04-Bio-A8 · Undated paper
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format: National Exams — 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.
Part (i) covers the glass pH electrode; part (ii) is a dedicated amplifier-specification question and part (iii) a more heavily weighted Severinghaus CO₂-electrode question.
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, ion-insulating glass interior that separates them, 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 why the measurement chain in Figure 5.1 includes automatic temperature compensation.
The glass membrane presents a very high source impedance — typically $10^8$–$10^9\,\Omega$ for a modern thin-bulb pH glass — because the ion-conduction path through the hydrated glass is intrinsically resistive, so the electrode behaves electrically like a high-value resistor in series with the small Nernstian EMF of interest. Any amplifier connected to it must therefore have an input impedance far above the electrode's own source impedance (specified at $\ge10^{12}\,\Omega$, i.e. at least three to four orders of magnitude higher) so that essentially none of the signal is lost across a voltage divider formed by the electrode's source impedance and the amplifier's input impedance — the classic loading problem, which for a high-impedance source becomes severe unless the amplifier draws almost no input current. This rules out an ordinary bipolar-input op-amp (whose base bias current, even at picoamps to nanoamps, would still produce a significant IR drop across a $10^9\,\Omega$ source) in favour of a JFET- or MOSFET-input electrometer amplifier, whose gate leakage/bias current is in the femtoamp-to-picoamp range. The amplifier must also be configured as a high-input-impedance unity-gain voltage follower (or high-impedance non-inverting stage) rather than an inverting configuration, since an inverting stage presents its (comparatively low) feedback-resistor impedance directly to the source. Finally, because leakage across the PCB and cable insulation, and stray input capacitance loading the high-impedance node, can be just as damaging as amplifier bias current, the practical specification also calls for a driven guard ring around the input trace/connector and a guarded (driven-shield) coaxial input cable, both held at the same potential as the signal so that no leakage current flows between the signal conductor and its surroundings.
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.
The complete Severinghaus sensor assembly therefore consists of the ordinary glass/reference pH electrode pair, a thin layer of the bicarbonate buffer trapped directly against the glass by a $CO_2$-permeable membrane (thin Teflon or silicone rubber, chosen for high $CO_2$ solubility/diffusivity and negligible permeability to ions or water), and an electrolyte-soaked spacer (often a single layer of nylon mesh soaked in the bicarbonate buffer) that holds this thin film in place against the glass surface. The membrane's thinness is a deliberate design trade-off: a thinner membrane and thinner buffer film shorten the diffusion path for $CO_2$ and so give a faster response time (tens of seconds rather than minutes), at the cost of a more fragile assembly that is more prone to membrane puncture or drying out. Because the whole sensor still reports its result as a pH change in the trapped bicarbonate film, it plugs into exactly the same high-impedance electrometer and temperature-compensation instrumentation described for the ordinary pH electrode in part (ii) — no new amplifier or electronic design is required, only the same mV-to-pH conversion, now recalibrated (via the Henderson–Hasselbalch relation) as a pH-to-$pCO_2$ conversion referenced against known $CO_2$ gas-calibration mixtures.
A bedside arterial blood-gas analyzer combines exactly these three elements: the same glass-electrode chemistry from part (i), a femtoamp-input-bias electrometer with a guarded input meeting the specification in part (ii), and a Severinghaus-membrane-covered channel built on an identical glass sensor from part (iii), so pH and $pCO_2$ are reported from the same small blood sample through the same class of front-end electronics.
