Endpoint vs Equivalence Point: The Difference in Titrations

You add sodium hydroxide to an acid, watching the solution carefully. Suddenly, the indicator changes colour. Have you added exactly enough base to react with all the acid, or has the colour changed slightly before or after that point?

These are two different events. The equivalence point is the theoretical point at which the acid and base have reacted in the exact mole ratio given by the balanced chemical equation. The endpoint is the experimentally observed point at which the indicator changes colour. A good titration aims to make these points as close together as possible, but they are not automatically identical.

Understanding the difference means separating what the reaction requires from what your eyes detect in the laboratory.

01Equivalence point vs endpoint: the essential difference

Imagine titrating hydrochloric acid with sodium hydroxide. You add the sodium hydroxide from a burette, one small volume at a time, into a conical flask containing the acid.

The reaction is:

\[
\ce{HCl + NaOH -> NaCl + H2O}
\]

The balanced equation tells you that one mole of hydrochloric acid reacts with one mole of sodium hydroxide.

At the equivalence point, the amount of sodium hydroxide added is exactly enough to react with all the hydrochloric acid originally present.

The endpoint is different. If you add an indicator such as phenolphthalein to the flask, it changes from colourless to pale pink when the solution enters its colour-transition range. You observe this colour change and stop adding the sodium hydroxide.

That observation is the endpoint.

The distinction is simple:

• Equivalence asks: Have the reacting substances been added in the correct mole ratio?
• Endpoint asks: Has the indicator changed colour enough for us to recognise the end of the titration?

An indicator does not count molecules or measure moles. It responds to the chemical conditions in the solution, particularly its pH.

02Establish equivalence using reaction stoichiometry first

Before considering indicator colours or pH, establish how much titrant is theoretically required.

This is the most important decision in a titration calculation. Do not assume that equal volumes mean equal reacting amounts.

Consider hydrochloric acid reacting with sodium hydroxide:

\[
\ce{HCl + NaOH -> NaCl + H2O}
\]

The mole ratio is \(1:1\). Therefore, at equivalence:

\[
n(\ce{HCl})=n(\ce{NaOH})
\]

The amount of substance is calculated using:

\[
n=cV
\]

where:

• \(n\) is the amount in moles (mol),
• \(c\) is the concentration in \(\mathrm{mol\,L^{-1}}\),
• \(V\) is the volume in litres (L).

Suppose the flask contains \(25.00\ \mathrm{mL}\) of \(0.1000\ \mathrm{mol\,L^{-1}}\) hydrochloric acid. You titrate it using \(0.1000\ \mathrm{mol\,L^{-1}}\) sodium hydroxide.

The initial amount of hydrochloric acid is:

\[
n=cV
\]

\[
=0.1000\times0.02500
\]

\[
=2.500\times10^{-3}\ \mathrm{mol}
\]

Because the reaction ratio is \(1:1\), you need the same number of moles of sodium hydroxide.

At \(0.1000\ \mathrm{mol\,L^{-1}}\), this requires:

\[
V=\frac{n}{c}
\]

\[
=\frac{2.500\times10^{-3}}{0.1000}
\]

\[
=0.02500\ \mathrm{L}
=25.00\ \mathrm{mL}
\]

The theoretical equivalence volume is therefore \(25.00\ \mathrm{mL}\).

Notice what this calculation tells you: the reaction’s stoichiometry determines the equivalence volume. The indicator has not entered the calculation at all.

What if the mole ratio is not 1:1?

This is where students can make a costly mistake.

Consider sulfuric acid reacting with sodium hydroxide:

\[
\ce{H2SO4 + 2NaOH -> Na2SO4 + 2H2O}
\]

One mole of sulfuric acid reacts with two moles of sodium hydroxide.

The equivalence condition is therefore:

\[
n(\ce{NaOH})=2n(\ce{H2SO4})
\]

You cannot simply set the two mole amounts equal. The balanced equation determines the relationship.

03Why does the indicator change colour at a different point?

Now consider what happens as you approach equivalence.

At first, the solution in the flask contains excess acid. As sodium hydroxide is added, it reacts with the acid, reducing the amount remaining.

Near equivalence, a very small additional volume of sodium hydroxide can produce a substantial change in pH. This happens because the solution is moving through the steep section of the titration curve.

An indicator responds to this pH change.

Indicators have a transition range, not one exact pH

An acid-base indicator is usually a weak acid or weak base whose different forms have different colours.

For a simplified indicator equilibrium:

\[
\ce{HIn <=> H+ + In-}
\]

The two forms, \(\ce{HIn}\) and \(\mathrm{In}^{-}\), have different colours.

As the pH changes, the balance between these forms changes. Eventually, one colour becomes dominant enough for the human eye to recognise the change.

This occurs over a transition range rather than at one perfectly precise pH.

Some common indicators are:

The endpoint depends on the indicator’s transition range and the pH change occurring during the titration.

A suitable indicator changes colour within the steep section of the titration curve. This keeps the endpoint close to the equivalence point.

A poor choice might change colour well before or after equivalence, producing a systematic error in the measured volume.

The crucial distinction: equivalence is not necessarily pH 7

You might be tempted to assume that the indicator should always change colour at pH 7 because that is neutral.

That is incorrect.

The equivalence pH depends on the acid and base involved, as well as the solution conditions. For example, a weak acid titrated with a strong base has a basic solution at equivalence because its conjugate base reacts with water.

The equivalence point can therefore occur above pH 7.

This is why phenolphthalein is often suitable for a weak-acid-strong-base titration, even though its transition range is above pH 7.

For a deeper explanation of the chemistry behind this, see Why the Equivalence Point Is Not Always pH 7.

04What happens when the endpoint is not the equivalence point?

Suppose the theoretical equivalence volume is \(25.00\ \mathrm{mL}\), but the indicator changes colour when the burette reading shows \(25.10\ \mathrm{mL}\).

The student has added \(0.10\ \mathrm{mL}\) more sodium hydroxide than the stoichiometric amount required.

The endpoint has occurred after equivalence.

This is called a positive titration error when the measured titrant volume is greater than the true equivalence volume.

If the indicator changes colour at \(24.90\ \mathrm{mL}\), the student stops too early. The measured volume is below the equivalence volume, producing a negative titration error.

05How do you choose an appropriate indicator?

The aim is not to find an indicator that changes colour exactly at the equivalence point. Instead, choose one whose transition range lies within the steep pH change near equivalence.

Consider three different titrations.

These are typical choices, not universal rules. The actual titration curve and the width of its steep region determine suitability.

A useful way to think about indicator selection is to ask:

1. What is the balanced reaction and its mole ratio?
2. Where is the theoretical equivalence point?
3. What pH occurs near equivalence?
4. Which indicator changes colour within the steep region?

The order matters. Establish the stoichiometry first, then consider the pH behaviour, and only then select the indicator.

Remember that the endpoint is an experimental signal, not proof that the reaction has reached exact stoichiometric equivalence.

06Improving the accuracy of an endpoint measurement

Even with a suitable indicator, technique affects how closely the endpoint matches equivalence.

A few practical choices make a substantial difference:

• Rinse the burette with the titrant before filling it, so residual water does not dilute the solution.
• Remove air bubbles from the burette tip before taking the initial reading.
• Read the bottom of the meniscus at eye level for a colourless solution.
• Swirl the conical flask continuously so the titrant mixes evenly.
• Add titrant slowly as the endpoint approaches.
• Use dropwise addition near the colour change.
• Stop at the first persistent colour change that meets the method’s stated endpoint criterion.

For phenolphthalein, this is commonly a very faint pink that persists briefly, rather than a strong pink colour.

Adding several extra drops after the colour has appeared is not harmless. It can move the measured endpoint further beyond equivalence.

A subtle limitation: a close endpoint does not guarantee an accurate concentration

Suppose the indicator endpoint is consistently \(0.10\ \mathrm{mL}\) beyond equivalence. If you repeat the titration several times, you might obtain almost identical readings.

Those readings are precise in the sense that they are closely grouped. However, they are systematically too high.

This illustrates the difference between precision and accuracy:

• Precision describes how closely repeated measurements agree.
• Accuracy describes how close a measurement is to the true value.

A consistent endpoint error can make a set of concordant titres precise but not accurate.

In practical titration work, a rough trial is often followed by more careful titrations, adding titrant dropwise near the expected endpoint. This reduces the risk of overshooting and helps produce concordant results.

07A reliable method for HSC titration questions

When a question mentions both an endpoint and an equivalence point, keep the experimental observation separate from the theoretical chemistry.

Use this sequence:

A common exam trap is to treat the indicator colour change as the definition of equivalence. It isn’t.

Another is to assume that equal volumes of acid and base must mean equivalence. That only works under particular conditions, including equal concentrations and a \(1:1\) mole ratio.

If a question gives an indicator and asks you to explain why it is suitable, don’t simply state that it changes colour near pH 7. Explain that its transition range overlaps the steep pH change around the theoretical equivalence point.

The calculation and the experimental observation answer different questions. Keep them separate.

08Questions and solutions

The following questions move from identifying the two points to evaluating actual titration results. All numerical data are illustrative. Unless stated otherwise, assume additive solution volumes and ordinary aqueous acid-base behaviour.

Question 1

A student titrates \(20.00\ \mathrm{mL}\) of \(0.1000\ \mathrm{mol\,L^{-1}}\) hydrochloric acid using \(0.1000\ \mathrm{mol\,L^{-1}}\) sodium hydroxide.

The indicator changes colour after \(20.15\ \mathrm{mL}\) of sodium hydroxide has been added.

a) Calculate the theoretical equivalence volume.

b) Identify the observed endpoint volume.

c) State whether the endpoint occurred before or after equivalence.

Solution 1

a) The theoretical equivalence volume is \(20.00\ \mathrm{mL}\).

The balanced equation is:

\[
\ce{HCl + NaOH -> NaCl + H2O}
\]

The mole ratio is \(1:1\).

Initial moles of hydrochloric acid:

\[
n=cV
\]

\[
=0.1000\times0.02000
=0.002000\ \mathrm{mol}
\]

The same amount of sodium hydroxide is required.

\[
V=\frac{0.002000}{0.1000}
\]

\[
\boxed{V_{\mathrm{eq}}=20.00\ \mathrm{mL}}
\]

b) The observed endpoint volume is \(20.15\ \mathrm{mL}\). This is the volume recorded when the indicator changes colour.

c) The endpoint occurs after equivalence because:

\[
20.15>20.00
\]

The student has added \(0.15\ \mathrm{mL}\) more sodium hydroxide than the theoretical amount required. The endpoint is therefore slightly beyond the equivalence point.

Question 2

A student titrates \(25.00\ \mathrm{mL}\) of ethanoic acid with \(0.1000\ \mathrm{mol\,L^{-1}}\) sodium hydroxide.

The equivalence point occurs at a pH above 7.

The student chooses bromothymol blue, which has an approximate transition range of pH 6.0-7.6.

Explain why phenolphthalein would generally be a more suitable indicator for this titration.

Solution 2

Phenolphthalein is generally more suitable because its transition range of approximately pH 8.2-10.0 overlaps the steep pH change near the equivalence point of a weak-acid-strong-base titration.

Ethanoic acid reacts with sodium hydroxide:

\[
\ce{CH3COOH + NaOH -> CH3COONa + H2O}
\]

At equivalence, the ethanoic acid has reacted in the correct \(1:1\) mole ratio. However, the ethanoate ions remaining in solution react with water, producing hydroxide ions.

\[
\ce{CH3COO^- + H2O <=> CH3COOH + OH^-}
\]

This makes the equivalence solution basic.

Bromothymol blue changes colour mainly below the expected equivalence pH. It may therefore change colour before the titration reaches the steep region around equivalence.

Phenolphthalein changes colour at a higher pH, making its transition range a better match for the sharp pH increase near equivalence.

The tempting mistake is to choose an indicator simply because its range includes pH 7. The correct choice depends on the actual pH change around equivalence, not on neutrality.

Question 3

A student titrates \(20.00\ \mathrm{mL}\) of sulfuric acid with \(0.1500\ \mathrm{mol\,L^{-1}}\) sodium hydroxide.

The sulfuric acid concentration is \(0.07500\ \mathrm{mol\,L^{-1}}\).

The student observes an indicator endpoint at \(19.80\ \mathrm{mL}\).

a) Calculate the theoretical equivalence volume.

b) Calculate the percentage titration error, using the theoretical equivalence volume as the reference.

c) Explain what the sign of the error tells you.

Solution 3

a) The theoretical equivalence volume is \(20.00\ \mathrm{mL}\).

The balanced equation is:

\[
\ce{H2SO4 + 2NaOH -> Na2SO4 + 2H2O}
\]

First, calculate the initial moles of sulfuric acid:

\[
n=cV
\]

\[
=0.07500\times0.02000
\]

\[
=0.001500\ \mathrm{mol}
\]

The mole ratio requires twice as many moles of sodium hydroxide:

\[
n(\ce{NaOH})=2(0.001500)
\]

\[
=0.003000\ \mathrm{mol}
\]

Therefore:

\[
V_{\mathrm{eq}}=\frac{0.003000}{0.1500}
\]

\[
\boxed{V_{\mathrm{eq}}=0.02000\ \mathrm{L}
=20.00\ \mathrm{mL}}
\]

b) Calculate the percentage error:

\[
\%\text{ error}
=
\frac{V_{\mathrm{endpoint}}-V_{\mathrm{eq}}}
{V_{\mathrm{eq}}}\times100
\]

\[
=\frac{19.80-20.00}{20.00}\times100
\]

\[
\boxed{-1.00\%}
\]

c) The negative error means the endpoint occurred before equivalence.

The student stopped adding sodium hydroxide when the indicator changed colour, even though some sulfuric acid had not yet reacted in the required stoichiometric ratio.

The error is not caused by the balanced equation or the concentration calculation. It arises because the observed indicator transition does not coincide exactly with the theoretical equivalence point.

Question 4

A student performs three titrations using the same acid, base, and indicator.

The theoretical equivalence volume is known to be \(25.00\ \mathrm{mL}\).

The observed endpoint volumes are:

a) Are the measurements reasonably precise?

b) Are they accurate relative to the theoretical equivalence volume?

c) Suggest a reason why the results are so consistent but systematically higher than the equivalence volume.

Solution 4

a) Yes. The measurements are reasonably precise because the three endpoint volumes are very close together.

The range is:

\[
25.21-25.19=0.02\ \mathrm{mL}
\]

The small spread indicates good agreement between repeated trials.

b) No. The measurements are systematically higher than the theoretical equivalence volume of \(25.00\ \mathrm{mL}\).

The mean endpoint volume is:

\[
\overline{V}
=
\frac{25.20+25.19+25.21}{3}
\]

\[
=25.20\ \mathrm{mL}
\]

The mean percentage error is:

\[
\%\text{ error}
=
\frac{25.20-25.00}{25.00}\times100
\]

\[
\boxed{+0.80\%}
\]

The results are precise but not accurate.

c) A likely explanation is a systematic endpoint error.

For example, the indicator may change colour slightly after the true equivalence point. If the student waits until the pink colour becomes too intense before stopping, they may consistently add excess sodium hydroxide.

Repeating the experiment improves confidence in the consistency of the readings, but it does not automatically remove a systematic error.

This is why concordant titres alone cannot prove that the measured endpoint matches equivalence.

Question 5

A student prepares two separate samples containing the same amount of hydrochloric acid. Both are titrated with the same sodium hydroxide solution.

The student uses phenolphthalein in the first titration and bromothymol blue in the second.

Both indicators produce clear, persistent colour changes, but the recorded endpoint volumes differ slightly.

The student concludes:

“The two indicators must be measuring different equivalence points because they give different volumes.”

Evaluate this conclusion.

In your response:

a) Explain whether the two titrations have different theoretical equivalence points.

b) Explain why their endpoint volumes can differ.

c) Predict what would happen if the student used an indicator whose transition range lay entirely outside the steep pH-change region.

d) Explain how the student could distinguish a genuine indicator-related bias from random experimental variation.

Solution 5

The student’s conclusion is incorrect. The two titrations have the same theoretical equivalence volume, provided the samples contain the same initial amount of hydrochloric acid and the sodium hydroxide solution has the same concentration.

However, their observed endpoint volumes can differ because the two indicators have different pH transition ranges.

a) The theoretical equivalence points are the same.

The reaction is:

\[
\ce{HCl + NaOH -> NaCl + H2O}
\]

The equivalence condition is:

\[
n(\ce{HCl})=n(\ce{NaOH})
\]

Neither the indicator’s identity nor its colour determines this mole ratio.

The same initial acid amount, titrant concentration, and balanced equation give the same theoretical equivalence volume in both experiments.

b) The endpoint volumes can differ because the indicators respond to different pH ranges.

Phenolphthalein changes colour over approximately pH 8.2-10.0, while bromothymol blue changes colour over approximately pH 6.0-7.6.

During a strong-acid-strong-base titration, the pH rises sharply near equivalence. Both indicators may change colour within this steep region, but not necessarily at exactly the same titrant volume.

One indicator might reach its visible colour-change criterion slightly before the theoretical equivalence volume, while the other reaches it slightly afterwards.

The important point is that the indicator detects a pH condition, whereas equivalence is defined by the reaction’s stoichiometric requirements.

c) An indicator with a transition range entirely outside the steep pH-change region would produce a poor endpoint.

The student might observe a colour change well before or well after equivalence.

This would create a larger systematic titration error.

A persistent colour change does not guarantee that the endpoint is chemically appropriate. Persistence simply makes the observed colour change easier to recognise.

d) The student should repeat the titrations and compare the endpoint volumes for each indicator separately.

For each indicator, several careful titrations should be performed under the same conditions. The student should use consistent endpoint criteria, add titrant dropwise near the transition, and calculate the mean titre for each indicator.

If each indicator produces a tightly grouped set of readings, but the two mean titres remain consistently different, this suggests an indicator-related systematic bias.

If the readings vary substantially within each group, random experimental variation may also be important.

The student should then compare each mean endpoint volume with the theoretical equivalence volume calculated from the initial acid amount, titrant concentration, and balanced equation.

This final comparison identifies which indicator gives the smaller endpoint error.

The deeper lesson is that two experiments can be internally consistent and still produce different answers because their measurement methods respond to different physical or chemical conditions. The reaction has one stoichiometric equivalence point; the experimental method determines how closely each observed endpoint approaches it.

09Where to go next

Once you can distinguish the endpoint from equivalence, the next step is understanding what happens to the solution’s pH on either side of equivalence.

That means identifying which reactant is in excess, calculating its concentration using the total solution volume, and then determining the pH.

Continue with Calculating pH Before and After Equivalence in Strong-Acid Titrations.

The key habit to carry into HSC questions is simple: use stoichiometry to locate equivalence, and use the indicator to observe the endpoint.