Construct the octahedral crystal-field splitting diagram for the metal in each species.
Cr4+
Mn(H2O)6^2+
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for Mn(H2o)6^2+ there would be a single electron in each of the five shells. This is because it has high spin.
Well, let's put on our 3D glasses and dive into the world of crystal-field splitting diagrams!
For Cr4+, the metal ion has four d electrons. In an octahedral crystal field, these d orbitals will split into two sets of different energy levels. The lower energy set will have three orbitals called t2g orbitals (which stands for "too 2 good") and the higher energy set will have two orbitals called eg orbitals (which stands for "eek, gone!"). So, the crystal-field splitting diagram for Cr4+ would look like this:
eg
|
________
\ /
\____/
|
t2g
Next up is Mn(H2O)6^2+. Mn2+ has five d electrons, so in an octahedral crystal field, these d orbitals will also split into two sets of different energy levels: t2g and eg. However, since there are now six ligands (H2O) surrounding the Mn2+ ion, the splitting will be different. The crystal-field splitting diagram for Mn(H2O)6^2+ would look like this:
eg
|
________
\ /
\ /
\ /
\/
|
t2g
And there you have it! The crystal-field splitting diagrams for Cr4+ and Mn(H2O)6^2+. Remember, when it comes to crystal-field splitting, it's all about the split personality of the d orbitals!
To construct the octahedral crystal-field splitting diagram for each species, we will first consider the number of d-electrons present in the metal ion. This will determine the number of orbitals that will be involved in the crystal-field splitting.
1. Cr4+:
Cr4+ has 3d electrons.
The five d-orbitals in an octahedral field can be split into two sets: the lower-energy set (t2g) containing three orbitals, and the higher-energy set (eg) containing two orbitals.
In the case of Cr4+, we have two d-electrons in the t2g set and one d-electron in the eg set.
Octahedral crystal-field splitting diagram for Cr4+:
↑ ↑
| |
eg| |
| |
| |
| ↓ |
t2g| |
| |
| |
| |
| |
2. Mn(H2O)6^2+:
Mn2+ has 5d electrons.
Similar to the previous example, the five d-orbitals are again split into t2g and eg sets.
In the case of Mn(H2O)6^2+, we have three d-electrons in the t2g set and two d-electrons in the eg set.
Octahedral crystal-field splitting diagram for Mn(H2O)6^2+:
↑ ↑
| |
eg| ↓ |
| |
| |
| |
t2g| ↓ |
| |
| |
| |
| |
Note: In the crystal-field splitting diagram, the up and down arrows represent the electron configurations in each orbital after the splitting due to the octahedral crystal field. The t2g orbitals are located lower in energy, while the eg orbitals are located higher in energy. The number of electrons in each set can be determined using the electron configurations of the respective metal ions.
To construct the octahedral crystal-field splitting diagram for a metal ion in a complex, we need to consider the interactions between the metal ion and the surrounding ligands.
For Cr4+, we know that it has a 3d4 electron configuration. In an octahedral crystal field, the d-orbitals split into two sets: a lower-energy set (t2g) and a higher-energy set (eg). The t2g orbitals consist of dxy, dyz, and dxz, while the eg orbitals consist of dx2-y2 and dz2.
In the case of Cr4+, since it has four unpaired electrons, we will first fill up the t2g orbitals with three electrons, and place the fourth electron in one of the eg orbitals.
The electron configuration for Cr4+ in an octahedral crystal field is as follows:
dxy ↑
dyz ↑
dxz ↑
dx2-y2 ↑↓
dz2
The diagram would look like this (with arrows representing the electrons):
t2g (lower energy) - dxy ↑, dyz ↑, dxz ↑
eg (higher energy) - dx2-y2 ↑↓, dz2
For Mn(H2O)6^2+, we need to consider the electron configuration of Mn2+ and the ligand field created by water molecules.
Mn2+ has a 3d5 electron configuration. Similar to Cr4+, we will fill up the t2g orbitals first with three electrons, and distribute the remaining two electrons in the eg orbitals.
The electron configuration for Mn2+ in an octahedral crystal field is as follows:
dxy ↑
dyz ↑
dxz ↑
dx2-y2 ↑↓
dz2 ↑
The diagram would look like this (with arrows representing the electrons):
t2g (lower energy) - dxy ↑, dyz ↑, dxz ↑
eg (higher energy) - dx2-y2 ↑↓, dz2 ↑
Note: It's important to keep in mind that the splitting of the d-orbitals into t2g and eg sets may vary depending on the ligand field strength. The diagrams provided are based on the typical octahedral crystal-field splitting.