Concentration of Hydrochloric Acid by Titration

In Practical Skills: Titration you find the concentration of a hydrochloric acid solution that is too concentrated to titrate directly.

You pipette 25.0 cm³ of the original acid into a 250 cm³ volumetric flask and make it up to the mark with distilled water.

You then titrate 25.0 cm³ portions (aliquots) of the diluted acid against a standardised sodium hydroxide solution of concentration 0.0800 mol dm⁻³ using phenolphthalein.

The mean titre gives the moles of alkali, the equation gives the moles of acid, and a scale-up of ten takes you back to the original solution.

The reaction is a strong acid neutralising a strong base:

HCl(aq) + NaOH(aq) → NaCl(aq) + H₂O(l)

The ionic equation, which is asked for at least as often, is H⁺(aq) + OH⁻(aq) → H₂O(l). The ratio is 1 : 1, so at the end point the moles of NaOH delivered from the burette equal the moles of HCl in the flask.

The sodium hydroxide has to be standardised first because it cannot be a primary standard: solid NaOH absorbs water and carbon dioxide from the air, so a solution made by weighing it never has the concentration you calculate.

Its concentration is found by titrating it against a primary standard such as anhydrous sodium carbonate (see Practical Skills: Standard Solutions (preparation of a standard solution)).

In Paper 3, a timed laboratory examination that assesses manipulation, observation, presentation of data, analysis and evaluation, the acid is normally supplied at a titratable concentration and labelled FA 1, with the standardised alkali labelled FA 2 and the indicator named on the paper.

The mole ratio is given by an equation on the question paper: you use it, you do not derive it.

The dilution step below is shown because a planning question can ask when and how a solution should be diluted before titration; in the practical exam itself you usually go straight to the titration.

You are assessed through Paper 3, a timed laboratory examination that assesses manipulation, observation, presentation of data, analysis and evaluation.

For this practical that means: the reasons for each technique step, the direction of the error each mistake causes, the treatment of the results table, the calculation with correct units and significant figures, and the percentage uncertainty budget.

Every step carries a reason. Method questions in Paper 3 are marked on the reasons and the numbers, not on the bare instruction, so learn the third column as carefully as the second.

The burette is rinsed with distilled water and then with the sodium hydroxide solution it will hold.

Filled with a wet burette, the alkali is slightly diluted, a larger volume is needed to supply the same moles of OH⁻, the titre is too large and the calculated acid concentration is too high.

The burette is filled through a small funnel, below eye level, and the tap is opened briefly to fill the jet.

An air bubble that sits in the jet at the start and is pushed out during the titration counts as delivered volume that never reached the flask, so again the titre is too large.

Then the funnel is removed before the initial reading; left in, it drips, the final reading is lower than it should be and the titre is too small.

The initial reading does not have to be 0.00 cm³. Read the bottom of the meniscus at eye level and record to the nearest 0.05 cm³, so every reading ends in 0 or 5 in the second decimal place.

Reading from the top of the meniscus every time cancels out in the titre, because the titre is a difference of two readings; reading inconsistently does not cancel and adds random error.

The conical flask is rinsed with distilled water only. Any water left in it makes no difference to the result because all the acid in the flask is titrated whatever its volume.

Rinsing the flask with the diluted acid, by contrast, adds acid that was not measured and enlarges the titre.

A conical flask rather than a beaker is used because it can be swirled vigorously without splashing out solution.

Two or three drops of phenolphthalein are enough; the indicator is itself a weak acid and consumes a trace of alkali.

During the titration the flask is swirled continuously so that the alkali mixes at once and the pink flashes where it lands disappear.

In the rough titration the alkali is run in steadily to find the approximate end point.

In the accurate titrations it is run in quickly to about 2 cm³ short of that value and then added drop by drop, with the flask swirled after each drop, so that the end point is fixed to within one drop, about 0.05 cm³.

The titration set-up: 50 cm³ burette of 0.0800 mol dm⁻³ NaOH(aq) clamped vertically with the funnel removed, 25.0 cm³ of diluted HCl(aq) with three drops of phenolphthalein in a 250 cm³ conical flask on a white tile, and the eye level with the meniscus.

Using the burette: rinse with the solution, fill with the funnel then remove it, open the tap to fill the jet, and read the bottom of the meniscus at eye level to the nearest 0.05 cm³ (here 9.15 cm³).

A funnel left in lowers the final reading; a bubble in the jet inflates the titre.

Results are set out with the initial reading before the final reading, every value to two decimal places, and the titre as final minus initial.

The first row is the rough titre, usually the largest because it is deliberately run past the end point; it is labelled as rough and never enters the mean.

Concordant titres are within 0.10 cm³ of each other. Below is a corrected set of sample data.

Titrations 1 and 3 differ by 0.05 cm³, so they are concordant. Titration 2 is 0.25 cm³ away from titration 3 and is rejected even though its readings were taken carefully.

Something, perhaps a pink flash mistaken for the end point or a slow drop after the tap was closed, made it drift.

Mean titre = (30.10 + 30.05) ÷ 2 = 30.075 cm³, written as 30.08 cm³ to two decimal places. If you carry the working on a calculator keep 30.075 and round only the final answer.

Students lose marks in three ways here: averaging every titre including the rough one, quoting the mean to three decimal places as if the burette could read it, and writing burette readings such as 30.1 or 30.12 that a burette graduated in 0.1 cm³ cannot give. Write 30.10 and 30.05.

In Paper 3, a timed laboratory examination that assesses manipulation, observation, presentation of data, analysis and evaluation you draw the table yourself.

Marks are awarded for headings with units (final burette reading / cm³, initial burette reading / cm³, titre / cm³).

There are marks for every reading to two decimal places ending in 0 or 5, for a clearly labelled rough column, for ticking the titres you use and for a mean calculated from ticked concordant titres only.

Marks are also given for the accuracy of your own titres against the supervisor’s value, so technique counts directly.

Evaluation questions want three things: the source of error, the direction it pushes the titre and the calculated concentration, and the improvement. Start with the measuring apparatus, using the maximum error of each reading (±0.05 cm³ per burette reading, ±0.06 cm³ for the 25 cm³ pipette, ±0.3 cm³ for the 250 cm³ flask).

The absolute uncertainty in the answer is 0.963 mol dm⁻³ × 0.0093 = 0.009, so the result is 0.963 ± 0.01 mol dm⁻³ (round the uncertainty to one significant figure).

The end point itself adds up to one drop, about ±0.05 cm³, which is why dropwise addition and a persistent colour matter.

The burette dominates, and its percentage uncertainty falls as the titre grows: this is the quantitative reason the acid was diluted only tenfold and not a hundredfold. A titre of 3 cm³ would carry 0.10 ÷ 3.00 × 100 = 3.3%.

Improvements that examiners credit: a larger titre (a more dilute alkali or a larger aliquot), a burette with finer graduations, repeating to get more concordant titres, a pipette rather than a measuring cylinder for every fixed volume.

Improvements they do not credit: “be more careful”, “use more accurate equipment” without naming it, and “do more repeats” with no reason.

• Writing HCl + NaOH → NaCl + H₂O without state symbols, or the ionic equation with (l) on the ions.
• Calling the sodium hydroxide a standard solution: it was standardised by titration against a primary standard.
• Leaving out why the acid was diluted: about 300 cm³ of alkali would be needed otherwise.
• Rinsing “everything with distilled water”: the pipette takes the acid, the burette takes the alkali, only the conical flask takes water.
• Including the rough titre in the mean, or averaging all the titres because “more data is better”.
• Burette readings written as 30.1 or 30.12: the second decimal place is 0 or 5.
• Getting an error direction backwards, especially a blown-out pipette: more acid means a larger titre and a concentration that is too high.
• Forgetting the factor of ten, or dividing by 0.250 dm³ instead of 0.0250 dm³, giving 0.0963 instead of 0.963 mol dm⁻³.
• Quoting the percentage uncertainty of one burette reading (0.05 cm³) instead of the titre (0.10 cm³, two readings).
• “Persists for a few seconds” for the end point: the accepted phrase is the first permanent pale pink, persisting for about 30 s on swirling.

Say

“Rinse the pipette with the acid so that residual water does not dilute it.” “Remove the funnel before taking the initial reading.”

“Concordant titres agree within 0.10 cm³ of each other; only these are averaged.”

“Phenolphthalein changes colour on the vertical part of the curve, so the end point coincides with the equivalence point to within one drop.”

“Percentage uncertainty of the titre = 0.10 ÷ 30.08 × 100 = 0.33%.”

Do not say

“Rinse the burette with water so it is clean.” “Add indicator until the colour is clear.” “The rough titre is included to give more results.” “A bigger flask would reduce the error.” “Blowing out the pipette makes the titre smaller.”

Watch for

Volumes in cm³ in the question but dm³ in n = c × V. The direction of the titration (alkali into acid) when describing the colour change.

The unit of the final answer, mol dm⁻³, and its three significant figures. Whether the question wants the percentage uncertainty of a single reading or of the titre. The word “standardised” against “standard”.