Chemistry · Analytical and physical chemistry · Year 1

Electrochemical analysis

How do we use an electric current to measure salt, fluoride and lead in water?

The situation

Three samples have been brought to a drinking-water monitoring laboratory in Tashkent: brackish water from a village well in the Aral Sea region, water from the city mains and water taken from the Akhangaran river. The chemist neither evaporates nor tastes them — he dips in electrodes, and within a few minutes the instruments show the salt content, the pH, the fluoride and even a few micrograms of lead per litre. How do electric current, potential and charge “tell” us the composition of a solution, and how far can these measurements be trusted?

Topic

Electrochemical analysis: conductivity, potentiometry, voltammetry. Drinking-water monitoring laboratory: brackish water brought from a well in the Aral Sea region in a conductivity meter, Tashkent tap water in a pH meter and a fluoride-selective electrode,…

Key ideas

Conductometry
Potentiometry
Voltammetry

Formulas

κ = \frac{K_{cell}}{R}, Λ = \frac{κ}{c}

Conductivity ( $κ$ ) and molar conductivity ( $Λ$ ); $K_{cell} = l / S$ is the cell constant. $Λ$ [S·cm²/mol] = 1000· $κ$ [S/cm] / $c$ [mol/L].

Λ = Λ^{\circ} - (A + B Λ^{\circ}) \sqrt{c}, Λ^{\circ} = λ_{+}^{\circ} + λ_{-}^{\circ}

The Kohlrausch–Onsager law (strong 1:1 electrolyte, water, 25 °C: $A$ = 60.2, $B$ = 0.229) and the law of independent migration of ions.

K = \frac{c α^{2}}{1 - α}, α = \frac{Λ}{Λ^{\circ}}

Ostwald’s dilution law: the degree of dissociation of a weak electrolyte is found from conductivity.

E = E^{\circ'} - 0,05916 pH (25^{\circ} C)

Glass electrode: when the pH changes by one unit, the potential changes by 59.16 mV. The same holds in ionometry: $E = E^{\circ} - S \lg a (F^{-})$ .

{\overline{i}}_{d} = 607 n D^{1 / 2} m^{2 / 3} t^{1 / 6} c, E = E_{1 / 2} + \frac{0,05916}{n} \lg \frac{i_{d} - i}{i}

The Ilkovič and Heyrovský–Ilkovič equations: wave height — quantity, half-wave potential — quality (which ion).

Theory

Electrolyte solutions: dissociation, activity, ionic strength

According to Arrhenius’s theory an electrolyte splits into ions in water; the fraction of dissociated molecules is the degree of dissociation $α$ . In a weak electrolyte (CH₃COOH, NH₃·H₂O) the equilibrium obeys the law of mass action: $K = c α^{2} / (1 - α)$ — Ostwald’s dilution law, $α \approx \sqrt{K / c}$ : on dilution $α$ increases. In a strong electrolyte ( $α \to 1$ ) each ion is surrounded by an ionic atmosphere of opposite charge (Debye–Hückel theory) — the “effective” concentration of the ion, its activity $a = γ c$ , is less than the analytical concentration. The ionic strength is $I = \frac{1}{2} \sum c_{i} z_{i}^{2}$ ; the Debye–Hückel laws: $\lg γ = - 0.509 z^{2} \sqrt{I}$ (limiting, $I$ < 0.01) and $\lg γ = - 0.509 z^{2} \sqrt{I} / (1 + \sqrt{I})$ (extended). So the thermodynamic constant (in activities) differs from the concentration constant $K_{c} = K / γ^{2}$ , and a constant that takes account of the conditions of the medium (pH, a complexing agent) is a conditional constant. The analytical concentration is the total amount of dissolved substance, the equilibrium concentration is that of a particular species ([CH₃COO⁻], [CH₃COOH]). Theories of acids and bases: Arrhenius (gives H⁺ / OH⁻), Brønsted–Lowry (proton donor / acceptor), Lewis (electron-pair acceptor / donor); a buffer (CH₃COOH + CH₃COO⁻) keeps the pH steady — a pH meter is calibrated with buffers. The school-level treatment is in the “Electrolytic dissociation” and “Acids, bases and indicators” experiments.

Conductivity: κ, Λ, Kohlrausch and Onsager

A conductivity meter measures the resistance of the solution between two platinum plates: $κ = K_{cell} / R$ ; the cell constant is calibrated with 0.0100 mol/L KCl ( $κ$ = 1.413 mS/cm at 25 °C). So that the electrodes do not polarise and no electrolysis takes place, alternating current (≈ 1 kHz) is used — low-frequency conductometry; in high-frequency (contactless) conductometry the electrodes do not touch the solution. Conductivity referred to one mole of electrolyte is the molar conductivity $Λ = κ / c$ , and referred to one mole of equivalents it is the equivalent conductivity $Λ_{eq} = κ / (z c)$ . In a strong electrolyte $Λ$ rises slowly on dilution — the Kohlrausch law $Λ = Λ^{\circ} - k \sqrt{c}$ ; the Onsager theory explains the slope by the relaxation and electrophoretic retardation of the ionic atmosphere. Extrapolation to $\sqrt{c} \to 0$ gives $Λ^{\circ}$ (Physical chemistry L16). At infinite dilution the ions move independently: $Λ^{\circ} = λ_{+}^{\circ} + λ_{-}^{\circ}$ . H⁺ (349.8) and OH⁻ (198.6) are 2.5–7 times faster than other ions: the proton “hops” along a chain of water molecules (the Grotthuss mechanism). The transport number $t_{\pm} = λ_{\pm} / Λ$ is the fraction of the current carried by that ion: in HCl $t (H^{+})$ ≈ 0.82, in KCl $t (K^{+})$ ≈ 0.49. In a weak electrolyte $Λ$ rises sharply on dilution because $α$ increases; its $Λ^{\circ}$ is found from the Kohlrausch law: $Λ^{\circ} (CH_{3} COOH) = Λ^{\circ} (HCl) + Λ^{\circ} (CH_{3} COONa) - Λ^{\circ} (NaCl)$ = 390.7; then $α = Λ / Λ^{\circ}$ and $K$ (L17). If $1 / Λ$ is plotted against $c Λ$ , a straight line results: the intercept is $1 / Λ^{\circ}$ , the slope $1 / (K Λ^{\circ 2})$ . Direct conductometry: the salinity of water — dry residue ≈ (0.55–0.75)· $κ$ [µS/cm] mg/L. $κ$ increases by ≈ 2 % for each 1 °C rise in temperature, so the result is converted to 25 °C.

Conductometric titration

Indirect conductometry is finding the equivalence point in a titration from the break in the $κ$ curve; no indicator is needed, and it also works in coloured and turbid solutions. When HCl is titrated with NaOH, the fast H⁺ (349.8) is replaced by the slow Na⁺ (50.1) — $κ$ decreases; after the equivalence point the excess OH⁻ (198.6) raises it sharply: a “V”-shaped curve (Physical chemistry L19). In ethanoic acid there is little H⁺: as Na⁺ and CH₃COO⁻ form, $κ$ rises slowly, and faster after the equivalence point. A mixture of HCl + CH₃COOH (L20) gives three straight-line segments: first HCl is neutralised ( $κ$ falls), then CH₃COOH ( $κ$ rises slowly), and at the end there is excess alkali. The break points: $n (HCl) = c (NaOH) V_{1}$ , $n (CH_{3} COOH) = c (NaOH) (V_{2} - V_{1})$ . For the segments to be straight, a concentrated titrant is used (the volume changes little) or $κ$ is corrected for dilution: $κ (V_{0} + V) / V_{0}$ . Direct conductometric determination (Analytical chemistry L22): from the $κ$ of an ethanoic acid solution, if $K$ and $Λ^{\circ}$ are known, $c$ is found through Ostwald’s law.

Potentiometry and ionometry

The electrochemical cell: an indicator electrode (its potential depends on the ion being determined) and a reference electrode (its potential is constant: the saturated calomel electrode — +0.241 V, Ag/AgCl in saturated KCl — +0.197 V, relative to the standard hydrogen electrode). Almost no current flows (a high-impedance voltmeter), so the emf obeys the Nernst equation. Glass electrode: the difference between the H⁺ activities on the two sides of a thin glass membrane produces a potential, at 25 °C $E = E^{\circ'} - 59.16 mV \cdot pH$ . A real electrode has an asymmetry potential and a slope slightly below 100 % — which is why a pH meter is calibrated with two buffers. Ion-selective electrodes (ionometry, Analytical chemistry L20): the fluoride electrode has a LaF₃ crystal membrane, $E = E^{\circ} - S \lg a (F^{-})$ ; to keep the ionic strength and pH the same, TISAB is added; the influence of other ions is taken into account by the Nikolsky equation (the selectivity coefficient). In reversible redox systems (Fe³⁺/Fe²⁺) the potential of a Pt electrode settles quickly and follows Nernst; in irreversible ones (MnO₄⁻/Mn²⁺, Cr₂O₇²⁻/Cr³⁺) it settles slowly and deviates from it. Potentiometric titration (Physical chemistry L22): the equivalence point is the steepest part of the pH(V) curve, the maximum of the first derivative $Δ pH / Δ V$ . A polybasic acid, H₃PO₄, gives two jumps (p $K_{a}$ 2.15 and 7.20 → pH ≈ 4.7 and 9.6); the third (p $K_{a}$ 12.35) is not visible in water. In a mixture of HCl + CH₃COOH the first jump is small — conductometry distinguishes them more clearly.

Voltammetry: polarography and stripping analysis

The potential of the working electrode is changed linearly and the current is recorded. In classical polarography the working electrode is a dropping mercury electrode: the drop is renewed about every 4 s, the surface is always clean, and the overpotential for hydrogen evolution on mercury is large (≈ 1 V) — Zn²⁺ is reduced even at negative potentials. An excess of background electrolyte (0.1 mol/L KCl) eliminates migration: the ion reaches the electrode only by diffusion. When the potential is sufficient, the ions at the surface are reduced completely and the current reaches the limiting diffusion current $i_{d}$ — concentration polarisation. The Ilkovič equation ${\overline{i}}_{d} = 607 n D^{1 / 2} m^{2 / 3} t^{1 / 6} c$ (µA; $D$ in cm²/s, $m$ in mg/s, $t$ in s, $c$ in mmol/L): the height is proportional to the concentration — quantitative analysis. The Heyrovský–Ilkovič equation $E = E_{1 / 2} + \frac{0.05916}{n} \lg \frac{i_{d} - i}{i}$ : the half-wave potential does not depend on concentration and identifies the ion — qualitative analysis. In 0.1 M KCl (relative to the saturated calomel electrode — SCE): Cu²⁺ +0.04 and −0.22, Pb²⁺ −0.40, Cd²⁺ −0.60, Zn²⁺ −1.00 V. Dissolved O₂ gives two waves (−0.05 and −0.9 V) — so nitrogen is bubbled through first. Stripping voltammetry (Analytical chemistry L21): metals are deposited onto a mercury film (an amalgam) at −1.2 V from a stirred solution, then dissolve again when the potential is scanned in the anodic direction; the peak height is proportional to $c \cdot t_{dep}$ — this is how Cd, Pb and Cu are determined at the µg/L level. The amount is found by the standard addition method: $c_{x} = c_{add} h_{1} / (h_{2} - h_{1})$ . If the electrode reaction itself is slow, kinetic polarisation (overpotential) is added — the Tafel equation is in the “Galvanic cells and corrosion” experiment.

Coulometry, safety and the model

Coulometry is based on Faraday’s laws: $n = Q / (z F)$ , $m = Q M / (z F)$ , $F$ = 96 485 C/mol; the condition is 100 % current efficiency (the current is spent on only one reaction). In direct (potentiostatic) coulometry the substance being determined itself reacts at the electrode; the current falls exponentially with time, and the charge is accumulated by an electronic coulometer. If copper is deposited on a platinum gauze cathode and the cathode is weighed, this is electrogravimetry: if Cu is deposited from brass at −0.30 V (SCE), the zinc stays in the solution. The indirect method is coulometric titration: the titrant is generated at the electrode by a constant current (here $2 H_{2} O + 2 e^{-} \overset{}{\to} H_{2} ↑ + 2 OH^{-}$ ), and its amount is $I t / F$ — neither a burette nor a standard solution is needed. Faraday’s laws themselves are in the “Electrolysis, Faraday's laws” experiment. Safety: mercury and its vapour are poisonous — mercury electrodes are used in a closed system, and spilled droplets are collected in a special way (today bismuth film electrodes are often used); wear safety goggles when working with acids and alkalis; fluoride solutions are poisonous — wear gloves; do not taste the solutions. Model: 25 °C; the ionic conductivities come from the extended form of the Onsager law (accurate to ≈ 1 % up to 0.1 mol/L), the pH and titration curves from the charge balance; the electrode slopes and asymmetry are typical values; $E_{1 / 2}$ and the Ilkovič parameters are from a handbook, $D$ from $λ^{\circ}$ ; the sensitivity of the stripping peaks is a model; the composition of the samples (Aral Sea region, Tashkent, Akhangaran) is a teaching model, not a real measurement; in polarography and coulometry time is speeded up 10–120 times; the vibration of ions in alternating current is shown slowed down.

Did you know?

Jaroslav Heyrovský created polarography in 1922 and received the Nobel Prize in Chemistry for this discovery in 1959; the equation of the diffusion current was derived in 1934 by his student Dionýz Ilkovič.
The appearance of a potential across a glass membrane was observed in 1906 by the German physiologist Max Cremer; in 1909 Fritz Haber and Zygmunt Klemensiewicz used the glass electrode to measure acidity and in titration — today’s pH meter began there.

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
Catalysis and enzymes — Year 2
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