Neglecting free co2, what fraction will be present as carbonic acid? (pka for h2co3 and hco3− are 6.3 and 10.25, respectively)

The correct answer is 5.93 %.

In blood, CO₂ dissolves and follow the following equilibrium:

CO₂ + H₂O ⇔ HCO₃⁻ + H⁺

In order to find the fraction of carbonic acid, we have to use Handerson-Hasselbalch equation, This equation illustrates the derivation of pH as a measure of acidity.

The equation is:

pH = PKa + log10 [A-] / [HA]

[HA] is the molar concentration of undissociated acid, and [A-] is the molar concentration of conjugate base.

Now, pH of blood is 7.5

PKa of H₂CO₃ is 6.3, and PKa for HCO₃⁻ is 10.25

Using equation,

pH = PKa + log10 [A-] / [HA]

Here, [A-] = [HCO₃⁻] and [HA] = [H₂CO₃]

7.5 = 6.3 + log10 [HCO₃]⁻ / [H₂CO₃]

7.5 - 6.3 = log10[HCO₃]⁻ / [H₂CO₃]

1.2 = log10[HCO₃]⁻ / [H₂CO₃]

10^(1.2) = [HCO₃]⁻ / [H₂CO₃]

15.84 = [HCO₃]⁻ / [H₂CO₃]

15.84 [H₂CO₃] = [HCO₃]⁻

Now concentration of [H₂CO₃] and its conjugate base must be equivalent to 1,

Therefore, [H₂CO₃]  + [HCO₃]⁻ = 1

[H₂CO₃]  + 15.84 [H₂CO₃] = 1

[H₂CO₃] [1 + 15.84] = 1

[H₂CO₃] [16.84] = 1

[H₂CO₃] = 1 / 16.84

[H₂CO₃] = 0.0593 = 5.93 %