Reference Electrodes, pH and Conductivity Measurement, Batteries and Fuel Cells

By the end you should be able to: Describe the construction and working of the standard hydrogen and calomel electrodes and the glass electrode, explain pH and conductivity measurement, and describe the Li-ion battery and the hydrogen-oxygen fuel cell.

Why reference electrodes exist

Measuring any electrode potential needs a second electrode of known, stable potential. That is a reference electrode, and the demands on it are strict: its potential must not shift with the solution being measured, and must not drift with time or with the small current drawn.

The standard hydrogen electrode (SHE)

Construction. A platinised platinum foil dipped in 1 M H⁺ solution, with pure hydrogen gas at 1 bar bubbled over it.

\text{Pt}\,|\,\text{H}_2(1\ \text{bar})\,|\,\text{H}^{+}(1\ \text{M})

Working. The platinum is inert — it takes no part chemically — and merely provides a surface for the equilibrium

\text{H}^{+} + e^{-} \rightleftharpoons \tfrac12\text{H}_2

The platinum is platinised, coated in finely divided platinum black, to give a large surface area so equilibrium is reached quickly.

Its potential is defined as exactly 0.000 V at all temperatures. This is a convention, not a measurement — the whole scale of electrode potentials is built on it.

Why nobody uses it. It is the primary standard and it is thoroughly impractical: it needs a supply of pure hydrogen at controlled pressure, the platinum is easily poisoned by traces of impurities, and the assembly is fragile and awkward. It defines the scale; something else does the work.

The calomel electrode

The practical secondary reference, calibrated against SHE.

Construction. Mercury at the bottom, covered by a paste of mercury and mercurous chloride (calomel, Hg₂Cl₂), over which sits a KCl solution. A platinum wire in the mercury makes contact, and a porous plug connects to the test solution.

\text{Hg}\,|\,\text{Hg}_2\text{Cl}_2(s)\,|\,\text{KCl}(\text{soln})

Electrode reaction:

\text{Hg}_2\text{Cl}_2 + 2e^{-} \rightleftharpoons 2\text{Hg} + 2\text{Cl}^{-}

The key point: the potential depends only on the chloride ion concentration, and Hg₂Cl₂ is almost insoluble, so as long as the KCl concentration is fixed the potential is fixed.

KCl concentration	Potential vs SHE
0.1 M	+0.334 V
1.0 M	+0.280 V
Saturated (SCE)	+0.242 V

The saturated calomel electrode (SCE) is the most used, because saturation is self-maintaining — excess solid KCl keeps the solution saturated even as temperature varies or solvent evaporates. You do not have to make up a solution accurately; you just leave crystals in it.

Advantages over SHE: compact, robust, easy to construct, stable over long periods, and no gas supply.

The glass electrode and pH measurement

Construction. A thin bulb of special glass, about 0.1 mm thick, containing a solution of known pH (usually 0.1 M HCl) with an internal Ag/AgCl reference electrode.

Working. When the bulb separates two solutions of different pH, a potential develops across the glass membrane proportional to the pH difference. Sodium ions in the glass lattice exchange with hydrogen ions at both surfaces, and the imbalance appears as a boundary potential.

E_{glass} = E°_{glass} - 0.0591\,\text{pH} \quad (\text{at }298\ \text{K})

Note $n = 1$ , so the sensitivity is the full 59.1 mV per pH unit — the largest possible, and the reason pH is measured this way.

Measuring pH. The glass electrode is combined with a reference (SCE or Ag/AgCl) and the cell EMF measured:

E_{cell} = E_{ref} - E_{glass}

Modern meters use a combination electrode with both in one body.

Calibration is not optional. $E°_{glass}$ varies between electrodes and drifts as the bulb ages, so the meter is calibrated with buffer solutions of known pH — usually pH 4, 7 and 10 — before each session. A pH meter that has not been calibrated is producing numbers, not measurements.

Advantages: wide pH range, unaffected by oxidising or reducing agents, works in coloured and turbid solutions, needs only a small sample. Limitations: the glass is fragile, has very high resistance so needs a high-impedance meter, and shows an alkaline error above about pH 9 where sodium ions compete with hydrogen ions.

Conductivity measurement

Conductance $G = 1/R$ in siemens. For a solution:

G = \kappa\frac{A}{l} \quad\Longrightarrow\quad \kappa = G \times \frac{l}{A} = G \times \text{cell constant}

$\kappa$ is the specific conductance or conductivity, in S m⁻¹, and $l/A$ is the cell constant in m⁻¹, fixed by the geometry of the electrodes.

Why the cell constant is measured rather than calculated. The electrodes' effective area is not their geometric area, and the field between them is not uniform. So the cell constant is found by measuring a standard solution — usually KCl of known conductivity — and dividing.

Why AC and not DC. A digital conductivity meter applies an alternating voltage, typically around 1 kHz. With DC, ions would migrate to the electrodes, react, and build up a polarisation layer that changes the reading continuously. Reversing the field thousands of times a second prevents any accumulation.

Temperature matters more than students expect: conductivity rises about 2% per °C, so meters have automatic temperature compensation and readings are quoted at 25 °C.

The lithium-ion battery

Construction.

Anode: graphite, which intercalates lithium between its layers.
Cathode: a lithium metal oxide, typically LiCoO₂.
Electrolyte: a lithium salt such as LiPF₆ in an organic solvent — not water, because lithium reacts violently with it.
Separator: a porous polymer preventing physical contact.

Working. It is a rocking chair cell: lithium ions shuttle between the two hosts and neither electrode dissolves.

Discharge: Li⁺ leaves the graphite, crosses the electrolyte and inserts into the oxide; electrons take the external circuit.

\text{LiC}_6 \rightarrow \text{C}_6 + \text{Li}^{+} + e^{-} \quad(\text{anode})

\text{CoO}_2 + \text{Li}^{+} + e^{-} \rightarrow \text{LiCoO}_2 \quad(\text{cathode})

Charging reverses it. Cell voltage is about 3.7 V.

Advantages: the highest energy density in common use, no memory effect, low self-discharge, long cycle life, and a high cell voltage so fewer cells are needed in series.

Limitations: costly, degrades with age whether used or not, and thermally unstable if damaged or overcharged — the organic electrolyte is flammable, and thermal runaway is a genuine hazard. Protection circuitry is mandatory rather than optional.

Lead-acid, nickel-cadmium and nickel-metal-hydride batteries are marked self study in the syllabus and are excluded from the end semester examination. Worth knowing; not worth exam practice.

The hydrogen-oxygen fuel cell (acid electrolyte)

The distinction from a battery, which is the point most worth holding: a battery is a closed system carrying its reactants inside and going flat when they are consumed. A fuel cell is open — fuel flows in continuously and it runs as long as it is fed. It does not store energy; it converts it.

Construction. Two porous carbon electrodes impregnated with a platinum catalyst, separated by an acid electrolyte or a proton exchange membrane. Hydrogen is fed to the anode, oxygen to the cathode.

Reactions (acid electrolyte):

\text{Anode:}\quad 2\text{H}_2 \rightarrow 4\text{H}^{+} + 4e^{-}

\text{Cathode:}\quad \text{O}_2 + 4\text{H}^{+} + 4e^{-} \rightarrow 2\text{H}_2\text{O}

\text{Overall:}\quad 2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}, \qquad E°_{cell} = 1.23\ \text{V}

The only product is water.

Advantages: high efficiency, because it is not limited by the Carnot cycle the way a heat engine is; no pollution at the point of use; quiet; and continuous operation while fuelled.

Limitations: the platinum catalyst is expensive; hydrogen is difficult to store and distribute; and — the point usually left unsaid — the cell is only as clean as its hydrogen. Most hydrogen today is made by steam reforming of natural gas, which emits CO₂. The fuel cell moves the emission rather than removing it, unless the hydrogen came from electrolysis using renewable electricity.