What is the IUPAC name of K_3[Co(C_2O_4)_3] ?

The given coordination compound is $\text{K}_3[\text{Co}(\text{C}_2\text{O}_4)_3]$.

The cation is potassium, which is written first.

The complex part is an anion, $[\text{Co}(\text{C}_2\text{O}_4)_3]^{3-}$. For anionic complexes, the name of the central metal ends with the suffix '-ate'. Thus, cobalt becomes cobaltate.

The ligand is oxalate ($\text{C}_2\text{O}_4^{2-}$), which is named 'oxalato'. Since there are three oxalate ligands, the prefix 'tri' is used, giving 'trioxalato'.

Let the oxidation state of cobalt be $x$.
The charge on one oxalate ligand is $-2$.
The sum of oxidation states in the complex anion is equal to its net charge:
$x + 3(-2) = -3$
$x - 6 = -3$
$x = +3$

The oxidation state of cobalt is (III).

Combining these parts, the IUPAC name of the compound is Potassium trioxalatocobaltate(III).

Answer: Potassium trioxalatocobaltate(III)