What is the equilibrium constant expression for the predominant equilibrium in HPO4^2- (aq)?

HPO4^-2 ==> H^+ + PO4^-3 and

The first one is
K3 = (H^+)(PO4^-3)/(HPO4^-2)

I answered that, but the teacher marked me wrong.. so I don't understand why?

The predominant reaction should be HPO4^2- acting as an acid right?

I wrote, then erased before I posted the response that there could be two competing reactions. The second one was

H^+ + H2PO4^-2 ==> H2PO4^-
Written as it is, this is the reverse of k2 and with a Keq of about 100,000 or so it could be. The problem with problems like this is one never knows exactly what predominant means (except to the person making up the problem).

I don't really understand what k2 and k3 means..

To find the predominant reaction, could I compare the ka and kb values for HPO4^2-?

k1 = (H^+)(HPO4^-2)/(H3PO4 = about 1E-2

k2 = (H^+)(HPO4^-2)/(H2PO4^-) = about 1E-8
k3 = (H^+)(PO4^-3)/(HPO4^-2) = about 1E-13

Here is what k1, k2, and k3 mean.
And yes, I don't see why you can't compare Ka and Kb to determine the reaction most likely to occur.

So I found the Ka for HPO4^2- which is 2.2x10^-13

Then i found HPO42- on right side of the table and found the ka value which is 6.2x10^-8.
Then, I used kb=kw/ka to and got 1.61x10^-7
Since kb>ka the reaction:
HPO4^2- + H2O <--> H2PO4- + OH-
would be the one most likely to occur?

The equilibrium constant expression for a chemical reaction gives us information about the relative concentrations or pressures of the different species involved in the reaction. In order to determine the equilibrium constant expression for the dissociation of HPO4^2- (aq), we first need to understand the dissociation reaction that occurs.

The predominant equilibrium for HPO4^2- (aq) is its dissociation into H+ (aq) and PO4^3- (aq). The chemical equation representing this dissociation reaction is as follows:

HPO4^2- (aq) ⇌ H+ (aq) + PO4^3- (aq)

To write the equilibrium constant expression, we use the concentrations of the products raised to their stoichiometric coefficients divided by the concentrations of the reactant raised to its stoichiometric coefficient. In this case, the equilibrium constant expression is as follows:

K = [H+][PO4^3-] / [HPO4^2-]

Here, [H+], [PO4^3-], and [HPO4^2-] represent the concentrations of the respective species at equilibrium. Note that the coefficients in the balanced chemical equation are used as the exponents in the equilibrium constant expression.

So, the equilibrium constant expression for the dissociation of HPO4^2- (aq) is K = [H+][PO4^3-] / [HPO4^2-].