Question 7 of 7: Electrochemical Sensors — pH (Potentiometric) and Oxygen (Amperometric)

Question 7: Electrochemical Sensors — pH (Potentiometric) and Oxygen (Amperometric) (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

a) The glass-membrane pH electrode is itself an extremely high-SOURCE-impedance device (commonly $10^8$–$10^9\ \Omega$) — the ion-exchange mechanism at the glass surface generates a genuine potential but can supply almost no current. Exactly as in Question 4(c)'s divider argument, if the meter's own input impedance is not many orders of magnitude larger than this source impedance, most of the true signal is dropped across the electrode's own impedance and never reaches the meter, giving a badly attenuated, inaccurate pH reading (and a reading that changes with the meter's own input impedance, which should never happen for a correctly designed instrument). A pH meter therefore needs an electrometer-grade (FET/CMOS) input stage reaching $10^{12}$–$10^{13}\ \Omega$, comfortably above the electrode's own impedance, so it draws negligible current and reads the true electrode potential.

b) A reference electrode provides a fixed, known, stable half-cell potential that does not depend on the composition of whatever solution it contacts, giving a constant baseline against which the sensing electrode's potential is measured. The common silver/silver-chloride (Ag/AgCl) construction: a silver wire coated with a layer of solid AgCl is immersed in a fixed-concentration chloride filling solution (typically saturated KCl), sealed inside a body that isolates that internal solution from the external test solution except through a small, controlled LIQUID JUNCTION (a porous frit or ceramic plug) that allows slow ionic contact (completing the electrical circuit) without letting the test solution contaminate, or significantly dilute, the fixed internal filling solution. Because the internal Ag/AgCl half-cell reaction and its surrounding chloride concentration are both fixed by construction, the electrode's potential stays constant regardless of what is being measured outside it; a saturated calomel electrode (Hg/Hg$_2$Cl$_2$ in KCl) is built the same way as an alternative.

c) This Clark-type sensor is deliberately DIFFUSION-LIMITED: the membrane restricts oxygen transport to the cathode so strongly that the electrochemical reduction reaction itself is fast by comparison and consumes essentially every oxygen molecule that arrives, holding the oxygen concentration at the cathode surface near zero. The measured current is therefore set purely by the DIFFUSION FLUX through the membrane, which by Fick's first law is directly proportional to the concentration gradient across it — and since the cathode-side concentration is pinned near zero by the fast reaction, that gradient (and hence the current) is directly proportional to the oxygen concentration on the OUTSIDE of the membrane. This built-in diffusion limitation is what makes the response inherently LINEAR, in contrast to a reaction-rate-limited sensor, whose response would instead follow more complex (generally non-linear) reaction kinetics.

d) Electrode fouling is the gradual coating or contamination of an electrode's active surface — by proteins, biofilm, precipitates, or other species carried in the sample — that physically interferes with the electrode's intended function. For the POTENTIOMETRIC pH sensor, fouling of the glass membrane or of the reference electrode's liquid junction changes the ion-exchange or junction potential in an unpredictable way, introducing an offset/drift error and a slower response — the sensor keeps producing A reading, but it is no longer the correct one. For the AMPEROMETRIC oxygen sensor, fouling of the outer membrane changes its permeability (diffusion resistance); since part (c)'s linear response depends entirely on that membrane's diffusion characteristics, fouling effectively changes the sensor's CALIBRATION SLOPE, causing it to systematically under-read the true oxygen concentration. In both cases fouling is a slow calibration drift rather than an outright failure, which makes it dangerous precisely because the sensor keeps producing plausible- looking numbers — both sensor types require periodic recalibration against a known standard, and periodic membrane/electrode cleaning or replacement, to catch and correct for it.