Each of the following pairs of complexes contains identical...

Each of the following pairs of complexes contains identical numbers of $d$ electrons, but in each pair, one complex is high-spin and the other is low-spin. In each case, predict which is high-spin and which is low-spin, and give the number of unpaired electrons present in each complex. (a) $\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}$ and $\left[\mathrm{Mn}(\mathrm{CN})_{6}\right]^{3-}$ (b) $\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}$ and $\left[\mathrm{Ru}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}$ (c) $\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}$ and $\left[\mathrm{Co}(\mathrm{CN})_{5}\left(\mathrm{H}_{2} \mathrm{O}\right)\right]^{3-}$

Each of the following pairs of complexes contains identical numbers of $d$ electrons, but in each pair, one complex is high-spin and the other is low-spin. In each case, predict which is high-spin and which is low-spin, and give the number of unpaired electrons present in each complex.
(a) $\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}$ and $\left[\mathrm{Mn}(\mathrm{CN})_{6}\right]^{3-}$
(b) $\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}$ and $\left[\mathrm{Ru}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}$
(c) $\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}$ and $\left[\mathrm{Co}(\mathrm{CN})_{5}\left(\mathrm{H}_{2} \mathrm{O}\right)\right]^{3-}$

Key Concepts

Crystal Field Theory

Crystal Field Theory explains the splitting of the degenerate d orbitals of a transition metal ion when surrounded by ligands. The nature of this splitting into lower and higher energy sets (typically t2g and eg in an octahedral field) is fundamental for predicting the electronic configuration, colors, magnetism, and reactivity of the complex.

Ligand Field Strength

Ligand field strength refers to the ability of a ligand to split the d orbital energies of a metal ion. Strong-field ligands, such as cyanide (CN?), generate a large splitting (high ?), favoring low-spin configurations by promoting electron pairing in the lower set of orbitals, whereas weak-field ligands, like water (H?O), result in smaller splitting and usually lead to high-spin configurations with more unpaired electrons.

High-spin versus Low-spin Configurations

The high-spin and low-spin designations describe whether electrons in a metal complex occupy orbitals in a way that maximizes the number of unpaired electrons (high-spin) or minimizes it by pairing electrons in the lower energy orbitals (low-spin). This distinction depends on the relative magnitude of the crystal field splitting energy (?) and the electron pairing energy, and it directly impacts the magnetic properties of the complex.

d Electron Count and Oxidation State Influence

The number of d electrons and the oxidation state of the transition metal are critical in determining the electronic arrangement within the split d orbitals. Knowing the d electron count helps predict whether the complex will adopt a high-spin or low-spin configuration, as well as the resulting number of unpaired electrons and magnetic behavior.

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