Problem 5 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Complex \(\mathrm{X}\) of composition \(\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6} \mathrm{Cl}_{\mathrm{n}}\) has a spin only magnetic moment of \(3.83 \mathrm{BM}\). It reacts with \(\mathrm{AgNO}_{3}\) and shows geometrical isomerism. The IUPAC nomenclature of \(\mathrm{X}\) is: (a) Hexaaqua chromium (III) chloride (b) Tetraaquadichlorido chromium (IV) chloride dihydrate (c) Dichloridotetraaqua chromium (IV) chloride dihydrate (d) Tetraaquadichlorido chromium (III) chloride dihydrate

Step-by-Step Solution

Answer

The IUPAC name is Tetraaquadichlorido chromium (III) chloride dihydrate.

Step 1: Analyze the Spin Magnetic Moment

The given spin only magnetic moment of the complex is 3.83 BM (Bohr Magnetons). The formula for the spin-only magnetic moment is \(\mu = \sqrt{n(n+2)}\), where \(n\) is the number of unpaired electrons. Solving for \(n\), if \(\mu = 3.83\), then \(3.83 = \sqrt{n(n+2)}\). Solving this equation gives \(n = 3\). This means there are three unpaired electrons in Cr.

Step 2: Deduce the Oxidation State of Chromium

Since there are three unpaired electrons, the oxidation state of Cr here must be +3. In a \(Cr^{3+}\) ion, there are three unpaired electrons (in the \(d^3\) configuration) which match the observed magnetic moment with \(n=3\).

Step 3: Identify Reaction with \(\mathrm{AgNO}_3\)

The complex is said to react with \(\mathrm{AgNO}_3\), which indicates that the chlorides are not all within the inner coordination sphere, some are free ions. This suggests the number of chlorides in the coordination sphere is less than the total number of \(Cl^-\) ions indicated in the molecular formula.

Step 4: Infer Coordination Sphere and Free Ions

Given the options, consider that the coordination number for chromium is 6 (hexaaqua or tetraacqua with chloro ligands). Since it reacts with \(\mathrm{AgNO}_3\), there should be at least one free chloride ion, indicating the formula contains negatively charged chlorides outside the coordination sphere.

Step 5: Determine Geometric Isomerism

The complex shows geometrical isomerism, indicating the presence of certain ligands in cis/trans positions. This is characteristic of coordination numbers such as 4 (with water and chlorides) or more commonly in octahedral arrangements with mixed ligands.

Step 6: Identify Correct IUPAC Nomenclature

Given the magnetic moment information and the need for geometric isomers, option (d) is most consistent: \(\text{Tetraaquadichlorido chromium (III) chloride dihydrate}\), indicating an octahedral \(\text{[Cr(H}_2\text{O})_4Cl_2]Cl\cdot2\text{H}_2\text{O}\) coordination.

Key Concepts

Spin-only magnetic moment

The spin-only magnetic moment helps us understand the number of unpaired electrons in a metal complex. It's an important concept in coordination chemistry, particularly when analyzing the magnetic properties of transition metal complexes. The formula for calculating the spin-only magnetic moment is \[ \mu = \sqrt{n(n+2)} \] where \( n \) is the number of unpaired electrons. For this complex, the magnetic moment is given as 3.83 Bohr Magnetons (BM). Solving the equation \[ 3.83 = \sqrt{n(n+2)} \] reveals that \( n = 3 \), indicating the presence of three unpaired electrons.
Understanding the number of unpaired electrons lets us deduce important characteristics of the metal center, such as its oxidation state and possible electron configurations. It's a useful calculation for determining the paramagnetic properties of the complex.
By knowing the number of unpaired electrons, students can identify the specific electron configuration and assess the overall magnetic behavior without requiring advanced equipment.

Geometric isomerism

Geometric isomerism arises when there are different positional arrangements of ligands in a coordination complex. It's a fascinating feature because it can significantly affect the properties and activities of the compound. In coordination chemistry, geometric isomers are often found in octahedral and square planar complexes.
For the complex in question, the presence of both water and chloride ligands allows for multiple configurations. This is a characteristic indication of geometric isomerism. It's particularly evident when there are two different types of ligands, such as water and chloro, which can switch places or be found in different positions relative to each other.
A common scenario for geometric isomerism is the cis/trans arrangement in octahedral complexes, where ligands can be adjacent (cis) or opposite (trans) to each other. Identifying these arrangements helps chemists understand how different isomers can have varying reactivities, stabilities, or even colors.

Oxidation state determination

Determining the oxidation state of a central metal atom in a coordination complex is crucial for understanding its chemical behavior and properties. The oxidation state is essentially the charge of the metal ion after accounting for the charges of all bonded ligands.
For chromium in the given complex, the oxidation state is +3, as indicated by the step-by-step analysis. The oxidation state is determined by knowing the number of unpaired electrons, which align with the electron configuration. This matches the known properties of chromium with three unpaired electrons in its 3+ oxidation state, typically in a \(d^3\) configuration.

• Add the charges from the neutral or charged ligands, like water or chloride.
• Adjust by the charge needed to balance to the overall charge in the complex.

Understanding the oxidation state is essential because it influences other chemical properties, such as reactivity and the ability to undergo further chemical transformations. The oxidation state determination process also allows students to identify possible electronic transitions and predict the magnetic behavior of the complex.