To determine the IUPAC name of the compound K₃[Co(C₂O₄)₃], let's follow the nomenclature rules for coordination compounds:

Identify the Cation and Anion: The compound consists of potassium ions (K⁺) and a complex anion [Co(C₂O₄)₃]³⁻.

Name the Cation First: The cation is named first. So, we start with "Potassium."

Determine the Ligand Name: The ligand C₂O₄²⁻ is called "oxalato."

Count the Number of Ligands: There are three oxalato ligands. Since "oxalato" does not contain any numerical prefixes (like di-, tri-), we use the prefixes "di-", "tri-", etc., for simple ligands. So, we use "trioxalato."

Name the Central Metal Atom: Since the complex ion is an anion, the metal name ends with the suffix "-ate." Therefore, "cobalt" becomes "cobaltate."

Specify the Oxidation State: The oxidation state of cobalt in this complex can be calculated:

Let the oxidation state of Co be x.

Each oxalato ligand has a charge of -2.

The overall charge of the complex ion is -3.

So, x + 3(-2) = -3 ⇒ x -6 = -3 ⇒ x = +3.

Therefore, we indicate the oxidation state as (III).

Combining all these, the IUPAC name is Potassium trioxalatocobaltate(III).

Answer: Option C

Potassium trioxalatocobaltate(III)