Problem 111 - A Complete Resource Book in Chemistry for JEE Main

Question

Select the correct increasing order of \(10 \mathrm{Dq}\) value for chromium complexes using the given codes (1) \(\left[\mathrm{Cr}(\mathrm{en})_{3}\right]^{3+}\) (2) \(\left[\mathrm{Cr}(\mathrm{ox})_{3}\right]^{3}\) (3) \(\left[\mathrm{CrF}_{6}\right]^{3}\) (4) \([\mathrm{Cr}(\mathrm{dtc})]^{3^{+}}\) (Here, dtc = dithiocarbamate) (a) \(1<2<3<4\) (b) \(3<4<2<1\) (c) \(4<1<2<3\) (d) \(3<1<4<2\)

Step-by-Step Solution

Answer

The correct increasing order of 10 Dq value is (b) 3 < 4 < 2 < 1.

Step 1: Understand the 10 Dq Concept

The value of 10 Dq (decaque) is related to the split in energy levels due to the ligand field in a coordination complex. Strong field ligands produce a larger 10 Dq, while weak field ligands have a smaller 10 Dq.

Step 2: Evaluate Relevant Ligands

Identify the ligands in each complex and their field strength relative to each other. The ligands in the complexes are: ethylenediamine (en), oxalate (ox), fluoride (F), and dithiocarbamate (dtc). According to the spectrochemical series, 'en' is a stronger field ligand than 'ox', 'ox' is stronger than 'dtc', and 'F' is the weakest among them.

Step 3: Assign 10 Dq Values Based on Ligand Strength

Assign higher 10 Dq values to complexes with stronger field ligands. The order of strength for the ligands given: en > ox > dtc > F, corresponds to 10 Dq values for each complex: (1) > (2) > (4) > (3).

Step 4: Match to Given Codes

Compare the deduced order (1 > 2 > 4 > 3) against the answer options. The order needs to be reversed to find the increasing order: 3 < 4 < 2 < 1, which matches option (b).

Key Concepts

Spectrochemical Series

The spectrochemical series is a list of ligands arranged by their ability to split the d-orbitals in the central metal ion within a coordination complex. This splitting occurs due to the interaction between the metal's d-orbitals and the ligand's electrons. The order is based on the ligand's ability to produce a strong or weak crystal field. In general, ligands that are higher up on the list have stronger field strengths and therefore produce a larger energy gap, denoted in this context as 10 Dq.

Understanding the spectrochemical series helps predict the geometry and magnetic properties of coordination complexes. It also aids in determining the color of complexes, as the size of the energy gap affects which wavelengths of light are absorbed and which are reflected. For example, ethylenediamine ( ) , being a strong field ligand, is higher in the series compared to oxalate ( ) and fluoride ( ), which is a weak field ligand.

Coordination Complexes

Coordination complexes are compounds consisting of a central metal atom or ion bonded to a surrounding array of molecules or anions, known as ligands. These complexes are essential in understanding various chemical phenomena, including catalysis, material science, and biology. The central metal ion and ligands form coordinate bonds through a donation mechanism, where the ligand donates a pair of electrons to the metal center.

The geometric arrangement of ligands around the central ion in coordination complexes can be influenced by several factors, including the metal's electronic configuration, the number and type of bonds, and the field strength of the ligands. These factors significantly impact the physical and chemical properties of the complex, such as its color, magnetic behavior, and reactivity.

• Ligand Types: Common ligands include water, ammonia, and chloride ions, among others.
• Geometry: Coordination number and shape (octahedral, tetrahedral, square planar) determine the spatial structure of complexes.

Ligand Field Strength

Ligand field strength refers to a ligand's ability to split the d-orbital energies of a metal ion in a coordination complex. This split, measured in terms of 10 Dq, determines the energy difference between the d-orbitals. The greater this split, the stronger the ligand field strength is considered to be.

The concepts of high-spin and low-spin complexes are directly influenced by ligand field strength. In situations where the ligand field is strong, like in the presence of a ligand such as ethylenediamine, electrons in the metal's d-orbitals are forced to pair, leading to low-spin configurations. Conversely, weak field ligands such as fluoride allow electrons to occupy higher energy orbitals, resulting in high-spin configurations.

• Impact on Complex Properties: Ligand field strength affects the color, magnetism, and stability of the complex.
• Field Versus Packing: Strong field ligands lead to more packed and stable structures due to larger splits and electron pairing.