Problem 106 - A Complete Resource Book in Chemistry for JEE Main

Question

Consider the following complex \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{CO}_{3}\right] \mathrm{ClO}_{4}\) The coordination number, oxidation number, number of d electrons and number of unpaired d electrons on the metal are, respectively (a) \(6,3,6,0\) (b) \(6,3,6,3\) (c) \(6,0,6,3\) (d) \(6,2,6,3\)

Step-by-Step Solution

Answer

(b) 6, 3, 6, 3

Step 1: Determine Coordination Number

The coordination number refers to the number of ligand attachments to the central metal atom. In the complex \([\mathrm{Cr}(\mathrm{NH}_{3})_{5}\mathrm{CO}_{3}]\mathrm{ClO}_{4}\), you can see there are 5 ammonia \(\mathrm{NH}_{3}\) molecules and 1 carbonate \(\mathrm{CO}_{3}^{2-}\). Thus, the coordination number is 6.

Step 2: Determine Oxidation Number of Chromium

Each ammonia molecule \((\mathrm{NH}_{3})\) is a neutral ligand, contributing 0 to the oxidation state. Carbonate \((\mathrm{CO}_{3}^{2-})\) contributes \(-2\). Perchlorate \((\mathrm{ClO}_{4}^{-})\), being an anion, must balance the positive charge due to chromium and the ligands. Thus, \(x + 0 - 2 = +1\). Solving for \(x\), the oxidation state of chromium is \(+3\).

Step 3: Determine Number of d Electrons in Chromium

Chromium has an atomic number of 24, with a neutral electron configuration of \([\mathrm{Ar}] 3d^5 4s^1\). In the \(+3\) oxidation state, it loses three electrons, the 4s electron and two 3d electrons, leaving it with \(3d^3\). Hence, chromium in this state has 3 d electrons.

Step 4: Determine Number of Unpaired Electrons

With a \(3d^3\) configuration, each electron occupies a separate d-orbital, following Hund's Rule, leading to three unpaired electrons. The number of unpaired d electrons is 3.

Key Concepts

Coordination Number

In coordination chemistry, the coordination number is an important concept that refers to the total number of ligand bonds formed with the central metal atom or ion. Ligands are molecules or ions that donate electron pairs to the metal center. To find the coordination number, simply count how many ligand atoms are directly bonded to the metal. In the complex \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{CO}_{3}\right]\mathrm{ClO}_{4}\), this is straightforward:

• There are 5 ammonia \(\mathrm{NH}_{3}\) molecules.
• There is 1 carbonate \(\mathrm{CO}_{3}^{2-}\) ion.

Together, they make a total of 6, resulting in a coordination number of 6.
This means six bonds are formed between the ligands and the chromium metal in this complex.

Oxidation Number

The oxidation number describes the degree of oxidation of an atom within a compound, indicating how many electrons the atom has gained, lost, or shared. To find the oxidation number of chromium in the complex \([\mathrm{Cr}(\mathrm{NH}_{3})_{5}\mathrm{CO}_{3}]\mathrm{ClO}_{4}\):

• Ammonia \((\mathrm{NH}_{3})\) is neutral, contributing \(0\) to the oxidation state.
• Carbonate \((\mathrm{CO}_{3}^{2-})\) contributes \(-2\).
• Perchlorate \((\mathrm{ClO}_{4}^{-})\), as an external anion, necessitates a positive chromium oxidation state to balance the overall charge of the complex.

Setting up the equation: \(x + 0 - 2 = +1\), where \(x\) is the oxidation number for chromium. Solving gives \(x = +3\).
This indicates that chromium has lost three electrons.

Electron Configuration

Electron configuration provides an overview of the distribution of electrons around an atom's nucleus, determining how atoms bond and interact. Chromium has an atomic number of 24, meaning it has 24 electrons in its neutral state, with a ground-state electron configuration of \([\mathrm{Ar}] 3d^5 4s^1\). When forming the complex:

• The chromium ion has an oxidation number of \(+3\).
• Certain electrons are lost: 1 from the \(4s\) orbital and 2 from the \(3d\) orbital.

After losing these electrons, the new electron configuration is \([\mathrm{Ar}] 3d^3\).
This configuration is crucial for understanding the metal's chemical behavior in the coordination complex.

Unpaired Electrons

Unpaired electrons are electrons occupying an atomic or molecular orbital alone, which makes compounds with such electrons paramagnetic. In coordination chemistry, detecting unpaired electrons helps predict magnetic properties.Given our complex, chromium with a \(3d^3\) electron configuration has three electrons in its \(d\)-orbitals.

• According to Hund's Rule, electrons will occupy separate \(d\)-orbitals as much as possible, each being unpaired.
• Thus, three unpaired electrons are present in this configuration.

These unpaired electrons imply that the compound will exhibit paramagnetic properties, which can be experimentally verified through magnetic susceptibility measurements.