Explanation:

Acetylacetone:
Acetylacetone (also known as 2,4-pentanedione or acac) is a β-diketone compound with the formula CH3COCH2COCH3. It is a yellow liquid with a fruity odor. Acetylacetone is a versatile ligand that forms stable complexes with many metal ions. It acts as a bidentate ligand, meaning it can form coordination bonds with a metal ion through two oxygen atoms.

Co(acac)3:
Co(acac)3 is the coordination compound formed when 3 molecules of acetylacetone (acac) coordinate with a central cobalt (Co) ion. The cobalt ion has a charge of +3, and each acetylacetone molecule acts as a bidentate ligand, coordinating through the oxygen atoms of the carbonyl groups.

Chelate Complex:
In a chelate complex, the ligand forms a ring structure with the central metal ion. This ring structure is called a chelate ring. The chelate ring is formed by the coordination of two or more atoms of the ligand to the metal ion. In the case of Co(acac)3, the anion of acetylacetone (acac) chelates with the cobalt ion.

Ring Formation:
The question asks about the ring size of the chelate formed between the anion of acetylacetone and the Co(acac)3 complex. To determine the ring size, we need to count the number of atoms involved in the chelation.

In Co(acac)3, there are 3 acetylacetone molecules coordinating with the cobalt ion. Each acetylacetone molecule has two oxygen atoms available for coordination. Therefore, the total number of oxygen atoms available for coordination is 3 x 2 = 6.

Since the anion of acetylacetone chelates with the cobalt ion, it should coordinate with two oxygen atoms. This means that the anion of acetylacetone forms a 6-membered chelate ring with the cobalt ion.

Answer:
Therefore, the correct answer is option 'D' - six-membered chelate ring.