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Ch.23 - Transition Metals and Coordination Chemistry
Chapter 23, Problem 62

Complete the exercises below. For each of the following metals, write the electronic configuration of the atom and its 3+ ion: b. Mo. Draw the crystal-field energy-level diagram for the d orbitals of an octahedral complex, and show the placement of the d electrons for each 3+ ion, assuming a weak-field complex. How many unpaired electrons are there in each case?

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1
Determine the atomic number of molybdenum (Mo) to find the number of electrons in a neutral atom. Molybdenum has an atomic number of 42, so it has 42 electrons.
Write the electronic configuration for a neutral Mo atom. The configuration is based on the order of filling orbitals: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d. For Mo, the configuration is: \[ \text{Mo: } [\text{Kr}]\ 4d^5\ 5s^1 \].
Determine the electronic configuration for the Mo^{3+} ion. Remove three electrons from the neutral atom configuration, starting with the highest energy level (5s) and then from the 4d orbitals: \[ \text{Mo}^{3+}: [\text{Kr}]\ 4d^3 \].
Draw the crystal-field energy-level diagram for the d orbitals in an octahedral complex. In an octahedral field, the d orbitals split into two sets: the lower energy \( t_{2g} \) (d_{xy}, d_{xz}, d_{yz}) and the higher energy \( e_g \) (d_{x^2-y^2}, d_{z^2}) orbitals.
Place the d electrons of Mo^{3+} in the crystal-field diagram for a weak-field complex. Since Mo^{3+} has 3 d electrons, place them in the \( t_{2g} \) orbitals, one in each, following Hund's rule. Count the number of unpaired electrons, which in this case is 3.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Electronic Configuration

Electronic configuration describes the distribution of electrons in an atom's orbitals. For transition metals like molybdenum (Mo), the configuration is crucial for understanding their chemical properties and behavior in compounds. The configuration for Mo is [Kr] 5s² 4d⁵, and for its 3+ ion, it loses three electrons, typically from the 4d and 5s orbitals.
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Crystal Field Theory

Crystal Field Theory (CFT) explains how the arrangement of ligands around a central metal ion affects the energy levels of its d orbitals. In an octahedral complex, the d orbitals split into two energy levels: t₂g (lower energy) and e_g (higher energy). This theory helps predict the magnetic properties and color of the complex based on the arrangement and strength of the ligands.
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The study of ligand-metal interactions helped to form Ligand Field Theory which combines CFT with MO Theory.

Unpaired Electrons and Magnetism

Unpaired electrons in an atom or ion contribute to its magnetic properties. In transition metal complexes, the number of unpaired electrons can be determined by the electron configuration and the splitting of d orbitals. A weak-field ligand leads to a higher number of unpaired electrons, resulting in paramagnetism, while a strong-field ligand can lead to paired electrons and diamagnetism.
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