Problem 179 - A Complete Resource Book in Chemistry for JEE Main

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 wavelength in the region of red, green, yellow and blue, respectively. The increasing order of ligand strength of the four ligands is: \([2014]\) (a) \(\mathrm{L}_{3}<\mathrm{L}_{2}<\mathrm{L}_{4}<\mathrm{L}_{1}\) (b) \(\mathrm{L}_{1}<\mathrm{L}_{2}<\mathrm{L}_{4}<\mathrm{L}_{3}\) (c) \(\mathrm{L}_{4}<\mathrm{L}_{3}<\mathrm{L}_{2}<\mathrm{L}_{1}\) (d) \(\mathrm{L}_{1}<\mathrm{L}_{3}<\mathrm{L}_{2}<\mathrm{L}_{4}\)

Step-by-Step Solution

Answer

(d) \(\mathrm{L}_{1}<\mathrm{L}_{3}<\mathrm{L}_{2}<\mathrm{L}_{4}\)

Step 1: Understanding Ligand Field Theory

In octahedral complexes, the arrangement and strength of ligands affect the splitting of d-orbitals in the central metal ion. The stronger the ligand, the greater the splitting it causes.

Step 2: Relate Absorption to Ligand Strength

The color absorbed by a complex is the complement of the color it appears. The energy (and thus wavelength) of the absorbed light is inversely related to the strength of the ligand field - strong field strengths cause absorption in the shorter wavelengths (higher energy), and weaker fields cause absorption in longer wavelengths (lower energy).

Step 3: Identify Wavelengths of Visible Spectrum

In the visible spectrum, red corresponds to longer wavelengths (~620-750 nm), and blue corresponds to shorter wavelengths (~450-495 nm). Green and yellow fall in between, with green (~495-570 nm) and yellow (~570-590 nm).

Step 4: Determine Ligand Strength Order

Ligands with absorbed wavelengths in the order from shortest to longest are stronger to weaker. Since blue light is absorbed suggesting it is absorbed by the strongest ligand, and red by the weakest: - Blue: L4 (strongest) - Green: L2 - Yellow: L3 - Red: L1 (weakest)

Step 5: State Increasing Order of Ligand Strength

The increasing order of ligand strength, from weakest to strongest, based on their absorption wavelengths, is L1 (red), L3 (yellow), L2 (green), L4 (blue). This corresponds to option (d).

Key Concepts

Octahedral Complexes

In the world of coordination chemistry, octahedral complexes are a common configuration where a central metal ion is surrounded by six ligands at the corners of an octahedron. Each ligand donates an electron pair to the metal ion, forming a bond. This arrangement is significant because it affects the electronic properties of the metal complex. Due to the symmetry of the octahedral shape, the d-orbitals of the metal ion experience splitting into two sets with different energy levels. This phenomenon is vital for understanding how octahedral complexes interact with light and why they often show vivid colors. The ligands' arrangement around the metal ion significantly influences the physical and chemical properties of the complex, playing a crucial role in its reactivity and color.

Ligand Strength

Ligand strength in the context of ligand field theory refers to a ligand's ability to cause d-orbital splitting in the central metal ion of a complex. Stronger ligands create a larger splitting of the d-orbitals, which affects both the color and the stability of the complex. Different ligands can vary in strength from weak field to strong field ligands.

• Weak field ligands cause smaller splitting, leading to absorption of longer wavelengths (lower energy light).
• Strong field ligands cause more significant splitting, absorbing shorter wavelengths (higher energy light).

The understanding of ligand strength helps predict and explain complex behaviors, such as their color and the magnetic properties. In our example, the sequence from weakest to strongest ligand is L1, L3, L2, L4, showing diverse abilities to influence d-orbital energies.

d-Orbital Splitting

d-Orbital splitting is at the heart of understanding how octahedral complexes absorb and reflect light. When a metal ion forms a complex, the surrounding ligands repel the d-electrons, causing the d-orbitals to split into two distinct energy levels.

• These two levels are called the t_2g (lower energy) and e_g (higher energy) sets.
• The energy difference, known as the crystal field splitting energy (9), is crucial because it determines the light absorption characteristics of the complex.

The extent of this splitting varies depending on the ligand field strength. This variation also affects whether the complex is a high-spin or low-spin complex, further influencing its magnetic and spectroscopic properties.

Visible Spectrum Absorption

Visible spectrum absorption is the process whereby a complex absorbs certain wavelengths of light, determining the color that the complex appears. This is because a complex reflects and transmits the color that is complementary to the absorbed light. In this discussion, the absorbed wavelengths correspond to colors like red, green, yellow, and blue, each representing different energies. For instance, our exercise indicates

• Blue light absorbed by the strongest ligand (L4), suggesting high energy and short wavelength.
• Red light is absorbed by the weakest ligand (L1), with low energy and long wavelength.

Understanding which wavelengths are absorbed is essential to determining not only the color of the compound but also its electronic transitions and ligand strength relationships.