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Chapter 20: Problem 27

For the same type of ligands, explain why the crystal field splitting for an octahedral complex is always greater than that for a tetrahedral complex.

Short Answer

Expert verified
The crystal field splitting in an octahedral complex is always greater than that in a tetrahedral complex due to the greater number of ligands and their direction of approach in an octahedral complex. In an octahedral complex, six ligands approach along the axes causing greater field splitting, whereas in a tetrahedral complex, four ligands approach between the axes causing less field splitting.

Step by step solution

01

Understand Octahedral Complex

An octahedral complex forms when six ligands coordinate to a central metal ion in an octahedral geometry. The arrangement results in a crystal field splitting of the d-orbitals into two sets of levels, one higher in energy (e_g) than the other (t_2g). The difference in energy \(\Delta_o\) is called the octahedral crystal field splitting.
02

Understand Tetrahedral Complex

A tetrahedral complex forms when four ligands coordinate to a central metal ion in a tetrahedral geometry. This arrangement results in a crystal field splitting of the d-orbitals into two sets of levels, one higher in energy (e) than the other (t_2). The difference in energy \(\Delta_t\) is called the tetrahedral crystal field splitting.
03

Crystal Field Splitting Comparison

In the octahedral complex, the ligands approach along the axes, causing the e_g orbitals to experience a greater increase in energy than the t_2g orbitals. Thus, \(\Delta_o\) is larger. In the tetrahedral complex, the ligands approach between the axes, causing the e orbitals to experience a lesser increase in energy than the t_2 orbitals. Thus, \(\Delta_t\) is smaller. Because the six ligands in the octahedral complex exert a stronger crystal field than the four ligands in the tetrahedral complex, \(\Delta_o > \Delta_t\).

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