How many unpaired electrons are in the following complex ions? a. Ru(NH3)6^2+ (low-spin case) b.

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How many unpaired electrons are in the following complex...

How many unpaired electrons are in the following complex ions?
a. $\mathrm{Ru}\left(\mathrm{NH}_{3}\right)_{6}^{2+}$ (low-spin case)
b. $\mathrm{Ni}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}$
c. $\mathrm{V}(\mathrm{en})_{3}{ }^{3+}$

Key Concepts

Crystal Field Theory

Crystal field theory explains how the degeneracy of metal ion d orbitals is broken when surrounded by ligands. In octahedral complexes, the d orbitals split into two energy levels (t2g and eg), and the distribution of electrons into these orbitals determines the magnetic and optical properties of the complex, including the number of unpaired electrons.

Oxidation State and d-Electron Count

Determining the oxidation state of the metal ion in a complex is crucial for finding the number of d electrons present. Once the oxidation state is known, the electron configuration of the metal can be established, forming the basis for predicting the distribution of electrons among the split d orbitals.

Spin States (High-Spin vs Low-Spin)

The choice between high-spin and low-spin configurations in coordination complexes depends on the relative magnitudes of the crystal field splitting energy (?) and the spin pairing energy. In low-spin complexes, electrons pair in the lower energy orbitals even if this means overcoming pairing energy, while in high-spin complexes, electrons remain unpaired as much as possible.

Ligand Field Strength and the Spectrochemical Series

Ligands are arranged in the spectrochemical series based on their ability to split the d orbital energies. Strong-field ligands produce a larger splitting (?), which often favors low-spin configurations, whereas weak-field ligands cause smaller splitting, leading to high-spin arrangements. This concept is essential in predicting magnetic properties such as the number of unpaired electrons.

Octahedral Coordination Geometry

Most of the complex ions discussed are octahedral, where six ligands symmetrically surround the metal ion. This specific geometry leads to the characteristic splitting pattern of the metal d orbitals into two sets, fundamentally influencing the electron configuration and resulting magnetic character.

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