Crystal Field Theory: Octahedral Complexes - Video Tutorials & Practice Problems
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concept
The crystal field splitting pattern for octahedral complexes has the d orbitals on or along the axes as having the higher energy.
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Now crystal field splitting is the separation of degenerate d orbitals into nondegenerate sets. So remember, the word degenerate means same energy. So we're taking the 5 d orbitals that are on the same level, same energy, and we're basically separating them, creating one tier that's lower in energy and one that's higher in energy. Now, the splitting pattern from a complex depends upon its geometry. So we'll see based on the geometry of our complex ion, these 5 d orbitals can orient themselves in different ways. Now here with octahedral crystal field splitting, we're gonna say recall that in octahedral complexes, the ligand orbital interactions are on the on the axes or along the axes are the strongest ones. We're gonna say, this increases the energies of the orbitals that are oriented on the axis. So if we take a look here, we have our 6 ligands that are the green dots. And remember the 2 orbitals that lie on the axis or along the axis are d x squared minus y squared or d z squared. They have the greatest energy, so we would orient them up here. And then these other 3 are the ones that lie in between the axes. They have less interaction, and therefore would have lower energy, so we're placing them down here. Now we're gonna say that the difference in energy between these three bottom ones and then these two top ones, it is designated as delta. Delta represents our crystal field splitting energy. And we're gonna say that this is the energy difference between the 2 sets, which are e and t 2 of orbitals. Alright. So which one is, e, which one is t 2? Well, in terms of this octahedral complex, we're gonna say that our e equals doublet, which means it's the pair of orbitals, the 2 orbitals. So these 2 would be our eset, and then t here stands for triplet, which is our 3 orbitals, so this would be our t set here. So just remember, when we talk about crystal field splitting, we're looking at our 5 original d orbitals and we're separating them. 1 on the bottom is lower in energy and then up here higher in energy. For octahedral species, it's the ones that lie on the axis or along the axis that have greater energy because of greater interaction. That's why d sub x squared minus y squared and d sub z squared are up here. The other ones lie in between the axes, less interaction, less energy, that's why they're lower down here. And again, their difference in levels is our delta, our crystal field splitting energy.
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example
Example
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43s
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For which of the following complexes the energy of the t two set is lower than the e set? So this question is actually easier than it appears. What they're really asking us to determine is which one of these complex ions represents an octahedral complex. So remember to be octahedral, you need your metal cation to be connected to 6 ligands. And if we look, the only option that has our metal cation connected to 6 ligands is option d. Here we have cobalt 3+ion connected to 6 water molecules. This would give us an octahedral orientation, which in turn would mean that our t 2 set of 3 orbitals is lower in energy than our e set of our pair of orbitals.
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Problem
Problem
The following diagram shows crystal field splitting pattern for a complex. Which one of the complexes given below should best match the given diagram?
A
[Ag(NH3)2]+
B
[Cu(ox)2]2–
C
[Cr(en)3]3+
D
[Fe(CO)5]
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