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The oxidation state of cobalt in $\left[ Co{{(N{{H}_{3}})}_{4}}({{H}_{2}}O)Cl \right]S{{O}_{4}}$ is:
(a)- 0
(b)- +4
(c)- -2
(d)- +3

Answer
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Hint: $\left[ Co{{(N{{H}_{3}})}_{4}}({{H}_{2}}O)Cl \right]S{{O}_{4}}$ is a coordination compound and the overall charge on the compound is zero, so the sum of all the atoms or molecules in the coordination compound is equal to 0.

Complete answer:
The oxidation number of an element may be defined as the charge which an atom of the element has in its ion or appears to have when present in the combined state with other atoms. We can also say oxidation number as oxidation state
Coordination compounds are defined as the compounds in which the central metal atom is linked to many ions or neutral molecules by coordinate bonds. A lone pair of electrons is donated by the ligand (ions or neutral molecules) molecules to the central metal atom.
The donor atoms, molecules, or anions that donate a pair of an electron to the central metal atom are called the ligands. The metal atom or ion to which ligands are attached is called the central metal atom or ion.
There are three types of ligands:
(i)- Negative ligand which has a negative charge.
(ii)- Neutral ligand which has zero charges.
(iii)- Positive ligand which has a positive charge.
The coordination compound $\left[ Co{{(N{{H}_{3}})}_{4}}({{H}_{2}}O)Cl \right]S{{O}_{4}}$ has an overall zero charge so, the sum of charges of all ligands and central metal atom in $\left[ Co{{(N{{H}_{3}})}_{4}}({{H}_{2}}O)Cl \right]S{{O}_{4}}$ will be zero.
So, the oxidation state of $N{{H}_{3}}$ is zero because it is a neutral ligand.
The oxidation state of ${{H}_{2}}O$ is zero because it is a neutral ligand.
The oxidation state of $Cl$is -1.
The oxidation state of $S{{O}_{2}}$ is -2.
So, equating all these, we get
Let the oxidation state of cobalt is x
$x\text{ + 4(0) + (0) + (-1) + (-2) = 0}$
$x\ \text{= +3}$
So, the oxidation state of cobalt in $\left[ Co{{(N{{H}_{3}})}_{4}}({{H}_{2}}O)Cl \right]S{{O}_{4}}$ is +3.

Hence, the correct answer is an option (d)- +3.

Note:
For finding the oxidation state of the central metal atom in the coordination compound, the oxidation state of ligands is mostly taken in combined form. If any overall charge is present on the compound then the sum of all atoms or molecules is equal to the overall charge of the compound.