Write an equation that represents how dihydrogen phosphate ion (H2PO4-) behaves as an Arrhenius acid. ( Be sure to include the correct charges for ions.)

The second one you had described turned out to be the answer.

An Arrhenius acid is one that releases(provides) H^+ when placed in solution.

H2PO4^- ==> H^+ + HPO4^2-

I see some sites where the definition has been modernized to include H2O like this
H2PO4^- + H2O ==> H3O^+ HPO4^2-
however then one must explain that the hydronium ion actually is the H^+ (really the other way around); I don't think Arrhenius knew anything about the hydronium ion.

The dissociation of dihydrogen phosphate ion (H2PO4-) as an Arrhenius acid can be represented by the following equation:

H2PO4- + H2O ⇌ H3O+ + HPO42-

In this equation:
- H2PO4- represents the dihydrogen phosphate ion.
- H2O represents a water molecule.
- H3O+ represents a hydronium ion (produced from the donation of a proton from H2PO4- to H2O).
- HPO42- represents the hydrogen phosphate ion (formed from the removal of a proton from H2PO4-).

Note that the symbol "⇌" indicates a reversible reaction.

To represent how dihydrogen phosphate ion (H2PO4-) behaves as an Arrhenius acid, we need to consider the dissociation of the ion in water. In water, the dihydrogen phosphate ion can donate a hydrogen ion (H+) to the water molecules, forming hydronium ions (H3O+).

The equation can be written as:

H2PO4- + H2O -> H3O+ + HPO42-

In this equation, H2PO4- (dihydrogen phosphate ion) reacts with a water molecule (H2O) to form a hydronium ion (H3O+) and a hydrogen phosphate ion (HPO42-).

Note that the charges need to be balanced on both sides of the equation. The dihydrogen phosphate ion carries a negative charge of -1, and the hydronium ion carries a positive charge of +1. The hydrogen phosphate ion carries a negative charge of -2.

Remember, this equation represents the behavior of dihydrogen phosphate ion as an Arrhenius acid, specifically in terms of its dissociation in water.