Step 1: Understanding the Concept:
Oxidation state is the formal charge an atom would bear if all ligands were removed along with the electron pairs that were shared with the central atom. Neutral ligands have zero charge.
Step 2: Key Formula or Approach:
Sum of oxidation states \(= \text{Total charge on the complex/molecule}\).
: Detailed Explanation:
1. \([Cr(H_{2}O)_{6]Cl_{3}\)}:
Water (\(H_{2}O\)) is neutral. The three \(Cl^{-}\) ions give a \(-3\) charge outside the bracket.
\(x + 6(0) + 3(-1) = 0 \Rightarrow x = +3\).
2. \([Cr(C_{6}H_{6})_{2]\) (Dibenzenechromium)}:
Benzene (\(C_{6}H_{6}\)) is a neutral \(\pi\)-ligand.
\(x + 2(0) = 0 \Rightarrow x = 0\).
3. \(K_{2}[Cr(CN)_{2(O)_{2}(O_{2})(NH_{3})]\)}:
Potassium (\(K^{+}\)) is \(+1\), Cyanide (\(CN^{-}\)) is \(-1\), Oxo (\(O^{2-}\)) is \(-2\), Peroxo (\(O_{2}^{2-}\)) is \(-2\), and Ammonia (\(NH_{3}\)) is neutral.
\(2(+1) + x + 2(-1) + 2(-2) + 1(-2) + 0 = 0\)
\(2 + x - 2 - 4 - 2 = 0\)
\(x - 6 = 0 \Rightarrow x = +6\).
Step 3: Final Answer:
The oxidation states are \(+3, 0, +6\).