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Q5.5 (i):
Specify the oxidation numbers of the metals: ([Co(H_{2}O)(CN)(en)_{2}]^{2+})

Solution :

Step 1: Identification of Coordination Sphere Components

To determine the oxidation state of the central metal ion (Cobalt, $\text{Co}$), we must identify the individual charges of all ligands coordinated to the metal within the coordination sphere $[ \text{Co}(\text{H}_2\text{O})(\text{CN})(\text{en})_2 ]^{2+}$.

Ligand Number of Ligands Charge per Ligand
$\text{H}_2\text{O}$ (Aqua) 1 $0$ [Neutral molecule]
$\text{CN}^-$ (Cyano) 1 $-1$ [Anionic ligand]
$\text{en}$ (Ethylenediamine) 2 $0$ [Neutral bidentate chelate]

Step 2: Mathematical Formulation of the Oxidation State

Let the oxidation number of Cobalt be denoted as $x$. According to the algebraic sum rule for coordination complexes, the sum of the oxidation numbers of all atoms in the complex ion must equal the net charge of the coordination entity [Per IUPAC Nomenclature Rules for Coordination Compounds].

The equation is structured as follows:

$x + [1 \times (\text{charge of } \text{H}_2\text{O})] + [1 \times (\text{charge of } \text{CN}^-)] + [2 \times (\text{charge of } \text{en})] = \text{Net Charge}$

Step 3: Algebraic Calculation

Substituting the values derived in Step 1 into the equation:

$x + [1 \times (0)] + [1 \times (-1)] + [2 \times (0)] = +2$

Solving for $x$:

$x + 0 - 1 + 0 = +2$

$x - 1 = +2$

$x = +2 + 1$

$x = +3$

Step 4: Geometric Contextualization

The complex is an octahedral species where Cobalt acts as the central metal atom. The oxidation state $+3$ indicates that Cobalt has lost three electrons to form the complex, typically resulting in a $d^6$ configuration for the $\text{Co}^{3+}$ ion.

Coยณโบ Hโ‚‚O CNโป en en

Final Solution: The oxidation number of the metal (Cobalt) is $+3$.


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