Question

Determine the total concentration of CO₂ solution whose pH 4.5. pKa of H₂CO₃ = 3.6 and the equilibrium constant of CO₂ hydration (to produce H₂CO₃) K = 0.0017. Show your work.

Answer 1

H2CO3 (aq) <---> H (aq) + HCO3- (aq) , pka = 3.6 , Ka = 10^ -3.6 = 2.5 x 10^ -4

goven pH = 4.5 , [H+] = 10^ -4.5 = 3.16 x 10^ -5 M = [HCO3-]

at equilibrium Ka = [H+] [HCO3-] /[H2CO3]

2.5 x 10^ -4 = (3.16 x 10^-5) ( 3.16 x 10^ -5) / ( [H2CO3]

[H2CO3] = 4 x 10^ -6

Initial [H2CO3] = equilibrium [H2CO3] + [H+]    ( since some part of H2CO3 is diddciated to form H+)

    = 4 x 10^ -6 + 3.16 x 10^ -5

   = 3.56 x 10^ -5

We now have another equilibrium

CO2 (aq) + H2O (l) <--> H2CO3 (aq) , K = 0.0017

K = [H2CO3] /[CO2]

0.0017 = ( 3.56 x 10^ -5) /[CO2]

[CO2] =0.02094

Initial [CO2] = equi [CO2] + {H2CO3]

= 0.02094 + 3.56x10^-5

= 0.021 M