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$\ce{[Co(edta)]^-}$ has 5 rings in total and in $\ce{[Co(en)_3]^{3+}}$, there are 3 rings. The stability of the former is more than that of the latter. The reason I was told was that a complex with more number of rings is more stable.

Why is this so?

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When polydentate ligands binds to a metal in a ring form, it is called chelate ring and the corresponding complex is called chelate complex.

Experimentally, it is observed that metal complexes of polydentate ligands with more rings are significantly more stable than the corresponding complexes of similar ligands but with less rings. Because, the larger the number of ring closures to a metal atom, the more stable the compound. This phenomenon is called the chelate effect.

But, do note that ring number is not the only factor to determine the stability of a complex. There are several other factors like nature of central metal ion or the ligands, ring size, ionic size. For this question, let's consider ring size.

The more the ring size, the less stable is the complex. The entropy of complex is changed if the size of chelating ring is increased or decreased. Four membered ring compounds are unstable, whereas five-membered are more stable because of negligible ring strain. Likewise, ligands with a flexible organic backbone like ethylenediamine are significantly more stable than complexes with six-membered chelate rings, which are in turn much more stable than complexes with four- or seven-membered rings.

Refer to the following articles for more details:

  1. https://chem.libretexts.org/Bookshelves/Inorganic_Chemistry/Modules_and_Websites_(Inorganic_Chemistry)/Coordination_Chemistry/Complex_Ion_Equilibria/Stability_of_Metal_Complexes_and_Chelation
  2. https://old.amu.ac.in/emp/studym/99996027.pdf
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