Problem 11 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Among the statements (A)-(D), the incorrect ones are: (A) Octahedral Co(III) complexes with strong field ligands have very high magnetic moments. (B) When \(\square_{0}<\mathrm{P}\), the \(d\)-electron configuration of \(\mathrm{Co}(\mathrm{III})\) in an octahedral complex is \(t_{2 \mathrm{~g}}^{4} e_{\mathrm{g}}^{2}\) (C) Wavelength of light absorbed by \(\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+}\) is lower than that of \(\left[\mathrm{CoF}_{6}\right]^{3-}\) (D) If the \(\square_{0}\) for an octahedral complex of \(\mathrm{Co}(\mathrm{III})\) is \(18,000 \mathrm{~cm}^{-1}\), the \(\square_{t}\) for its tetrahedral complex with the same ligand will be \(16,000 \mathrm{~cm}^{-1}\). (a) (A) and (D) only (b) (C) and (D) only (c) (A) and (B) only (d) (B) and (C) only

Step-by-Step Solution

Answer

(A) and (D) are incorrect.

Step 1: Identify the Type of Complexes

Analyze statement (A). Strong field ligands cause low spin configurations, leading to paired electrons and low magnetic moments. Octahedral Co(III) complexes generally have low or no magnetic moments when strong field ligands are present. Thus, statement (A) is incorrect.

Step 2: Examine Electron Configuration

Consider statement (B). When \(\Delta_0 < \text{P}\), the complex is a high spin, leading to the electron configuration \(t_{2g}^4 e_g^2\). If \(\Delta_0 < \text{P}\), the pairing energy \(\text{P}\) is greater, and thus unpaired electrons will fill first which aligns with the statement. Therefore, (B) is correct.

Step 3: Compare Wavelengths of Absorbed Light

Look at statement (C). The \([\text{Co(en)}_3]^{3+}\) complex has strong field ligands (en), while \([\text{CoF}_6]^{3-}\) has weak field ligands. Strong field ligands absorb higher energy (shorter wavelength) light. Hence, (C) is correct.

Step 4: Calculate Spectrochemical Factors

Analyze statement (D). The relationship for spectrochemical values between octahedral complexes \(\Delta_0\) and tetrahedral \(\Delta_t\) is \(\Delta_t = \frac{4}{9}\Delta_0\). So, \(\Delta_t = \frac{4}{9} \times 18000 = 8000\) cm\(^{-1}\), not 16000 cm\(^{-1}\). Statement (D) is incorrect.

Key Concepts

Magnetic Moments in Complexes

Magnetic moments in coordination complexes depend on the arrangement of electrons in the d-orbitals, which are influenced by the strength of the ligands surrounding the metal ion. Here's a closer look:

• In coordination chemistry, metal ions with unpaired electrons exhibit magnetic properties, known as magnetic moments.
• These are mostly seen in high-spin complexes, where electrons fill all orbitals singly before pairing, leading to higher magnetic moments.
• Strong field ligands, such as CN⁻ or en, can pair electrons in the lower energy orbitals in octahedral complexes, resulting in a low-spin configuration.
• This pairing reduces the number of unpaired electrons, thereby reducing the magnetic moment.

For example, an octahedral Co(III) complex with strong field ligands will generally exhibit a low or negligible magnetic moment as all electrons are paired. Conversely, with weak field ligands, a high magnetic moment is observed due to the presence of unpaired electrons.

Crystal Field Theory

Crystal Field Theory (CFT) helps explain the electronic structure of transition metal complexes. It is based on the idea that metal-ligand interactions cause splitting of the metal's d-orbitals. Let's dive deeper:

• In octahedral complexes, the electrostatic interaction with the ligands splits the d-orbitals into two groups: a higher energy set (eg) and a lower energy set (t2g).
• The energy difference between these two sets is called the crystal field splitting parameter (Δ, sometimes noted as Δ0 for octahedral complexes).
• The magnitude of Δ depends on the nature of the ligands; strong field ligands can cause a large splitting, while weak field ones cause less.
• An important consideration is whether Δ is greater or smaller than the pairing energy (P):
  • If Δ > P, electrons tend to pair up (low spin).
  • If Δ < P, electrons tend to remain unpaired (high spin).

Overall, CFT provides a framework for understanding the properties, such as color and magnetism, of metal complexes.

Ligand Field Strength

The strength of ligands and their ability to influence the properties of metal complexes is vital in coordination chemistry. Here are some key aspects:

• Ligands are classified as either strong field or weak field ligands, based on their capacity to split the d-orbitals of the metal ions.
• Strong field ligands such as CN⁻, en, and CO, cause a large splitting of the d-orbitals and can lead to electron pairing.
• Weak field ligands like F⁻, Cl⁻, and H₂O cause smaller splitting, often resulting in unpaired electrons and high-spin situations.

The ligand field strength profoundly affects the magnetic properties, electron configuration, and color of the coordination complex. It is crucial to consider the field strength when predicting and explaining these properties within metal complexes.

Spectrochemical Series

The Spectrochemical Series is a sequence that ranks ligands based on their ability to split the d-orbitals of the transition metals they coordinate with. This concept is instrumental for understanding the variation in color and magnetism of different complexes.

• The series orders ligands from those that produce the weakest field (smallest splitting) to those with the strongest field (largest splitting).
• The series generally looks like this: I⁻ < Br⁻ < Cl⁻ < F⁻ < OH⁻ < H₂O < NH₃ < en < CN⁻ < CO.
• Spectrochemical differences can explain why compounds like [CoF₆]³⁻ (using F⁻ as a weak field ligand) and [Co(en)₃]³⁺ (using en as a strong field ligand) differ in the color and wavelengths of light they absorb.

Understanding the Spectrochemical Series allows chemists to rationalize and predict the optical and magnetic behavior of coordination complexes based on their constituent ligands.