Problem 36 - A Complete Resource Book in Chemistry for JEE Main

Question

The oxidation number of cobalt in \(\mathrm{K}_{3}\left[\mathrm{Co}\left(\mathrm{NO}_{2}\right)_{6}\right]\) is (a) \(-3\) (b) \(+3\) (c) \(-4\) (d) \(+4\)

Step-by-Step Solution

Answer

The oxidation number of cobalt is \(+3\), choice (b).

Step 1: Identify Known Oxidation Numbers

In the compound \(mathrm{K}_{3}left[mathrm{Co}left(mathrm{NO}_{2}right)_{6}right]\), we first identify the oxidation numbers of elements we know: Potassium (K) has an oxidation number of \(+1\), and the nitrite ion \(mathrm{NO}_{2}^{-}\) has an oxidation number of \(-1\) for each nitrite group.

Step 2: Calculate Total Charge Contribution Outside the Complex Ion

The complex ion \([mathrm{Co}left(mathrm{NO}_{2}right)_{6}]^{n}\) is paired with 3 potassium ions, each with a charge of \(+1\). Therefore, the total positive charge from potassium is \(+3\). This means the complex ion must have a total charge of \(-3\) to balance the overall charge to zero (neutral compound).

Step 3: Express the Charge of the Complex Ion

Let the oxidation number of Cobalt (Co) be denoted as \(x\). Since there are 6 nitrite ions each with a charge of \(-1\), the expression for the charge of the entire complex ion is \(x + 6(-1) = -3\).

Step 4: Solve the Oxidation Number Equation

Set up the equation from the expression:\[ x + 6(-1) = -3 \]Simplify and solve for \(x\):\[ x - 6 = -3 \]Add 6 to both sides:\[ x = -3 + 6 \]Thus, the oxidation number of cobalt is \(+3\).

Key Concepts

Cobalt

Cobalt (Co) is a chemical element that belongs to the group of transition metals on the periodic table. It is found in the center block of the periodic table, which is known for including elements that often have multiple possible oxidation states. Cobalt's most common oxidation state is +2 or +3, but it can show other oxidation numbers under specific conditions.
Cobalt is an important element in biological systems and industrial applications. It is used in the manufacturing of super alloys, wear-resistant and corrosion-resistant alloys, and magnets. Cobalt is also essential in vitamin B12, a vital nutrient in human nutrition.

Complex Ion

A complex ion consists of a central metal ion bonded to one or more ligands. These ligands are molecules or ions with lone pairs of electrons that can be shared with the metal ion to form coordinate covalent bonds.
The compound \(K_3[Co(NO_2)_6]\) contains the complex ion \([Co(NO_2)_6]^3-\). Here, cobalt acts as the central metal ion, and the six nitrite ions (NO\(_2^−\)) act as the ligands, creating a stable coordination complex.
The charge on the complex ion is determined by the oxidation state of the metal and the charges of the ligands. If ligands are negative like nitrite, they contribute a negative charge, which is counterbalanced by the metal's positive oxidation number. In this exercise, the net charge of the complex is -3, which includes the oxidation state of cobalt and the contributions from the six nitrite ions.

Charge Balance

Charge balance refers to the scenario where the total positive and negative charges in a compound add up to zero, resulting in a neutral compound. In coordination complexes, charge balance is crucial for understanding the overall charge and the oxidation states of the involved metals and ligands.

• The compound \(K_3[Co(NO_2)_6]\) needs to have an overall charge of zero to be stable as a compound.
• Potassium (K) provides a positive charge of +3 (since each potassium ion carries a +1 charge).
• Therefore, the complex ion \([Co(NO_2)_6]\) must carry a charge of -3 to balance out the +3 from potassium, achieving an overall neutral charge for the compound.

This exercise showcases how to calculate the metal's oxidation number by ensuring charge balance in the overall compound.

Transition Metals

Transition metals, including cobalt, are elements found in the d-block of the periodic table. They exhibit a wide range of oxidation states and are known for their ability to form colorful and complex ions.
These metals are characterized by:

• Variable oxidation states: Transition metals can exist in more than one oxidation state, due to the involvement of d-electrons in bonding.
• Formation of colored compounds: Many transition metal complexes are vibrantly colored due to d-d electron transitions.
• Ability to form complex ions: They readily bond with various ligands to form coordination complexes with unique properties.

Cobalt, as a transition metal, can form numerous coordination compounds, each showing different properties and oxidation numbers based on the surrounding ligands. This flexibility in forming complex ions and varied oxidation states makes transition metals especially interesting in chemistry.