Question

Carbon dioxide dissolves in water to form carbonic acid, which is primarily dissolved CO2 . Dissolved CO2 satisfies the equilibrium equation CO2(g)↽−−⇀CO2(aq)?=0.032 CO 2 ( g ) ↽ − − ⇀ CO 2 ( aq ) K = 0.032 The acid dissociation constants listed in most standard reference texts for carbonic acid actually apply to dissolved CO2 CO 2 . For a CO2 CO 2 partial pressure of 2.6×10−4 bar 2.6 × 10 − 4 bar in the atmosphere, what is the pH of water in equilibrium with the atmosphere? For carbonic acid, ?a1=4.46×10−7 K a1 = 4.46 × 10 − 7 and ?a2=4.69×10−11 K a2 = 4.69 × 10 − 11 . pH= pH =

Answer 1

Carbon dioxide dissolves in water to form carbonic acid. The dissolved carbon dioxide is in equilibrium with the gaseous carbon dioxide:

  

K = 0.032 mol/l.bar. (As no unit has been given, I am assuming that this is the unit). The partial pressure of CO₂ is 2.6×10^-4 bar.

  

                     = 0.032 mol/l atm × 2.6×10^-4 bar

                     = 8.32×10^-6 M.

Therefore, the concentration of dissolved CO₂ is 8.32×10^-6 M.

Now, the concentration of CO₂ dissolved in water at equilibrium is equal to the concentration of H₂CO₃ in the solution.

⸫ [H₂CO₃] = [CO₂]_aq = 8.32 ×10^-6 M.

  

  

As K_a1 >> K_a2, the small fraction of HCO₃^- ions formed in the 1^st step will go on to dissociate in the 2^nd step. This implies that [H⁺] = [HCO₃^-].

Since and [H⁺] = [HCO₃^-], therefore

             

           

            

            

Therefore, the pH of water containing the dissolved carbon dioxide will be:

       = -log(1.926 × 10^-6) = 5.71.