The glass pH electrode and ion-selective electrodes

Dip a pH meter into a mixture of 0.10 M NaOH and 0.90 M NaCl and the display says 11.0 — yet the solution’s pH is 13.0. The meter is not broken and the buffers have not expired; the glass membrane has been fooled by a flood of $\ce{Na+}$. The glass electrode is the most widely used chemical sensor in the world, with millions of measurements a day relying on it. Knowing how it works and when it goes wrong underpins every pH measurement.

The sensing part of a pH electrode is a thin glass bulb about 0.1 mm thick. Glass is a network of silicate tetrahedra whose negative charges are balanced by cations such as $\ce{Na+}$ and $\ce{Li+}$. The inner and outer surfaces carry hydrated gel layers tens of nanometres thick, where $\ce{Si-O-}$ sites exchange with $\ce{H+}$ from the solution: the more acidic the outside, the more $\ce{H+}$ binds there, and a potential difference builds across the membrane. Inside the glass, $\ce{Na+}$ carries the current; $\ce{H+}$ itself never crosses.

The bulb holds a chloride buffer of fixed pH and an Ag/AgCl internal reference wire; a combination electrode also packs the external reference (another Ag/AgCl with KCl filling) into the same body. The electrode’s potential is a straight line in sample pH with a slope close to the Nernst slope and an intercept (the zero point, or asymmetry potential) that varies between electrodes and drifts with use — which is why it must be calibrated with buffers every time.

Calibrate properly: use two (or three) buffers that bracket the sample — 7.00 and 4.01 for acidic samples, 7.00 and 10.01 for basic ones; rinse with distilled water and blot between solutions; wait for a stable reading; keep samples and buffers at the same temperature or use automatic temperature compensation. With one buffer only, the meter can only assume a 100 % slope, and the error grows with distance from the calibration point.

No electrode responds to one ion alone. When $[\ce{H+}]$ is tiny and $[\ce{Na+}]$ large, $\ce{Na+}$ takes over the exchange sites, the electrode mistakes it for $\ce{H+}$ and reads low — the alkaline (sodium) error. In very strong acid the membrane’s response saturates and it reads high — the acid error.

The Nikolsky–Eisenman equation converts each interfering ion j into an “equivalent” amount of the measured ion: the smaller $K_{ij}$, the more selective the electrode. General-purpose glass has $K_{\ce{H+},\ce{Na+}}$ near 10⁻¹¹, which gives an error of about −1 unit at pH 12 in 1 M $\ce{Na+}$; lithium-based “low-sodium-error” glass cuts it below 0.1.

Ion-selective electrodes swap the glass for a membrane sensitive to another ion: a single crystal of $\ce{LaF3}$ doped with $\ce{EuF2}$ for $\ce{F-}$; a pressed $\ce{Ag2S}$ pellet for $\ce{Ag+}$ and $\ce{S^2-}$; a PVC membrane holding valinomycin for $\ce{K+}$ (selectivity against $\ce{Na+}$ about 10⁻⁴); a gas-permeable membrane over a pH electrode for $\ce{CO2}$ and $\ce{NH3}$. The $\ce{Na+}$, $\ce{K+}$, $\ce{Ca^2+}$ and $\ce{Cl-}$ results of a clinical blood-gas analyser are measured this way.

The fluoride electrode suffers almost only from $\ce{OH-}$ ($K_{\ce{F-},\ce{OH-}} \approx 0.1$), but the sample pH must be right: below pH 5 fluoride is protonated to HF (p$K_\mathrm{a}$ 3.17) and the electrode cannot see it; above pH 8 hydroxide impersonates fluoride. So samples are mixed 1 : 1 with total ionic strength adjustment buffer (TISAB): concentrated NaCl fixes the ionic strength (so standards and samples share activity coefficients), an acetate buffer holds pH 5–5.5, and CDTA frees fluoride bound to $\ce{Al^3+}$ and $\ce{Fe^3+}$.