[nihil.ad.rem]

I need help solving this problem. The multiple parts are supposed to guide you through it, but I still don't understand how do it.

a. The principal equilibrium in a solution of NaHCO₃ is
    HCO₃^- + HCO₃^- <---> H₂CO₃ + CO₃^2-
    Calculate the value of the equilibrium constant for this reaction.

For this part, I got that K_eq = K_a2 / K_a1, and after looking up the values, I got that K_eq = 1.3x10^-4.

Here's where I stop knowing what to do...

b. At equilibrium, what is the relationship between [H₂CO₃] and [CO₃^2-]?

No values are given for these. Are they equal? Am I just supposed to give an equation?

c. Using the equilibrium H₂CO₃ <---> 2H⁺ + CO₃^2-, derive an expression for the pH of the solution in terms of K_a1 and K_a2 using the results from part b.

K_eq for this rxn would be equal to (K_a1)(K_a2), but I don't know how the answer to part b fits in, or how to relate both to pH.

d. What is the pH of a solution of NaHCO₃?

I don't know how to go about this, and I don't understand how I am supposed to get a numerical answer for part d (which is what I am supposed to get) when no values for any of the concentrations are given.

I don't expect anyone to do my homework for me, but I really need help getting started. Thanks in advance.

[AWK]

K₁K₂=[H₃O⁺]²_total[CO₃^2-]/[H₂CO₃]

[Borek]

Honestly, I don't understand suggestions given. First of all, I would not call this reaction

HCO₃^- + HCO₃^- -> H₂CO₃ + CO₃^2-

principal - if it will be true, there will be no pH change when dissolving sodium bicarbonate, as there are no H⁺ produced nor consumed during the reaction. What is happening is HCO₃^- reacts with water - either dissociating

HCO₃^- + H₂O -> H₃O⁺ + CO₃^2-

or hydrolyzing

HCO₃^- + H₂O -> H₂CO₃ + OH^-

Both these reactions can change pH of the solution and both are responsible for the final equilibrium. But - none of them dominates! See the discussion (and the way of finding solution) here:

http://www.chembuddy.com/?left=pH-calculation&right=pH-amphiprotic-salt