Draw a crystal field energy-level diagram for the 3 d orbitals of titanium in [Ti(H 2 O) 6 ] 3+ ]. Indicate the crystal field splitting, and explain why is [Ti(H 2 O) 6 ] 3+ ] colored.

All right. Hi everyone. So this question says using crystal field theory provide the splitting energy diagram of chromium three positive in cr cl 63 negative and rationalize why cr cl 63 negative is color. So in this case, the ion in question is hex. So chloro chromate three. Now Hexaco chromate has a central metal ion of chromium three positive as well as six chloride ligands. Now recalled chloride is mono dentate, which means that the co ordination number of this complex is going to be equal to six, which if you recall corresponds to octahedral geometry. Now, octahedral complexes require the use of a specific splitting energy diagram in which we have 3d orbitals that are lower energy, meaning they're on the bottom and two higher energy orbitals at the top. Now the lower energy orbitals are DXY DXZ and DYZ, whereas the higher energy orbitals are DX squared and DX squared subtracted by Y squared. So now the question is to identify the number of D electrons in chromium three positive. So first, let's consider the electronic configuration of chromium as a neutral Arab. Now, chromium, chromium has an atomic number of 24 which if you recall corresponds to 24 protons inside of its nucleus. And so when an atom is neutral, the number of protons is equal to the number of electrons. So in this case, when chromium, when chromium is neutral, the electronic configuration is an argon core followed by four S one and 3d 5 recall, it chromium is an exception to standard electronic configuration because ad orbital would prefer to be half filled rather than having a full s orbital. So now in the case of the electronic configuration of chromium three positive recall that electrons must be removed from the highest energy levels. So in this case, we're removing three electrons, one from the four S orbital and the remaining two from 3d, which means that the electronic configuration of chromium three positive is argon followed by 3D 3. So this means that we have 3d electrons. So in filling out our energy diagram recall that each lower energy D orbital must be filled first before their respective electrons are paired. So in this case, each lower energy de orbital is going to receive one electron. And so that completes our splitting or splitting energy diagram. Excuse me. And so what I want to point out here is that the the higher energy de orbitals are empty, meaning that they can accommodate electrons, should they transition from the lower orbitals or lower energy orbitals to the higher energy ones? So that would explain why hex aloro chromate three is colored right hexaco chroma three is colored because an electron can be promoted to the higher energy the orbitals bye absorbing light in the visible spectrum. Because by absorbing light in the visible spectrum, the electron has gained enough energy to transition or jump, so to speak from the lower energy orbitals to the higher energy one. And so with that being said, thank you so very much for watching and I hope you found this helpful.

Ch.21 - Transition Elements and Coordination Chemistry

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McMurry 8th Edition

Ch.21 - Transition Elements and Coordination Chemistry

Problem 21.102

Chapter 21, Problem 21.102

Draw a crystal field energy-level diagram for the 3d orbitals of titanium in [Ti(H₂O)₆]³⁺]. Indicate the crystal field splitting, and explain why is [Ti(H₂O)₆]³⁺] colored.

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Identify the oxidation state of titanium in [Ti(H_2O)_6]^{3+}. Since the complex has a 3+ charge and water is a neutral ligand, titanium must be in the +3 oxidation state.

Determine the electron configuration of the Ti^{3+} ion. Titanium in its elemental form has the electron configuration [Ar] 3d^2 4s^2. When it loses three electrons to form Ti^{3+}, the configuration becomes [Ar] 3d^1.

Draw the crystal field energy-level diagram for the 3d orbitals. In an octahedral field, the 3d orbitals split into two sets: the lower-energy t_{2g} set (d_{xy}, d_{xz}, d_{yz}) and the higher-energy e_g set (d_{x^2-y^2}, d_{z^2}).

Place the single 3d electron of Ti^{3+} in one of the t_{2g} orbitals, as these are lower in energy compared to the e_g orbitals.

Explain the color of [Ti(H_2O)_6]^{3+}. The complex is colored because the electron in the t_{2g} level can absorb visible light to be promoted to the e_g level, resulting in a d-d transition. The specific wavelength of light absorbed corresponds to the energy difference between these levels, which is perceived as color.

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Key Concepts

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

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 like [Ti(H2O)6]3+, the d orbitals split into two sets: the lower-energy t2g and the higher-energy eg orbitals. This splitting occurs due to the electrostatic interactions between the negatively charged ligands and the positively charged metal ion.

Crystal Field Splitting Energy (Δ)

Crystal Field Splitting Energy (Δ) is the energy difference between the split d orbital sets in a coordination complex. The magnitude of Δ influences the electronic transitions of the metal ion, which in turn affects the color observed in the complex. A larger Δ typically results in different colors due to the specific wavelengths of light absorbed during these transitions.

Color in Transition Metal Complexes

The color of transition metal complexes, such as [Ti(H2O)6]3+, arises from the absorption of specific wavelengths of light that promote electrons from the lower-energy t2g orbitals to the higher-energy eg orbitals. The color observed is complementary to the color of light absorbed. For example, if the complex absorbs light in the red region, it will appear green, as green is the complementary color to red.