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

Solution :

Step 1: Identification of Coordination Entity Components

To determine the oxidation state of the central metal atom in the coordination entity $[Co(H_{2}O)(CN)(en)_{2}]^{2+}$, we must first identify the charge contributions of each ligand coordinated to the cobalt (Co) atom.

Ligand / Species Chemical Formula Charge contribution
Central Metal $Co$ $x$ (unknown)
Aqua (Water) $H_{2}O$ $0$ (Neutral molecule)
Cyano $CN^{-}$ $-1$ (Anionic ligand)
Ethylenediamine $en$ (or $NH_{2}CH_{2}CH_{2}NH_{2}$) $0$ (Neutral bidentate ligand)

Step 2: Mathematical Formulation of Oxidation State

The sum of the oxidation numbers of all atoms in a coordination entity must equal the net charge residing on the complex ion [Per the Rules of Nomenclature for Coordination Compounds].

The equation is structured as follows:

$(Charge\ of\ Co) + (Charge\ of\ H_{2}O) + (Charge\ of\ CN) + 2 \times (Charge\ of\ en) = \text{Net Charge of Entity}$

Step 3: Algebraic Substitution and Calculation

Substituting the identified values into the equation:

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

Solving for $x$:

$x - 1 = 2$

$x = 2 + 1$

$x = 3$

Step 4: Geometric Contextualization (Visualization)

The cobalt atom exists in a coordination environment where six donor atoms surround the metal center (octahedral geometry). The following diagram represents the coordination sphere conceptually.

Co H₂O CN⁻ en en

Final Solution: The oxidation number of the metal Cobalt ($Co$) in $[Co(H_{2}O)(CN)(en)_{2}]^{2+}$ is $+3$.


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