04-Bio-A8 · December 2017
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format: National Exams, December 2017 — 04-Bio-A8 Biophysical Measurements. Three hours, open book, any non-communicating calculator. Seven questions of equal value (20 marks each); five constitute a complete paper and only the first five appearing in the answer book are marked. All seven are solved here, because this set is a study resource rather than an examination script. Every question is qualitative/descriptive — there is no numerical data to compute — so each answer follows flowing prose with instrumentation block diagrams where the question explicitly asks for one.
Reference texts (the books an open-book candidate should have on the desk for this subject):
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 modern combination pH electrode packages two half-cells in one probe body. The sensing half-cell is a thin bulb of pH-sensitive glass (a lithium or sodium silicate glass) enclosing a fixed internal filling solution of known, constant pH (commonly a chloride-buffered solution) into which an internal Ag/AgCl reference wire is immersed. The external reference half-cell — typically also Ag/AgCl, or a calomel electrode — is immersed in a saturated KCl (or similar) electrolyte and contacts the sample solution through a porous junction (a ceramic frit or fibre), completing the circuit while its own potential stays fixed regardless of the sample's composition.
The underlying scientific basis is ion-exchange equilibrium at the hydrated gel layers that form on both the inner and outer surfaces of the glass membrane when it is soaked in an aqueous solution: hydrogen ions from solution exchange with alkali-metal ions (Li$^+$/Na$^+$) at fixed exchange sites within these gel layers, and the glass is manufactured so that this exchange is highly selective for H$^+$ over other cations. Because the inner gel layer is in equilibrium with the fixed-pH internal filling solution while the outer gel layer equilibrates with the sample, a boundary potential develops across the thin, dry glass interior that separates them (which conducts only feebly, by migration of Li$^+$/Na$^+$ ions, and so gives the electrode its very high resistance), proportional to the difference in H$^+$ activity (and hence pH) on the two sides. Summing this boundary potential with the (constant) internal and external reference-electrode potentials gives a net electrode EMF that obeys the Nernst relation:
$$E = E^{0} - \frac{2.303\,RT}{F}\,\text{pH} \approx E^{0} - 59.2\,\text{pH}\ \ (\text{mV, at }25^\circ\text{C})$$so the measured cell voltage falls by about 59.2 mV for every unit increase in sample pH — the Nernst slope, whose temperature dependence (through the $RT/F$ term) is addressed in part (iii).
A conventional pH electrode is converted into a $pCO_2$ sensor (the Severinghaus principle) by enclosing its glass bulb, together with a thin film of a bicarbonate–buffered electrolyte, inside a $CO_2$-permeable but ion-impermeable membrane (thin silicone or Teflon). Dissolved $CO_2$ in the sample diffuses freely across this membrane (H$^+$ and HCO$_3^-$ cannot) and equilibrates with the thin trapped bicarbonate film, where it hydrates and dissociates:
$$\text{CO}_2 + \text{H}_2\text{O} \rightleftharpoons \text{H}_2\text{CO}_3 \rightleftharpoons \text{H}^+ + \text{HCO}_3^-$$The resulting change in H$^+$ activity in the thin film — and hence the pH the underlying glass electrode reports — is related to the log of the $CO_2$ partial pressure via the Henderson–Hasselbalch relation, so the electrode's ordinary pH output becomes, after a logarithmic calibration against known $CO_2$ gas mixtures, a direct measure of $pCO_2$. No new transducer principle is needed: the same glass-membrane/ion-exchange mechanism of part (i) is simply re-purposed by interposing a selective gas-permeable membrane and a thin reactive electrolyte film ahead of it.
Because the glass membrane is extremely thin and only weakly conductive, the electrode presents a very high source impedance (typically $10^8$–$10^9\,\Omega$), so any amplifier loading it must draw negligible input current or the measured voltage sags and becomes nonlinear. The first stage is therefore a dedicated electrometer (high-input-impedance buffer) built around a JFET- or MOSFET-input operational amplifier with input impedance well above $10^{12}\,\Omega$ and picoampere-level bias current, wired as a unity-gain voltage follower; a driven guard-ring on the PCB and a driven (guarded) coaxial input cable shield are used to prevent leakage and cable capacitance from corrupting this very-high-impedance node. Because the Nernst slope $2.303RT/F$ is directly proportional to absolute temperature (about 54.2 mV/pH at 0°C, rising to 61.5 mV/pH at 37°C), the buffered signal is fed to a temperature-compensated scaling amplifier whose gain is set by a thermistor (or platinum RTD) immersed with the electrode, so that the mV-to-pH conversion is corrected automatically for the sample's actual temperature before the value is digitized and displayed.
A bedside arterial blood-gas analyzer draws exactly this design: the same glass-electrode/electrometer/temperature-compensation chain reports blood pH directly, while a second, Severinghaus-membrane-covered channel built on an identical pH sensing element reports $pCO_2$ from the same small blood sample, both automatically corrected to the sample's measured temperature.
