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 %
