Problem 170 - A Complete Resource Book in Chemistry for JEE Main

Question

In which of the following octahedral complexes of Co (Atomic number 27), will the magnitude of \(\Delta\). be the highest? [2008] (a) \(\left[\mathrm{Co}(\mathrm{CN})_{6}\right]^{3-}\) (b) \(\left[\mathrm{Co}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3-}\) (c) \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}\) (d) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}\)

Step-by-Step Solution

Answer

(a) 95[C95(95N)95]^{3-} has the highest 94 value due to the strong field CN- ligand.

Step 1: Understanding Octahedral Complexes

We need to determine the magnitude of crystal field splitting (94) for different octahedral complexes of Cobalt (Co). In octahedral complexes, ligands cause the splitting of d-orbitals into two groups: t2g and eg. The magnitude of this splitting, 94, is influenced by the nature of the ligands in the complex.

Step 2: Knowing Ligand Strength

The crystal field splitting parameter, 94, is greater for strong field ligands compared to weak field ligands. According to the spectrochemical series, ligands can be arranged based on their strength as field splitters. From strongest to weakest, the given ligands are ranked as follows: CN- > NH3 > H2O > C2O4^2-.

Step 3: Identifying Ligands in Each Complex

The complexes given are: (a) 95[C95(95N)95]^{3-} - contains CN-, (b) 95[C( C_2O_4)95]^{3-} - contains C2O4^2-, (c) 95[C(H_2O)95]^{3+} - contains H2O, (d) 95[C(NH_3)95]^{3+} - contains NH3. According to the spectrochemical series, CN- is the strongest field ligand followed by NH3, H2O, and finally, C2O4^2-.

Step 4: Determining Highest 94 Value

The complex with the strongest field ligand will have the highest 94 value. From the list, 95[C95(95N)95]^{3-} has the CN- ligand, which is the strongest among the given options. Thus, 95[C95(95N)95]^{3-} will have the highest 94 value.

Key Concepts

Octahedral Complexes

Octahedral complexes are a common type of coordination compound where a central metal atom is surrounded by six ligands arranged at the corners of an octahedron. In these complexes, the ligands are molecules or ions that donate electron pairs to the metal atom. This arrangement forms a cage-like structure around the metal, influencing its electronic properties.
The octahedral geometry leads to the splitting of the metal's d-orbitals into two groups: the lower energy t_{2g} orbitals (d_{xy}, d_{xz}, d_{yz}) and the higher energy e_{g} orbitals (d_{z^2}, d_{x^2-y^2}).
This splitting is crucial for understanding how light interacts with these compounds, affecting their color and magnetic properties.

Spectrochemical Series

The spectrochemical series is a list that categorizes ligands based on their ability to split the d-orbitals of a transition metal. This splitting is known as crystal field splitting and is denoted by the parameter \( \Delta \).
The spectrochemical series ranks ligands from those that create a strong field and large splitting to those that generate a weak field with small splitting. A typical portion of the series is:

• Strong-field ligands: CN^- > NO_2^- > en (ethylenediamine) > NH_3
• Weak-field ligands: H_2O > OH^- > F^- > Cl^-, etc.

In this series, cyanide \( \text{CN}^{-} \) is one of the strongest, causing significant d-orbital splitting, whereas water (\( \text{H}_2\text{O} \)) is relatively weak, resulting in minimal splitting.

Ligand Field Strength

Ligand field strength refers to the effect different ligands have on the splitting of the d-orbitals in coordination compounds. This strength determines the degree to which ligands can alter the electronic environment of the metal.
Strong field ligands like CN^- and NH_3 create a large \( \Delta \), increasing the energy difference between the t_{2g} and e_{g} orbitals. They often lead to low-spin complexes, where the electrons are paired in the lower energy orbitals. On the other hand, weak field ligands like H_2O and C_2O_4^{2-} result in a smaller \( \Delta \), which often leads to high-spin complexes, as the energy required for pairing electrons is higher than for occupying higher energy orbitals.
Understanding ligand field strength is key in predicting the properties and behaviors of octahedral complexes, such as their color and magnetic characteristics.

d-Orbital Splitting

The concept of d-orbital splitting is central to Crystal Field Theory, which explains the impact of ligands on the energy distribution of a metal's d-orbitals.
In an octahedral complex, the presence of six ligands creates a symmetrical electric field that causes the degeneracy (equal energy) of the d-orbitals to be lifted. This results in their splitting into two distinct energy levels: the t_{2g} orbitals, which lie at a lower energy level, and the e_{g} orbitals, which are at a higher energy level due to higher repulsion between the electrons in these orbitals and the ligands.
The energy difference between these two sets, known as the crystal field splitting energy (94), determines many of the chemical and physical properties of the complex such as color and magnetic properties. The magnitude of 94 varies with the nature of the ligands: strong field ligands induce large splitting, while weak field ligands result in smaller splitting.