Problem 30 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The octahedral complex of a metal ion \(\mathrm{M}^{3+}\) with four monodentate ligands \(L_{1}, L_{2}, L_{3}\) and \(L_{4}\) absorb wavelengths in the region of red, green, yellow and blue, respectively. The increasing order of ligand strength of the four ligands is: (a) \(L_{4}

Step-by-Step Solution

Answer

The increasing order of ligand strength is: (b) \(L_1 < L_3 < L_2 < L_4\).

Step 1: Understanding Absorption and Color

In a coordination complex, ligands can cause splitting of the d-orbitals in the metal ion. The wavelength of light absorbed corresponds to the difference in energy between these orbitals. A ligand that causes a larger splitting absorbs light of a shorter wavelength, while a smaller splitting absorbs longer wavelengths.

Step 2: Relate Color Absorbed to Wavelength

The visible spectrum ranges from violet (short wavelengths) to red (long wavelengths). Order the colors of light absorbed by wavelength: - Red (longest wavelength) - Yellow - Green - Blue (shortest wavelength)

Step 3: Determine Ligand Field Strength

Ligands that absorb light at shorter wavelengths cause greater splitting of the d-orbitals and hence are stronger field ligands. Order the ligands based on their absorption: - Red: weakest field ligand - Yellow: second weakest - Green: stronger - Blue: strongest field ligand

Step 4: Order Ligands by Strength

Using the absorptions provided:- Ligand absorbing red light is the weakest- Ligand absorbing blue light is the strongestThus, the increasing order of ligand strength:- Weakest: Ligand absorbing red (\(L_1\))- - Strongest: Ligand absorbing blue (\(L_4\))

Step 5: Match with Given Options

The calculated increasing order of ligand strength is: \(L_1 < L_3 < L_2 < L_4\). This matches option (b).

Key Concepts

Ligand Field Strength

In coordination chemistry, the strength of a ligand is determined by how much it can influence the splitting of the d-orbitals in a metal ion. This is referred to as "Ligand Field Strength." The degree of splitting that a ligand can cause affects which wavelengths of light the complex will absorb and, thus, its color. Ligand field strength is significant because it affects the properties of a metal complex. For example:

• Stronger ligand field means greater splitting of d-orbitals.
• Larger energy gaps correspond to absorption of light with shorter wavelengths.
• Weak field ligands result in smaller d-orbital splitting and absorption of longer wavelengths.

By understanding the ligand field strength, chemists can predict the colors of complexes and manipulate properties like stability and reactivity. This plays a crucial role in designing complexes for specific functions and applications in industry and research.

Octahedral Complex

An octahedral complex is a coordination compound where a metal central atom is surrounded by six ligands forming an octahedral shape. This is one of the most common geometries in coordination chemistry and is often seen in metal ions with six attached entities.

The nature of the ligands in an octahedral complex influences the d-orbital splitting.

• Ligands can approach along the axes, interacting with the d-orbitals and splitting their energies.
• The specific spatial arrangement leads to two distinct energy levels among the d-orbitals.
• This splitting impacts the complex's ability to absorb certain wavelengths of light.

Understanding octahedral complexes helps in studying the complex's electronic transitions, providing insights into its magnetic properties and reactivity. The study of octahedral complexes is a fundamental aspect of inorganic chemistry.

d-orbital Splitting

The concept of d-orbital splitting is crucial for explaining the colors and properties of metal complexes. D-orbitals in a free ion are degenerate, meaning they have the same energy. However, when ligands coordinate to a metal ion, the repulsion due to these ligands causes the d-orbitals to split into different energy levels.

In octahedral complexes, this splitting results in two groups of orbitals:

• The lower-energy set is referred to as the t2g orbitals.
• The higher-energy set is called the eg orbitals.

The energy difference between these two sets of orbitals is known as the "crystal field splitting energy" (∆0). A larger ∆0 means that the complex absorbs high-energy (shorter wavelength) light. Conversely, a smaller ∆0 means absorption occurs at longer wavelengths. Knowing the pattern of d-orbital splitting helps chemists in predicting the optical and magnetic properties of complexes. It also aids in elucidating structural information and reactivity patterns for coordination compounds.