Question

Coordination number of $$\text{Cr}$$ is six. A complex with $${\text{C}}_{\text{2}}{\text{O}}_{\text{4}}^{\text{2 - }}$$​, en and superoxide $${\text{O}}_{\text{2}}^{\text{ - }}$$ will be in the ratio to make complex $\text{[Cr(}{\text{C}}_{\text{2}}{\text{O}}_{\text{4}}{\text{)}}_{\text{x}}{\text{(en)}}_{\text{y}}\text{(}{\text{O}}_{\text{2}}{\text{)}}_{\text{z}}{\text{]}}^{\text{ - }}$
1. $$\text{x = 1, y = 1, z = 1}$$
2. $$\text{x = 1, y = 1, z = 2}$$
3. $$\text{x = 1, y = 2, z = 2}$$
4. $$\text{x = 2, y = 1, z = 1}$$

Answer 1

Hint:The coordination number of chromium is six, hence it is in $$\text{ + 3}$$ oxidation state. It can form a coordinate bond through six donor ligand atoms. Therefore, the denticity of each ligand given should be known.

Complete step by step answer:
The given coordination compounds are as follows.
$\text{[Cr(}{\text{C}}_{\text{2}}{\text{O}}_{\text{4}}{\text{)}}_{\text{x}}{\text{(en)}}_{\text{y}}\text{(}{\text{O}}_{\text{2}}{\text{)}}_{\text{z}}{\text{]}}^{\text{ - }}$
In this compound we have to find the $$\text{x,y and z}$$ values.
The central metal atom – Chromium.
Chromium atomic number – $$\text{24}$$
Electronic configuration -$$\text{[Ar]3}{\text{d}}^{\text{4}}\text{4}{\text{s}}^{\text{2}}$$. And it is $\text{3}{\text{d}}^{\text{4}}\text{4}{\text{s}}^{\text{2}}$system. Hence, it has a total six valence electrons available for the formation of coordinate bonds.
For $$\text{x}$$ value:
The ligand oxalate (${\text{C}}_{\text{2}}{{\text{O}}_{\text{4}}}^{\text{2 - }}$) is a bi-dendate ligand means which donate two pairs of electrons to a central metal atom.

Figure 1: Oxalate ion
Hence, the coordination number is $$\text{2}$$.
For $$\text{y}$$ value:
The ligand ethylenediamine (en) is also bi-dendate ligand and it is a neutral ligand.

Figure 2: Ethylene diamine
Hence, the coordination number is $$\text{2}$$.
For $$\text{z}$$ value
The ligand superoxide (${{\text{O}}_{\text{2}}}^{\text{ - }}$) is a mono-dendate ligand. Hence, the coordination number is $$\text{1}$$.
Since, the coordination number central metal atom is $$6$$. All these $$\text{x, y and z}$$ values are equal to the $$6$$.
$\text{2x + 2y + z = 6}$………………………(1)
From Charge-balance equation:
$\text{[Cr(}{\text{C}}_{\text{2}}{\text{O}}_{\text{4}}{\text{)}}_{\text{x}}{\text{(en)}}_{\text{y}}\text{(}{\text{O}}_{\text{2}}{\text{)}}_{\text{z}}{\text{]}}^{\text{ - }}$
The $\text{Cr}$oxidation state $\text{ + 3}$, Oxalate ion (${\text{C}}_{\text{2}}{{\text{O}}_{\text{4}}}^{\text{2 - }}$) oxidation state is $\text{ - 2}$ , ethylenediamine oxidation number is zero and superoxide ion oxidation number is $\text{ - 1}$.
$3\times 1+(-2)\times x+0\times y+(-1)\times z=-1$
$\text{ - 2x - z = - 4}$
$\text{2x + z = 4}$………………………………..(2)
Substitute this value in equation (1)
$\text{4 + 2y = 6}$
$\text{y = 1}$
Now, since, $$\text{x,y and z }$$represent the number of ligands. Hence, it has an integral value and it cannot be zero.
Therefore, $$\text{x = 1}$$.
$$\text{x = 1}$$ and $\text{y = 1}$
Substitute these values in equation (1)
$$\begin{gathered} \text{2(1) + 2(1) + z = 6} \\ \text{4 + z = 6} \\ \text{z = 2} \end{gathered}$$
Therefore, $$\text{x = 1}$$,$\text{y = 1}$ and $$\text{z = 2}$$.
Hence, the correct option is $$\text{2}$$.

Additional information:
-A coordination compound is basically a neutral species consisting of an uncoordinated ion and coordinated complexes to maintain the overall charge balance of a complex.
-In these compounds $$\text{[ ]}$$ are mainly used to indicate the atomic composition of those are atoms and the ligands.
-Species which are present in the outside of $$\text{[ ]}$$ are not coordinated to the central metal atom but these maintain overall charge of a complex.

Note:
Denticity of the ligand is the number of pairs of electrons shared with the metal atom. The poly-dendate ligands form the ring structure with the metal ion and hence contribute to extra stability. This is known as chelate effect.