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Ch.21 - Transition Elements and Coordination Chemistry
All textbooksMcMurry 8th EditionCh.21 - Transition Elements and Coordination ChemistryProblem 132
Chapter 21, Problem 132

Describe the bonding in [Mn(CN)_6]^3-, using both crystal field theory and valence bond theory. Include the appropriate crystal field d-orbital energy-level diagram and the valence bond orbital diagram. Which model allows you to predict the number of unpaired electrons? How many do you expect?

Verified step by step guidance
1
Step 1: Identify the central metal ion and its oxidation state. Manganese (Mn) in [Mn(CN)_6]^3- has an oxidation state of +3, making it Mn^3+.
Step 2: Determine the electron configuration of the Mn^3+ ion. Manganese has an atomic number of 25, so Mn^3+ has lost 3 electrons, resulting in the configuration [Ar] 3d^4.
Step 3: Apply crystal field theory to determine the splitting of the d-orbitals. In an octahedral field created by the six cyanide (CN^-) ligands, the d-orbitals split into two sets: t2g (lower energy) and eg (higher energy).
Step 4: Use the strong field ligand property of CN^- to predict the electron arrangement. CN^- is a strong field ligand, which causes a large splitting (Δ) and leads to pairing of electrons in the lower energy t2g orbitals before occupying the eg orbitals.
Step 5: Apply valence bond theory to describe the hybridization. The Mn^3+ ion uses d^2sp^3 hybrid orbitals to form sigma bonds with the CN^- ligands. This model helps predict the number of unpaired electrons, which, due to pairing in the t2g orbitals, results in 1 unpaired electron.

Key Concepts

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

Crystal Field Theory (CFT)

Crystal Field Theory explains how the presence of ligands around a central metal ion affects the energy levels of its d-orbitals. In an octahedral complex like [Mn(CN)6]3-, the d-orbitals split into two energy levels: the lower-energy t2g and the higher-energy eg. The extent of this splitting depends on the nature of the ligands, which can be classified as strong or weak field ligands, influencing the electron configuration and magnetic properties of the complex.
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The study of ligand-metal interactions helped to form Ligand Field Theory which combines CFT with MO Theory.

Valence Bond Theory (VBT)

Valence Bond Theory describes how atomic orbitals combine to form bonds in a molecule. In the case of [Mn(CN)6]3-, the theory suggests that the d-orbitals of manganese hybridize with the orbitals of the cyanide ligands to form sigma bonds. This model emphasizes the role of orbital overlap and can be used to visualize the bonding in terms of hybridization, which is crucial for understanding the geometry and bonding characteristics of the complex.
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Valence Shell Electron Pair Repulsion Theory

Unpaired Electrons and Magnetic Properties

The number of unpaired electrons in a complex is critical for determining its magnetic properties. In [Mn(CN)6]3-, the strong field cyanide ligands cause the d-orbitals to split significantly, leading to a low-spin configuration where electrons pair up in the lower energy t2g orbitals. By analyzing the electron configuration through both CFT and VBT, one can predict that [Mn(CN)6]3- will have no unpaired electrons, resulting in a diamagnetic complex.
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Magnetic Quantum Example
Related Practice
Textbook Question

Give a valence bond description of the bonding in each of the following complexes. Include orbital diagrams for the free metal ion and the metal ion in the complex. Indicate which hybrid orbitals the metal ion uses for bonding, and specify the number of unpaired electrons.

(d) [MnCl6]32 (high-spin)

Textbook Question

There are three coordination compounds with the empirical

formula Co1NH3231NO223 in which all the nitrite ions

are bonded through the N atom. Two isomers have the

same molar mass but different nonzero dipole moments.

The third compound is a salt with singly charged ions and a molar mass twice that of the other compounds.

(a) Draw the structures of the isomeric compounds.