buffer and solubility

Question

10. Given a patient’s pCO2 of 38 mm Hg and a pH of 7.15, what is the bicarbonate concentration? (NOTE: solubility coefficient of pCO2 is 0.0306 mmol/L/mm Hg and pKa is 6.10)

Answer 1

The concentration of dissolved CO₂ is calculated by multiplying the pCO₂ by the solubility factor 0.0306 mmol·L^-1·mmHg^-1

[CO₂]_dissolved = (0.0306 mmol·L^-1·mmHg^-1)(38 mmHg) = 1.2 mmol/L

The dissolved CO₂ will quickly and practically completely combine with water to form carbonic acid, which dissociates into bicarbonate anion and hydronium ion.

[CO₂]_dissolved + H₂O → H₂CO₃ ↔ HCO₃^- + H⁺

The pKa of carbonic acid is 6.10. Therefore the Ka is 10^-6.1, so

[H⁺][HCO₃^-]÷[H₂CO₃] = 10^-6.1

Since pH is defined as the negative logarithm of the hydronium ion concentration (in moles per L): pH = -log[H⁺].

[H⁺] can be calculated from pH by the equation [H⁺] = 10^-pH.

Therefore, [H⁺] = 10^-7.15 mol/L

Solving for [HCO₃^-]

[HCO₃^-] = (0.0306 mmol·L^-1·mmHg^-1)(38 mmHg)(10^-3 mol·mmol^-1)(10^-6.10)÷10^-7.15 mol·L^-1= 13 mmol·L^-1