Question

2d. Bicarbonate does buffer the blood because carbonic acid is generated from dissolving CO2 (g) in liquid water:

CO2 (g) + H2O (l) ↔ H2CO3 (aq) pKeq° = 2.52 at 37°C

This reaction is catalyzed by the enzyme carbonic anhydrase. Consequently, the reaction that really represents what’s happening when bicarbonate buffers the blood is: CO₂ (g) + H₂O (l) ↔ HCO₃- (aq) + H+ (aq).

Calculate the equilibrium constant for this reaction (Hint: use Hess’s law and one of the equilibrium expressions from question 2ci above). Would you expect this to be an adequate buffer system at physiological pH? Explain.

My answer to 2ci:

2c. The pKa’s for carbonic acid and bicarbonate at 37°C are 3.83 and 10.25, respectively.

i. Write the equation for each of these equilibria.

H₂CO₃ + H₂O ⇄ HCO₃⁻ + H₃O⁺ (pKa = 3.83)

HCO₃⁻ + H₂O ⇄ CO₃²⁻ + H₃O⁺   (pKa = 10.25)

Answer 1

Sol:-

As, pK_a = - log K_a

So, K_a1 = 10^-pKa1 = 10^-2.52 = 3.02 x 10^-3

and

K_a2 = 10^-pKa2 = 10^-3.83 = 1.48 x 10^-4

Given reactions are :

CO₂ (g) + H₂O (l) <--------------> H₂CO₃ (aq) , pK_a1 = 2.52 , K_a1 = 3.02 x 10^-3.........................(1)

H₂CO₃ (aq) + H₂O (l) <---------> HCO₃^- (aq) + H₃O⁺ (aq) , pK_a2 = 3.83, K_a2 = 1.48 x 10^-4

OR

H₂CO₃ (aq) <---------> HCO₃^- (aq) + H⁺ (aq) , pK_a2 = 3.83, K_a2 = 1.48 x 10^-4 .....(2)

Aim equation is : CO₂ (g) + H₂O (l) <-------------------> HCO₃^- (aq) + H⁺ (aq) , K_a = ?

Aim equation can be obtained by adding equations (1) and (2). Now, the relationship between K_a1, K_a2 and K_a becomes :

K_a = K_a1 x K_a2

So,

K_a of aim equation = 3.02 x 10^-3 x 1.48 x 10^-4 = 4.47 x 10^-7

Hence, equilibrium constant of the reaction = 4.47 x 10^-7

Its pK_a = - log 4.47 x 10^-7 = 6.35