalence point (pH 7 for strong-strong, basic for weak acid plus strong base, acidic for strong acid plus weak base, no clear jump for weak-weak), and a usable indicator is one whose colour-change range falls inside that steep region, so that the end point (where the indicator changes colour) coincides with the stoichiometric equivalence point.