The physiochemical approach to acid base is derived from fundamental chemical principles (laws of mass action, water dissociation, conservation of mass and electroneutrality).
pH depends on CO2 and bicarbonate according to the Henderson Hasselbalch equation:
$$pH = 6.1 + \ln \frac{[HCO3-]}{0.03 x PaCO2}$$
The PaCO2 is directly set by the alveolar ventilation.
But [HCO3-] is not under physiological control; it depends on the strong ion difference and total quantity of weak acids. This is because electroneutrality must be maintained (i.e. total bicarb cannot exceed the SID) and because bicarb is in competition with other weak acids for potential anion space.
$$\require{AMScd}$$
$$\begin{CD} @. \substack{\text{Dead} \\ \text{space}} @. @. @. \\ @. @VVV @. @. @. \\ \substack{\text{Minute} \\ \text{volume}} @>>> \substack{\text{alveolar} \\ \text{ventilation}} @>>> {\mathbf{PaCO_2}} @<<< \substack{\text{Metabolic} \\ \text{rate}} @. \\ @. @. @VVV @. @. \\ @. @. {pH} @. @. \\ @. @. @AAA @. @. \\ \substack{PO_4^- \\ \text{(renal clearance)}} @>>> {\mathbf{A_{TOT}}} @>>> {HCO_3^-} @<<< {\mathbf{SID}} @<<< \substack{\text{Other strong} \\ \text{anions}} \\ @. @AAA @. @AAA @. \\ @. \substack{\text{Albumin} \\ \text{ }} @. @. \substack{\text{Na/Cl} \\ \text{balance}} \end{CD}$$
SID is under renal control, because the kidneys can
\(A_{TOT}\) is 75% albumin, ~10% phosphate.
Strong ion gap = \(SID_{apparent} - SID_{effective}\), where
$$SID_{apparent} = [Na^+] + [K^+] + 2[Ca^{2+}] + 2[Mg^{2+}] - [Cl^-] - [Lactate^-]$$
$$SID_{effective} = [PO4-] + 0.25 \cdot Albumin$$
Analogous to anion gap but incorporates lactate and albumin, therefore only altered by the presence of ketones, pyroglutamate, salicylates, toxic alcohols etc.