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, corresponding to option (b).

Step 1: Understanding the Coordination Compound

The compound given is \( \mathrm{K}_{3}[\mathrm{Co}(\mathrm{NO}_{2})_{6}] \). This is a coordination compound where the cobalt ion is the central metal ion, surrounded by six nitrite ions (\( \mathrm{NO}_{2}^{-} \)) as ligands. There are also three potassium ions (\( \mathrm{K}^{+} \)) outside the coordination complex to balance the charge.

Step 2: Determine the Charges

In coordination compounds, the sum of the oxidation numbers is equal to the charge on the complex. The compound given is neutral, so the sum of the charges must be zero. Each potassium ion contributes a charge of \( +1 \), totaling \( +3 \) from the three potassium ions.

Step 3: Calculate the Charge Contribution of Nitrite Ions

Each nitrite ion (\( \mathrm{NO}_{2}^{-} \)) carries a charge of \( -1 \). Since there are six nitrite ions, their total contribution to the charge is \(-6\).

Step 4: Calculate the Oxidation Number of Cobalt

Let the oxidation state of cobalt be \( x \). Using the equation: \[ 3(+1) + x + 6(-1) = 0 \]Simplifying the equation gives:\[ 3 + x - 6 = 0 \]\[ x - 3 = 0 \]\[ x = +3 \] Thus, the oxidation state of cobalt is \(+3\).

Step 5: Choose the Correct Option

The correct oxidation number of cobalt calculated is \(+3\), which corresponds to the option (b).

Key Concepts

Coordination Compounds

Coordination compounds are a fascinating aspect of chemistry involving complex structures with a central metal atom or ion. In our example, the complex is \( \mathrm{K}_{3}[\mathrm{Co}(\mathrm{NO}_{2})_{6}] \). Here, the cobalt ion, \( \mathrm{Co}^{3+} \), is the central ion and it is coordinated to six nitrite ligands, \( \mathrm{NO}_{2}^{-} \).
Coordination compounds are characterized by their unique structural formations where:

• The central metal atom or ion is usually a transition metal.
• Ligands, such as nitrite ions, donate electron pairs to the metal center creating a coordinate covalent bond.
• The number of ligands attached to the central metal is called the coordination number; in this case, it is six, corresponding to the six \( \mathrm{NO}_{2}^{-} \) ions.

Outside the coordination sphere, three potassium ions \( \mathrm{K}^{+} \) balance the overall charge.
This arrangement results in a neutral compound overall. Coordination chemistry is rich in structures and can greatly alter the properties of the elements involved.

Oxidation States in Chemistry

Understanding oxidation states in chemistry is crucial for analyzing the redox behaviors and bonding in compounds. The oxidation state, also known as oxidation number, is a conceptual charge assigned to an atom based on certain rules. Here’s how it works for our compound
To determine the oxidation state of cobalt:

• The sum of the oxidation numbers in a compound should equal the overall charge of the compound. In our example, the compound is neutral.
• Potassium ions \( \mathrm{K}^{+} \) each have an oxidation state of \(+1\), totaling \(+3\) because there are three.
• Nitrite ions \( \mathrm{NO}_{2}^{-} \) each contribute an oxidation state of \(-1\). With six ions, that’s a total of \(-6\).

Adding the contributions and solving for the cobalt oxidation state, we set up the equation:\[ 3(\text{oxidation state of } \mathrm{K}^{+}) + x (\text{cobalt}) + 6(\text{oxidation state of } \mathrm{NO}_{2}^{-}) = 0 \]The math works as follows: \( 3(+1) + x - 6 = 0 \), so \( x = +3 \).This mathematical approach helps in recognizing how each component affects the whole.

Transition Metals Chemistry

Transition metals, such as cobalt, are central to the field of coordination chemistry. They are characterized by their ability to form complex structures with varied oxidation states.
Some key features of transition metals include:

• The ability to adopt multiple oxidation states. For cobalt in particular, it can exist in various states like \(+2\) and \(+3\).
• Transition metals can form colored compounds, thanks to electron d-d transitions available in their partially filled d-orbitals.
• They act as excellent catalysts in many chemical reactions due to their ability to change oxidation states.

In the case of \( \mathrm{K}_{3}[\mathrm{Co}(\mathrm{NO}_{2})_{6}] \), cobalt exists in the \(+3\) state, illustrating its versatile chemistry.
This adaptation allows cobalt to form diverse compounds with different colors and reactivities.