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

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)

$${\text{2(1) + 2(1) + z = 6}} \\\ {\text{4 + z = 6}} \\\ {\text{z = 2}} \\\$$

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.