In the complex $[Ce(NO_{3})_{6}]^{2-}$ the number of oxygen atoms used by each $NO_{3}^{-}$ to coordinate the metal are:

Question

Accepted Answer

In the complex $[Ce(NO_{3})_{6}]^{2-}$, each nitrate ion $(NO_{3}^{-})$ acts as a bidentate ligand. This means that each nitrate ion coordinates to the central metal atom, cerium (Ce), using two of its oxygen atoms. Here's a detailed explanation of why Option 2 is correct and why the other options are incorrect:

1. **Explanation for Option 2 (Correct Answer):**
   - Each nitrate ion $(NO_{3}^{-})$ has three oxygen atoms. In the context of coordination chemistry, a bidentate ligand is one that uses two donor atoms to bind to a central metal atom. In this complex, each nitrate ion uses two of its oxygen atoms to coordinate with the cerium ion. This is a common coordination mode for nitrate ions in metal complexes, where two oxygen atoms form coordinate bonds with the metal center, creating a chelate ring. Therefore, the correct answer is that each $(NO_{3}^{-})$ uses 2 oxygen atoms to coordinate with the metal, supporting Option 2.

2. **Explanation for why Option 1 is incorrect:**
   - Option 1 suggests that all three oxygen atoms of the nitrate ion are used to coordinate with the metal. However, this is not feasible because it would require the nitrate ion to act as a tridentate ligand, which is not typical for nitrate ions. The geometry and electronic structure of the nitrate ion do not favor such coordination, making this option incorrect.

3. **Explanation for why Option 3 is incorrect:**
   - Option 3 suggests that only one oxygen atom is used for coordination. While it is possible for a ligand to coordinate through a single donor atom, nitrate ions typically act as bidentate ligands in metal complexes. Using only one oxygen atom would not take full advantage of the potential chelating ability of the nitrate ion, making this option less favorable and incorrect.

4. **Explanation for why Option 4 is incorrect:**
   - Option 4 implies that none of the oxygen atoms are used for coordination, which would mean that the nitrate ion does not participate in binding to the metal at all. This is clearly incorrect, as the nitrate ions are integral to the structure of the complex and are known to coordinate through their oxygen atoms.

In conclusion, the correct answer is Option 2, as each $(NO_{3}^{-})$ uses two oxygen atoms to coordinate with the cerium ion in the complex $[Ce(NO_{3})_{6}]^{2-}$.