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

The correct option is (b) \(6,3,6,3\).

Step 1: Identify the Coordination Number

The coordination number is determined by the number of ligand atoms bonded to the central metal atom, which in this case is chromium, \( \text{Cr} \). Here, the ligands are five \( \text{NH}_3 \) groups and one \( \text{CO}_3^{2-} \) group. Each ammonia can donate one pair of electrons and \( \text{CO}_3^{2-} \) acts as a bidentate ligand. Hence, the coordination number is 6.

Step 2: Determine the Oxidation Number of Chromium

To find the oxidation number of chromium, sum the charges of the ligands and the complex. \( \text{NH}_3 \) is neutral, \( \text{CO}_3^{2-} \) has a charge of \(-2\), and \( \text{ClO}_4^- \) (perchlorate ion) is \(-1\). The overall charge of the complex is neutral (0). Setting up the equation: \( x + 5(0) + (-2) -1 = 0 \), solve for \( x \): \( x = +3 \). Thus, the oxidation number of chromium is +3.

Step 3: Calculate the Number of d Electrons

Chromium has an atomic number of 24, with an electron configuration of \([\text{Ar}] 3d^5 4s^1\). In its \(+3\) oxidation state, 3 electrons are lost, typically from the 4s and 3d orbitals: \([\text{Ar}] 3d^3\). Thus, there are 3 d electrons.

Step 4: Find the Number of Unpaired d Electrons

In the \(3d^3\) configuration, electrons will occupy separate orbitals due to Hund's Rule, which states electrons will fill an empty orbital before they pair up. Therefore, there are three unpaired d electrons in the 3d orbitals.

Key Concepts

Coordination Number

The coordination number in a coordination complex is a critical concept. It refers to the number of ligand atoms that are directly bonded to the central metal atom. In the complex \([\text{Cr}(\text{NH}_3)_5 \text{CO}_3]\text{ClO}_4\), the central metal atom is chromium (Cr). Here, five ammonia (NH₃) molecules and one carbonato (CO₃²⁻) group are attached to the chromium. It's important to note that while each ammonia molecule donates one pair of electrons to form one bond, the carbonate group acts as a bidentate ligand, contributing two bonding interactions. Therefore, adding these gives chromium a total coordination number of 6.
Understanding the coordination number is essential because it informs us about the complex's geometry, stability, and reactivity. Common coordination numbers range from 2 to 8, with 6 being particularly common, often leading to an octahedral geometry.

Oxidation Number

The oxidation number in a coordination complex indicates the charge of the central metal atom after accounting for the charge contributions from all ligands. It is crucial for understanding the electron distribution and redox properties of the complex. In the \([\text{Cr}(\text{NH}_3)_5 \text{CO}_3]\text{ClO}_4\) complex, determining the oxidation state of chromium involves considering the charges of ligands and the complex itself.
Ammonia is a neutral ligand, contributing 0 charge. The carbonato ligand contributes a \-2\ charge, and the complex as a whole is neutral. Given that the perchlorate ion \[\text{ClO}_4^-\] is a \-1\ ion, the equation used to find the oxidation state is \(x + 5(0) - 2 - 1 = 0\), where \(x\) is the oxidation number of chromium. Solving for \(x\), we find that the oxidation state of chromium is \+3\.

Electronic Configuration

Electronic configuration sheds light on how electrons are arranged in an atom's orbitals, which influences the chemical properties and reactivity of the metal, especially in complexes. For chromium in the \([\text{Cr}(\text{NH}_3)_5 \text{CO}_3]\text{ClO}_4\) complex, first note the electronic configuration of a neutral chromium atom: \[\text{[Ar]} 3d^5 4s^1\]. Chromium is known to exhibit variable oxidation states, with \+3\ being particularly stable for forming complexes.
In this case, chromium in a \+3\ oxidation state loses three electrons. These are typically removed first from the \4s\ and then from the \3d\ orbitals, resulting in the configuration \[\text{[Ar]} 3d^3\]. This electronic arrangement also dictates properties like magnetism, as these three electrons occupy separate orbitals, which leads us to explore their pairing next.

Ligand Chemistry

Ligands play a vital role in coordination chemistry as they can influence the geometry, reactivity, and properties of the metal complex. In \([\text{Cr}(\text{NH}_3)_5 \text{CO}_3]\text{ClO}_4\), we encounter two types of ligands: ammonia (NH₃) and carbonate (CO₃²⁻).
Ammonia acts as a monodentate ligand, meaning it donates a pair of electrons from a single donor atom—in this case, nitrogen—to the chromium center. On the other hand, carbonate is a bidentate ligand capable of forming two bonds with the metal through its oxygen atoms. Understanding these interactions is crucial as they dictate the overall shape, stability, and reactivity of the complex. Ligands strongly influence the electronic environment of the metal, which can alter electron distribution and contribute to phenomena such as color changes, stability, or catalytic activity. The nature of the ligand and its strength also determine the splitting of d-orbitals, which is important in understanding the complex’s color and magnetic properties.