Given the following information for a bicarbonate buffer solution, what is the pH?

Answer

pH=pK-log{[CO2]/[HCO3-]}
    =6.1-log{0.5/20)
    =6.1-log(0.025)
    =6.1-(-1.60)
    =7.7

Derivation of the pH Equation for the Carbonic-Acid-Bicarbonate Buffer

We may begin by defining the equilibrium constant, K1, for the left-hand reaction in Equation 10, using the Law of Mass Action:
K1 calculation.

(13)

Ka (see Equation 9, above) is the equilibrium constant for the acid-base reaction that is the reverse of the left-hand reaction in Equation 10. It follows that the formula for Ka is
eq 14.

(14)

The equilibrium constant, K2, for the right-hand reaction in Equation 10 is also defined by the Law of Mass Action:
eq 15.

(15)

Because the two equilibrium reactions in Equation 10 occur simultaneously, Equations 14 and 15 can be treated as two simultaneous equations. Solving for the equilibrium concentration of carbonic acid gives
eq 16.

(16)

Rearranging Equation 16 allows us to solve for the equilibrium proton concentration in terms of the two equilibrium constants and the concentrations of the other species:
eq 17.

(17)

Because we are interested in the pH of the blood, we take the negative log of both sides of Equation 17:
eq 18,

(18)

k=ka/k2

Recalling the definitions of pH and pK (Equations 2 and 12, above), Equation 18 can be rewritten using more conventional notation, to give the relation shown in Equation 11, which is reproduced below:

pH=pK-log{[CO2]/[HCO3-]}