the principles of volumetric analysis including acid-base and redox titrations, the use of primary and secondary standard solutions and indicators, and stoichiometric calculations including back-titration to determine the concentration or amount of analyte

What this dot point is asking

VCAA wants you to describe the principles of volumetric analysis, to perform acid-base and redox titrations (including the choice of indicator based on the equivalence-point pH), to use primary and secondary standards, and to do the stoichiometric calculations that turn a titre into a concentration or mass, including back-titration.

The answer

What a titration measures

A titration determines the concentration (or amount) of an analyte by reacting it with a known volume of a solution of known concentration (a standard solution) until the reaction is just complete (the equivalence point), signalled by a colour change at the endpoint.

Apparatus: a burette delivers the standard (the titrant); a pipette delivers a known aliquot of the analyte solution to a conical flask; an indicator changes colour at (or near) the equivalence point.

Replicate titres should agree to within about 0.10 mL; the average of concordant titres (usually three) is the mean titre used in calculations.

Primary and secondary standards

A primary standard is a substance you can weigh directly and trust as the basis of an accurate solution. Criteria:

• High purity (more than 99.9%).
• Stable in air (does not absorb water, react with CO2, oxidise on standing).
• High molar mass (small mass errors are diluted out).
• Soluble in water and reacts in a known stoichiometry.

Common primary standards: anhydrous sodium carbonate (Na2CO3), oxalic acid dihydrate (H2C2O4.2H2O), potassium hydrogen phthalate (KHP), AgNO3.

A secondary standard is a solution whose concentration was determined by titration against a primary standard (or another secondary standard already traced to one). NaOH and HCl are usually used as secondary standards because they absorb CO2 / are not pure as supplied.

Acid-base titrations and indicator choice

The shape of the titration curve depends on whether the acid and base are strong or weak.

Indicator end-point ranges:

• Methyl orange: pH 3.1 to 4.4, red to yellow.
• Methyl red: pH 4.2 to 6.3, red to yellow.
• Bromothymol blue: pH 6.0 to 7.6, yellow to blue.
• Phenolphthalein: pH 8.2 to 10.0, colourless to pink.

The chosen indicator must change colour within the steep vertical section of the titration curve around the equivalence point.

Redox titrations

Same workflow with a redox reaction instead of acid-base. The standard may be itself coloured (KMnO4 is intensely purple) and acts as its own indicator: the first persistent pink colour beyond the analyte signals the endpoint. Iodine titrations use starch (deep blue with I2). Acidified KMnO4 is used to titrate Fe^2+ and other reductants.

The stoichiometric calculation

The unbreakable workflow:

1. Calculate moles of titrant from c x V (use the mean titre and volumes in litres).
2. Convert to moles of analyte using the mole ratio from the balanced equation.
3. Calculate concentration or mass of the analyte from c = n / V (analyte aliquot volume) or m = n x M.
4. If the analyte is in a diluted aliquot, scale back up to the original sample concentration using the dilution factor.

Back-titration

Used when:

• The analyte reacts too slowly with a titrant for a direct titration.
• The analyte is volatile or insoluble in the usual solvent.
• An exact endpoint is hard to see.

Procedure:

1. Add a known excess of a standard reagent that reacts completely with the analyte.
2. Titrate the unreacted excess against a second standard.
3. Moles of analyte = (moles of first reagent added) - (moles of first reagent left over) all corrected by the mole ratio with the analyte.

Classic example: an antacid tablet (calcium carbonate) dissolved in excess HCl, with the leftover HCl back-titrated against NaOH. The titration of CaCO3 directly is impractical because the solid reacts slowly and produces CO2 bubbles that disrupt the endpoint.

Worked example

A 1.00 g sample of a CaCO3 marble chip is dissolved in 50.0 mL of 1.00 mol L^-1 HCl (an excess). The unreacted HCl in the resulting solution is titrated with 0.500 mol L^-1 NaOH. The mean titre is 20.00 mL. Calculate the percentage purity of the marble chip (its %m/m CaCO3).

Step 1. Moles of HCl initially added:
n1 = 1.00 x 50.0 / 1000 = 0.0500 mol.

Step 2. Moles of NaOH used to back-titrate unreacted HCl:
n(NaOH) = 0.500 x 20.00 / 1000 = 0.01000 mol.
HCl + NaOH is 1:1, so unreacted HCl = 0.01000 mol.

Step 3. Moles of HCl reacted with the carbonate:
n(HCl, reacted) = 0.0500 - 0.01000 = 0.0400 mol.

Step 4. Apply CaCO3 + 2HCl -> CaCl2 + CO2 + H2O (1:2):
n(CaCO3) = 0.0400 / 2 = 0.0200 mol.

Step 5. Mass of CaCO3 and percentage:
m(CaCO3) = 0.0200 x 100.1 = 2.002 g. But the sample was only 1.00 g, so 200% purity is impossible.

This is a test of sanity-checking. The textbook number for a realistic back-titration would give a purity in the 80 to 99% range. A back-titration calculation that exceeds 100% should always prompt a re-check of the mole ratio, the dilution, or whether another base in the sample is also reacting.

Common traps

Using the wrong mole ratio. Always pull the ratio from a balanced equation. Sulfuric acid is diprotic: H2SO4 + 2NaOH -> Na2SO4 + 2H2O, so the ratio is 1:2.

Forgetting to convert mL to L. c x V with V in mL gives moles 1000 times too large.

Choosing the wrong indicator. A weak acid titrated with a strong base has a basic equivalence point; phenolphthalein, not methyl orange.

Treating NaOH as a primary standard. NaOH absorbs water and CO2 from air. It must be standardised against a primary standard (oxalic acid or KHP).

Using a single titre instead of the mean of concordant titres. Always run at least three concordant trials and average.

In a back-titration, subtracting on the wrong side. Moles of analyte come from (initial standard) - (excess found by back-titration), then divided by the appropriate mole ratio.

In one sentence

Volumetric analysis adds a standard solution from a burette to a measured aliquot of the analyte until an indicator marks the equivalence point, the titre and a balanced equation give the moles of analyte via c x V then mole ratio, and a back-titration with a known excess of one reagent and a second standard against the remainder gives a quantitative answer for analytes that are too slow or messy to titrate directly.