Question

While \(\mathrm{Ti}^{3+}, \mathrm{V}^{3+}, \mathrm{Fe}^{3+}\) and \(\mathrm{Co}^{2+}\) can afford a large number of tetrahedral complexes, \(\mathrm{Cr}^{3+}\) never does this, the reason being (a) crystal field stabilisation energy in octahedral vis-à-vis tetrahedral \(\mathrm{Cr}^{3+}\) system plays the deciding role (b) \(\mathrm{Cr}^{3^{3}}\) forces high crystal field splitting with a varieties of ligands (c) electronegativity of \(\mathrm{Cr}^{3+}\) is the largest among these trivalent 3 d-metals and so chromium prefers to be associated with as many ligands as its radius permits (d) both (b) and (c)

Short answer

(a) Crystal field stabilization energy in octahedral versus tetrahedral Cr^{3+} system plays the deciding role.

Step-by-step solution

Understanding the Problem

We need to determine why Cr^{3+} rarely forms tetrahedral complexes compared to Ti^{3+}, V^{3+}, Fe^{3+}, and Co^{2+}. The options refer to crystal field stabilization energy (CFSE) and other characteristics of the Cr^{3+} ion.

Review Crystal Field Theory

The Crystal Field Stabilization Energy (CFSE) is the energy difference between an ion's octahedral and tetrahedral environments. Octahedral complexes usually have higher crystal field splitting than tetrahedral complexes, which can affect the preference for forming certain complexes.

Understanding Octahedral vs Tetrahedral Preference

Transition metals often form complexes based on CFSE. Generally, octahedral complexes provide more stabilization than tetrahedral complexes due to higher crystal field splitting.

Assessing Cr^{3+} Characteristics

Cr^{3+} has a relatively high crystal field splitting energy because it has a d^3 configuration which results in significant stabilization in octahedral complexes. This deters Cr^{3+} from forming tetrahedral complexes, which have lower CFSE.

Evaluate Each Option

(a) CFSE plays a key role, matching the preference of Cr^{3+} for octahedral complexes. (b) Cr^{3+} indeed results in significant crystal field splitting with various ligands, fitting the description but not providing a full perspective. (c) Electronegativity is not typically as relevant in determining crystal field preference. (d) While (b) is accurate, (a) gives a broader and more direct explanation for the unique behavior of Cr^{3+}.

Conclude with the Correct Explanation

The tendency for Cr^{3+} to form octahedral over tetrahedral complexes is largely due to the crystal field stabilization energy, as stated in option (a). This is the most direct reason for Cr^{3+}'s behaviour based on its electronic configuration and crystal field theory.

Key concepts

Crystal Field Stabilization Energy (CFSE)

Crystal Field Stabilization Energy (CFSE) is a crucial concept in understanding the behavior of transition metal ions in complexes. It refers to the difference in energy between the d-orbitals in a complex when the metal ion is surrounded by ligands. The arrangement of these d-orbitals is influenced by the geometrical arrangement of the ligands around the metal ion.

In octahedral complexes, the ligands create a stronger splitting of the d-orbitals compared to tetrahedral complexes. This stronger splitting results in a higher stabilization energy. For a metal ion like \(\mathrm{Cr}^{3+}\), with its \(d^3\) electronic configuration, the energy gain due to this splitting can be quite significant. The t\(_{2g}\) orbitals are lower in energy compared to the e\(_g\) orbitals, leading to a more stable arrangement in an octahedral complex.

By contrast, in tetrahedral complexes, the d-orbital splitting is much smaller. For \(\mathrm{Cr}^{3+}\), this leads to lesser stabilization compared to the octahedral arrangement. The role of CFSE is therefore pivotal in determining why certain ions, like \(\mathrm{Cr}^{3+}\), prefer octahedral over tetrahedral complexes.

Octahedral vs Tetrahedral Complexes

Transition metals can form both octahedral and tetrahedral complexes, depending on various factors including the central ion, the ligands, and the resulting crystal field splitting. An octahedral complex consists of a central metal ion surrounded by six ligands arranged at the corners of an octahedron. This configuration results in a higher crystal field splitting because more ligands directly interact with the d-orbitals of the central metal.

On the other hand, a tetrahedral complex has four ligands arranged at the corners of a tetrahedron. The smaller number of ligands and the different spatial arrangement leads to a weaker interaction and thus a smaller split between the orbitals.

• Octahedral complexes are generally more stable than tetrahedral ones because of the greater stabilization energy they provide.
• Complexes like those of \(\mathrm{Cr}^{3+}\)prefer the octahedral configuration due to these stability considerations.
• The spatial configuration affects the d-orbital splitting, which directly influences the crystal field stabilization energy and ultimately determines the preference for one geometry over the other.

Understanding these concepts helps explain why some transition metal ions form certain geometries more readily than others.

Transition Metal Complexes

Transition metal complexes are fascinating structures in coordination chemistry. These complexes are formed when ligands donate pairs of electrons to a central transition metal ion and create coordinate bonds.

Transition metals are unique because they have partially filled d-orbitals. This characteristic allows them to form various stable complexes with different coordination geometries, such as octahedral and tetrahedral. The choice of geometry greatly depends on the Crystal Field Stabilization Energy (CFSE) generated by the interaction between the metal ion and its surrounding ligands.

• The coordination chemistry of transition metals is influenced by factors such as electronic configuration, oxidation state, and the nature of ligands.
• Electrons in the d-orbitals play a key role in defining the properties and reactivity of these complexes.
• Different transition metal ions have different preferences for complex geometries based on their electronic structures and the resulting CFSE.

Thus, transition metal complexes display a rich variety of structures and are a cornerstone in understanding chemical bonding and reactivity in inorganic chemistry.