Problem 77 - Chemistry An Atoms First Approach

Question

Would it be better to use octahedral \(\mathrm{Ni}^{2+}\) complexes or octahedral \(\mathrm{Cr}^{2+}\) complexes to determine whether a given ligand is a strong-field or weak-field ligand by measuring the number of unpaired electrons? How else could the relative ligand field strengths be determined?

Step-by-Step Solution

Answer

It would be better to use octahedral Cr²⁺ complexes to determine whether a given ligand is a strong-field or weak-field ligand by measuring the number of unpaired electrons, as the difference in unpaired electrons between high-spin and low-spin configurations for Cr²⁺ complexes is 4, which is more significant than the difference in Ni²⁺ complexes. Alternatively, the relative ligand field strengths can be determined by measuring ligand-field stabilization energies (LFSE) or using the spectrochemical series.

Step 1: 1. Electron configurations of Ni²⁺ and Cr²⁺

First, let's look at the electron configurations for Ni²⁺ and Cr²⁺. Nickel has an atomic number of 28, and its electron configuration is [Ar] 3d^8 4s^2. When it loses two electrons to form Ni²⁺, its electron configuration becomes [Ar] 3d^8. Chromium has an atomic number of 24, and its electron configuration is [Ar] 3d^5 4s^1. When it loses two electrons to form Cr²⁺, its electron configuration becomes [Ar] 3d^4.

Step 2: 2. Identifying high-spin and low-spin complexes

In the presence of ligands, metal ions in their complexes can form high-spin or low-spin configurations, depending on the strength of the ligand field. For a strong-field ligand, the energy splitting between the d orbitals is large, which favors the low-spin configuration. For a weak-field ligand, the energy splitting is small, and the high-spin configuration is preferred. To determine which configuration is present, we need to count the unpaired electrons in the complex.

Step 3: 3. Comparing Ni²⁺ and Cr²⁺ complexes for determining ligand strength

With Ni²⁺ complexes, we have 8 electrons to distribute across the d orbitals. The difference in unpaired electrons between high-spin and low-spin configurations is only 2. This makes it difficult to clearly distinguish between strong-field and weak-field ligands. On the other hand, with Cr²⁺ complexes, we have 4 electrons to distribute across the d orbitals. In this case, the difference in unpaired electrons between high-spin and low-spin configurations is 4, which is more significant than the difference in Ni²⁺. Due to this, it would be a better choice to use octahedral Cr²⁺ complexes to determine the strength of a given ligand by measuring the number of unpaired electrons.

Step 4: 4. Alternative method to determine relative ligand field strengths

One alternative method to determine the relative strength of ligands is to measure their ligand-field stabilization energies (LFSE). LFSE is the difference in energy between the complex formed by the ligand in question and the free metal ion. The higher the LFSE, the stronger the ligand. This can be done experimentally by measuring the energy difference between the complex and the free ion, or by using the spectrochemical series, which ranks ligands based on their ligand-field strengths.