To calculate the pH of the blood sample after the bicarbonate-carbonic acid buffer system has come to equilibrium, we need to consider the Henderson-Hasselbalch equation, which relates the pH of a buffer system to the pKa and the ratio of the concentrations of the conjugate acid and base.
The bicarbonate-carbonic acid buffer system involves the equilibrium reaction:
H₂CO₃ ⇌ H⁺ + HCO₃⁻
Given that the initial concentration of carbonic acid (H₂CO₃) is 62 g and the volume is 2 L, we need to convert the mass of carbonic acid to moles:
62 g H₂CO₃ * (1 mol H₂CO₃ / molar mass of H₂CO₃) = x mol H₂CO₃
To find the concentration (in moles per liter) of H₂CO₃, we divide the moles of H₂CO₃ by the volume:
x mol H₂CO₃ / 2 L = [H₂CO₃]
Since the ratio of [H₂CO₃] to [HCO₃⁻] is 1:1, we can write [H₂CO₃] = [HCO₃⁻].
Using the Henderson-Hasselbalch equation:
pH = pKa + log([HCO₃⁻] / [H₂CO₃])
We can substitute [H₂CO₃] with [HCO₃⁻]:
pH = pKa + log([HCO₃⁻] / [HCO₃⁻])
Simplifying:
pH = pKa
Therefore, the pH of the blood sample after the bicarbonate-carbonic acid buffer system has come to equilibrium is equal to the pKa of carbonic acid, which is 3.49.