Problem 31 - A Complete Resource Book in Chemistry for JEE Main

Question

The effective atomic number (EAN) of \({ }_{24} \mathrm{Cr}\) in \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{6}\right] \mathrm{Cl}_{3}\) is (a) 24 (b) 27 (c) 30 (d) 33

Step-by-Step Solution

Answer

(d) 33

Step 1: Identify the Elements

First, identify the elements in the compound \([\text{Cr(NH}_3\text{)}_6]\text{Cl}_3\). Chromium (Cr) is the central metal atom, and there are six ammonia ligands (\(\text{NH}_3\)) around it. Additionally, consider that chloride (\(\text{Cl}^-\)) is the counterion.

Step 2: Determine Atomic Number of Chromium

Chromium (Cr) has an atomic number of 24.

Step 3: Determine Charge of the Complex

Since the compound \([\text{Cr(NH}_3)_6]\text{Cl}_3\) is neutral overall and Cl is a monovalent anion, each carries a \(-1\) charge. Three chloride ions contribute \(-3\) charge, so the coordination sphere \([\text{Cr(NH}_3)_6]\) must have a \(+3\) charge to balance it.

Step 4: Calculate Oxidation State of Chromium

Each ammonia (\(\text{NH}_3\)) ligand is neutral, so they do not contribute to the charge on the complex. Given the coordination complex \([\text{Cr(NH}_3)_6]^{3+}\), chromium must be in the \(+3\) oxidation state to account for the positive charge.

Step 5: Calculate the Effective Atomic Number (EAN)

The effective atomic number (EAN) is given by the sum of the atomic number, the number of electrons gained from the oxidation state, and the number of electrons donated by ligands. Calculate:- Atomic number of Cr: 24- Electrons from oxidation state: +3 (loss)- Electrons donated by ligands: 6 Ammonia molecules donate 2 electrons each, totaling 12 electrons.Calculate EAN: \[ \text{EAN} = 24 - 3 + 12 = 33 \]

Step 6: Conclude with the Correct Option

Based on the effective atomic number calculation, the EAN for \([\text{Cr(NH}_3)_6]\text{Cl}_3\) is 33.

Key Concepts

Coordination Compounds

Coordination compounds are an intriguing and essential part of chemistry. They consist of a central metal atom or ion, surrounded by molecules or ions known as ligands. These ligands are attached through coordinate bonds, which are a type of covalent bond where both shared electrons originate from the same atom, usually the ligand. In the compound \( [\text{Cr(NH}_3\text{)}_6]\text{Cl}_3 \), the central metal atom is chromium (Cr), and it is coordinated by six ammonia (\( \text{NH}_3 \)) ligands.

Ligands play a crucial role as they can affect the color, reactivity, and stability of a coordination compound. They come in various categories based on their binding sites:

• Monodentate ligands: Attach at a single site on the metal. Examples include \( \text{NH}_3 \), \( \text{H}_2\text{O} \), and \( \text{Cl}^- \).
• Bidentate ligands: Bind at two points. A common example is ethylenediamine.
• Polydentate ligands: Can attach at multiple sites. Examples include EDTA, which can attach at six points.

In coordination chemistry, understanding the number and type of ligands is vital to predicting the behavior and properties of the compound.

Oxidation States

Oxidation states refer to the hypothetical charge a central atom would have if all bonds to it were completely ionic. This concept helps in determining the electron distribution in compounds, especially in redox reactions.

In the coordination compound \( [\text{Cr(NH}_3\text{)}_6]\text{Cl}_3 \), the chromium atom is found in a \(+3\) oxidation state. Determining this requires knowledge of the charges of all components:

• Chloride ions (\( \text{Cl}^- \)) are negative with a charge of -1 each.
• To balance the three chloride ions outside the coordination sphere, the coordination compound must have an overall charge of \(+3\).
• As ammonia (\( \text{NH}_3 \)) is neutral, it doesn't affect the oxidation state directly.

The oxidation state is calculated by ensuring the total positive charge of the metal counterbalances the charge contributed by any anions, resulting in a stable, neutral compound overall. Understanding oxidation states in coordination compounds helps in predicting reactivity and stability.

Ligand Field Theory

Ligand Field Theory (LFT) extends our understanding of coordination compounds by explaining the electronic structures of transition metal complexes. It provides insights into magnetic properties, colors, and stability of these complexes.

In a complex, ligands surrounding the central metal ion create an electric field, called the "ligand field," which affects the energies and configurations of the central metal's d orbitals. Here's how:

• The coordination of ligands causes splitting of these d orbitals into different energy levels.
• The extent of this splitting depends on factors like the nature of the ligands and the geometry of the complex (octahedral or tetrahedral).
• Strong field ligands, like \(\text{NH}_3 \), lead to larger splitting of d orbitals, potentially causing changes in the number of unpaired electrons.

This change can explain magnetic and spectral properties:

• Strong field ligands: Lead to low spin states, where electrons pair up in lower energy orbitals, often involving diamagnetism.
• Weak field ligands: Lead to high spin states, with unpaired electrons in higher orbitals, potentially resulting in paramagnetism.

Understanding LFT is vital for chemists to predict the behavior and interaction of coordination compounds with other substances.