[confusedcollegestudent]

The problem states to calculate the concentrations of all the species in a 0.455 M Na₂CO₃ solution.
The species include:
[CO₃^2-]
[HCO₃^-]
[H₂CO₃]
[Na⁺]
[OH^-]
[H⁺]
And that for H₂CO₃, K_a1 = 4.2 x 10^-7 and that K_a2 = 4.8 x 10^-11
I understand how the mathematics works behind this, though I don't understand how it ionizes and re-ionizes.
Is Na₂CO₃ the starting species or is H₂CO₃?
If Na is the starting species, is water added to it to cause it to dissociate, forming a separate ion from the sodium ion? At which point, the water would react to form OH or is it opposite where H simply dissociates in a water solution and NaOH is added?
Could someone help by writing the ionization equations? Since I'm completely lost in regards to that.

[Burner]

The following equilibrium exists:

H₂O  H⁺ + OH^-

2H⁺ + CO₃^2- H₂CO₃

H₂CO₃  H⁺ + HCO₃^-

H⁺ + CO₃^2-  HCO₃^-

And of course Na₂CO₃ completely ionizes in water upon dissolving in water:

Na₂CO₃  2Na⁺ + CO₃^2-

[AWK]

http://www.chem1.com/acad/webtext/pdf/c3carb.pdf

[Borek]

2H⁺ + CO₃^2- H₂CO₃

H₂CO₃  H⁺ + HCO₃^-

H⁺ + CO₃^2-  HCO₃^-

I find posting all three confusing and not necessary. There are only two real, independent equilibria present in the solution. As dissociation is a stepwise process, I prefer listing the first and the second dissociation steps only. Overall reaction - while often useful in calculations - is just a sum of these two.

Is Na₂CO₃ the starting species or is H₂CO₃?

Actually choice of a starting point doesn't matter. If you really understand the math behind, system is described by the system of equations - mass balances, charge balance and three individual equilibria. Assuming Na⁺ doesn't hydrolyze (it does, but in negligible amounts) amount of Na⁺ present will be inserted into the charge balance equation and that's enough to correctly solve the problem.

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

[confusedcollegestudent]

Actually choice of a starting point doesn't matter. If you really understand the math behind, system is described by the system of equations - mass balances, charge balance and three individual equilibria. Assuming Na⁺ doesn't hydrolyze (it does, but in negligible amounts) amount of Na⁺ present will be inserted into the charge balance equation and that's enough to correctly solve the problem.

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

Thank you! I see.
So since the concentration of Na₂CO3 is 0.445 M, we would use the K_b of CO₃^2-, correct?

[Borek]

Single Kb value is not enough, you need to take into account both dissociation steps. As long as you include Kw (water dissociation equilibrium) in your attempts to find tehsolution, it doesn't matter whether you use Ka1,2 or Kb1,2 values.