Chemistry · Analytical and physical chemistry · Year 2

Titrimetric analysis

How can we tell, to the drop, how much soda is in technical caustic soda?

The situation

In the quality-control laboratory of the Kungrad soda plant, raw materials and products are checked on every shift. Today the laboratory technician has three tasks on the bench: how much soda ( $Na_{2} CO_{3}$ ) has built up in technical caustic soda that has stood in the air for a long time, how much nitrogen there is in an ammonium salt, and whether the hardness of the water entering the boiler house is within the norm. In a row of burettes stand solutions of acid, alkali, permanganate, EDTA and silver nitrate. Which titration method, which indicator and how many parallel determinations make the result reliable?

Topic

Titrimetric analysis. Quality-control laboratory of the Kungrad Soda Plant: a row of burettes, a magnetic stirrer, indicators; today's task — the soda content of technical NaOH,…

Key ideas

Titration curves
Redox and complexometric titration
Metrology

Formulas

N_{1} V_{1} = N_{2} V_{2}, m = N V M_{eq}

Law of equivalents: at the equivalence point the numbers of mole-equivalents of the two substances are equal ( $N$ is the normality, mol-eq/L).

pH = p K_{a} + \lg \frac{c (A^{-})}{c (HA)}, {pH}_{eq} = 7 + \frac{1}{2} (p K_{a} + \lg c_{A^{-}})

A buffer (Henderson–Hasselbalch) and the pH at the equivalence point of a weak acid.

E = E^{\circ'} + \frac{0.059}{n} \lg \frac{[Ox]}{[Red]}, E_{eq} = \frac{n_{1} E_{1}^{\circ'} + n_{2} E_{2}^{\circ'}}{n_{1} + n_{2}}

The Nernst equation (25 °C) and the potential at the equivalence point of a redox titration.

K^{'} = α (Y^{4 -}) \cdot K (MY), \lg K^{'} \geq 8

Conditional stability constant of the EDTA complex: the lower the pH, the smaller $α (Y^{4 -})$ .

\overline{x} \pm \frac{t_{P, f} s}{\sqrt{n}}, s = \sqrt{\frac{\sum {(x_{i} - \overline{x})}^{2}}{n - 1}}

Confidence interval of parallel results (Student's coefficient $t$ , $P$ = 0.95, $f = n - 1$ ).

Theory

Titrimetric analysis: basic concepts

Analytical chemistry determines the composition of a substance: water, soil, air, alloys, ores, biological and environmental samples. In titrimetry, a titrant of accurately known concentration is added from a burette to the sample up to the equivalence point, and the amount of the substance is calculated from the volume used. Requirements for the reaction: it must be stoichiometric, fast, practically complete ( $K$ large), and it must be possible to detect the equivalence point. Primary standards (borax $Na_{2} B_{4} O_{7} \cdot 10 H_{2} O$ , oxalic acid $H_{2} C_{2} O_{4} \cdot 2 H_{2} O$ , $K_{2} Cr_{2} O_{7}$ , zinc) are accurately weighed and dissolved; NaOH, HCl, KMnO₄, $Na_{2} S_{2} O_{3}$ and EDTA are standardised against them. Methods: direct, back (Volhard) and replacement (iodometric) titration. A pipette is filled to the mark and emptied with its tip touching the wall of the vessel (the drop at the tip is not blown out); a burette is rinsed with the titrant, set to zero and read at the bottom of the meniscus to 0.01 mL; a volumetric flask is filled to the mark and shaken.

Acid–base equilibrium and titration curves

In the Brønsted–Lowry theory an acid is a proton donor and a base is a proton acceptor; for a conjugate pair $K_{a} K_{b} = K_{w}$ . The pH is calculated exactly from the charge balance: for a strong acid $pH = - \lg c$ , for a weak acid $pH \approx \frac{1}{2} (p K_{a} - \lg c)$ , for a buffer the Henderson–Hasselbalch equation, and for an amphoteric ion ( $HCO_{3}^{-}$ ) $\frac{1}{2} (p K_{1} + p K_{2})$ . The buffer capacity $β = d c / d pH$ is greatest at $c (HA) = c (A^{-})$ . The titration jump (within ±0.1 %) narrows by 1 pH unit on each side for every tenfold decrease in concentration (strong acid — strong base) and depends on $K_{a}$ : titration is possible if $c K_{a} \geq 10^{- 8}$ . $H_{3} PO_{4}$ has two jumps ( $K_{1} / K_{2} > 10^{4}$ ) and no third. An indicator changes colour at its own titration exponent pT, and pT must lie inside the jump; otherwise there is an indicator error (hydrogen, hydroxyl, acid error). The two-indicator method: $V_{1}$ with phenolphthalein (NaOH + $CO_{3}^{2 -} + H^{+} \overset{}{\to} HCO_{3}^{-}$ ), $V_{2}$ with methyl orange: $n (Na_{2} CO_{3}) = c (V_{2} - V_{1})$ , $n (NaOH) = c (2 V_{1} - V_{2})$ . The carbonate hardness of water is found by titrating $HCO_{3}^{-}$ with HCl to methyl orange.

Redox titration

The electrode potential obeys the Nernst equation; besides the standard $E^{\circ}$ , the formal potential $E^{\circ'}$ , which takes the medium into account, is used: for $Fe^{3 +} / Fe^{2 +}$ it is 0.77 V, in 1 M $H_{2} SO_{4}$ 0.68 V, and with phosphoric acid ≈ 0.46 V. The direction and completeness of a reaction: $\lg K = n (E_{1}^{\circ} - E_{2}^{\circ}) / 0.059$ . The jump on the titration curve depends on the difference between the potentials of the two couples. Permanganate titration: KMnO₄ is its own indicator (an excess drop is pale pink); it is standardised with oxalic acid at 70–80 °C, the first drops decolourise slowly — the reaction is accelerated by the $Mn^{2 +}$ that forms (autocatalysis). Iron(III) is first reduced with $SnCl_{2}$ , the excess $Sn^{2 +}$ is removed with $HgCl_{2}$ , and the Zimmermann–Reinhardt reagent ( $MnSO_{4} + H_{3} PO_{4}$ ) stops the oxidation of chloride and binds $Fe^{3 +}$ into a colourless complex. Iodometry: dichromate displaces an equivalent amount of $I_{2}$ from KI (5 min in the dark), and this is titrated with thiosulfate; starch is added at the end (at pale yellow), otherwise the iodine binds firmly to the starch and the end point is delayed. Other oxidising agents: $K_{2} Cr_{2} O_{7}$ , $Ce^{4 +}$ , $KBrO_{3}$ , $I_{2}$ ; reducing agents: $Na_{2} S_{2} O_{3}$ , $SnCl_{2}$ , $Fe^{2 +}$ (Mohr's salt), oxalic acid.

Complexometry and the hardness of water

EDTA ( $H_{4} Y$ ; Trilon B is $Na_{2} H_{2} Y \cdot 2 H_{2} O$ ) forms 1 : 1 chelates with metal ions. The stability constant is $K = [MY] / ([M] [Y])$ : lg K is 8.79 for Mg, 10.65 for Ca and 16.5 for Zn. The ligand is protonated, so the conditional constant $K^{'} = α (Y^{4 -}) K$ is used: $α$ = 0.30 (pH 10), $4 \cdot 10^{- 3}$ (pH 8), $2 \cdot 10^{- 5}$ (pH 6). For titration lg K' ≳ 8 is needed — from this the lowest pH for each metal is found. For stepwise complexes the formation function $\overline{n} = \sum i β_{i} {[L]}^{i} / (1 + \sum β_{i} {[L]}^{i})$ is introduced — the average number of ligands per metal atom. Metallochromic indicators: Eriochrome Black T (pH 10) is wine red with a metal and blue when free; murexide (pH 12–13) is pink with calcium and violet when free. Total hardness (Ca + Mg) is determined with Eriochrome Black T, calcium hardness at pH 12 with murexide (Mg(OH)₂ precipitates), and magnesium hardness from the difference: $H = 2 c (EDTA) V \cdot 1000 / V_{water}$ mmol-eq/L. For drinking water the CIS standards (GOST 2874-82, SanPiN 2.1.4.1074-01) allow up to 7.0 mmol-eq/L. Softening of hardness is covered in the “Water purification and softening” experiment.

Precipitation titration

The reaction must be fast and the precipitate very sparingly soluble ( $K_{s}$ of AgCl = 1.8·10⁻¹⁰). The titration curve is plotted against pAg. Mohr's method: the indicator is $K_{2} CrO_{4}$ ; once the AgCl has precipitated completely, ${[Ag^{+}]}^{2} [CrO_{4}^{2 -}] > K_{s} (Ag_{2} CrO_{4}) = 1.1 \cdot 10^{- 12}$ and brick-red $Ag_{2} CrO_{4}$ is deposited. The medium is pH 6.5–10.3: in an acidic medium chromate turns into $HCrO_{4}^{-}$ and the end point is delayed, and in a strongly alkaline medium $Ag_{2} O$ precipitates. Volhard's method is a back titration: an excess of $AgNO_{3}$ is added, and the remainder is titrated with $NH_{4} SCN$ in the presence of $Fe^{3 +}$ until red $FeSCN^{2 +}$ appears; AgCl is more soluble than AgSCN, so if the precipitate is not filtered off (or coated with nitrobenzene), $AgCl + SCN^{-} \overset{}{\to} AgSCN + Cl^{-}$ takes place — the colour fades and the result is too low. Fajans' method uses an adsorption indicator (dichlorofluorescein): before the equivalence point $Cl^{-}$ is adsorbed on the surface of the precipitate, afterwards $Ag^{+}$ — the indicator anion sticks to the surface and turns the precipitate pink; dextrin is added to keep the particles small.

Metrology, safety and the model

The stages of an analysis: sampling, decomposition of the sample (by dissolving, acids or fusion), measurement, calculation and evaluation. Errors: systematic (glassware not calibrated, wrong indicator) shift the result in one direction; random (pipette, reading the meniscus) cause scatter; gross (splashing) are rejected with the Q test; absolute $Δ = x - μ$ and relative $Δ / μ$ . Glassware is calibrated: water is weighed, $V_{20} = m / ρ (t)$ with a correction for air and the expansion of glass. The result is taken from ≥ 3 parallel determinations: $\overline{x}$ , $s$ and the confidence interval. Luminescent titration (in a coloured or turbid sample) is in the “Optical methods of analysis” experiment. Safety: wear safety glasses; fill a pipette with a pipette filler, not by mouth; add acid to water; $HgCl_{2}$ and $K_{2} Cr_{2} O_{7}$ are poisonous and their waste is collected separately; $AgNO_{3}$ blackens the skin; open the ammonia buffer in a fume cupboard. Model: the solutions are ideal (activities = concentrations), 25 °C; pH, potential, pM and pAg are calculated exactly from the equilibrium; the permanganate kinetics, the binding of iodine to starch, the AgCl → AgSCN transition, and the pipette error (±0.015 mL) and burette reading error (±0.01 mL) are typical values; the complexation of Zn with ammonia is not taken into account; a drop is 0.05 mL.

Did you know?

The first form of the burette was created in 1791 by the French chemist F. Descroizilles; the terms “burette” and “pipette” were introduced in 1824 by J. L. Gay-Lussac.
EDTA was synthesised in 1935 by the German chemist F. Münz; complexometric titration was developed in the 1940s by the Swiss chemist G. Schwarzenbach.

Inside the experiment

The experiment starts from a real-life situation: you predict the result, change the controls, run the experiment and draw a conclusion. Inside are missions, theory, a quiz and a guided tour in which the camera moves and explains the key points.

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Alloys: phase diagrams — Year 2
Chemical kinetics and Arrhenius — Year 2
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