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?

Short answer

To determine whether a given ligand is a strong-field or weak-field ligand by measuring the number of unpaired electrons, it would be better to use octahedral \(\mathrm{Ni}^{2+}\) complexes as there is a distinct difference in the number of unpaired electrons between strong-field and weak-field cases for \(\mathrm{Ni}^{2+}\). Alternatively, one can determine the relative ligand field strengths by measuring the energy difference between the two split sets of d orbitals (the crystal field splitting parameter, ∆) for different ligands in a series of complexes with the same metal ion. The higher the energy difference, the stronger the ligand field.

Step-by-step solution

Octahedral \(\mathrm{Ni}^{2+}\) Complexes Electronic Configuration

First, let's take a look at the electronic configuration of the \(\mathrm{Ni}^{2+}\) ion. Nickel is in the 3d8, 4s2 configuration. When \(\mathrm{Ni}^{2+}\) is formed, two electrons are removed, and it becomes a 3d8 ion. In an octahedral crystal field, the d orbitals are split into two levels: the lower t2g orbitals (dxy, dyz, dxz) and the higher eg orbitals (d3z^2-r^2,dx^2-y^2). Now, let's fill in the eight d-electrons and see how the electrons will be distributed among these orbitals depending on the ligand's strength.

Octahedral \(\mathrm{Cr}^{2+}\) Complexes Electronic Configuration

Now, let's take a look at the electronic configuration of the \(\mathrm{Cr}^{2+}\) ion. Chromium is in the 3d5, 4s1 configuration. When \(\mathrm{Cr}^{2+}\) is formed, two electrons are removed, and it becomes a 3d3 ion. In an octahedral crystal field, the d orbitals are split into the already mentioned levels t2g orbitals and eg orbitals. Let's fill in the three d-electrons and see how the electrons will be distributed among these orbitals depending on the ligand's strength.

Comparing the Number of Unpaired Electrons for \(\mathrm{Ni}^{2+}\) and \(\mathrm{Cr}^{2+}\)

For octahedral \(\mathrm{Ni}^{2+}\) complexes: - In a strong-field case, the d-electrons will completely fill the t2g orbitals before moving to the eg orbitals, resulting in 0 unpaired electrons. - In a weak-field case, the d-electrons will partially fill the t2g orbitals and then move to the eg orbitals, resulting in 2 unpaired electrons. For octahedral \(\mathrm{Cr}^{2+}\) complexes: - In both strong-field and weak-field cases, the d-electrons will completely fill the t2g orbitals with one unpaired electron remaining in the eg orbitals, resulting in 1 unpaired electron in both cases.

Choosing the Better Complex to Determine Ligand Strength

Based on the comparison of the number of unpaired electrons in both complexes, octahedral \(\mathrm{Ni}^{2+}\) complexes will be better to determine whether a given ligand is a strong-field or weak-field ligand by measuring the number of unpaired electrons, as there is a distinct difference in the number of unpaired electrons between strong-field and weak-field cases for \(\mathrm{Ni}^{2+}\).

Another method to determine relative ligand field strengths

Another method to determine the relative ligand field strengths of different ligands is to measure the energy difference between the two split sets of d orbitals (the crystal field splitting parameter, ∆) for different ligands in a series of complexes with the same metal ion. The higher the energy difference, the stronger the ligand field. By comparing ∆ for each ligand, we can determine their relative field strengths.