Question

(a) For the equilibrium \(\mathrm{Al}_{2} \mathrm{R}_{6} \rightleftharpoons 2 \mathrm{AlR}_{3},\) comment on the fact that values of \(K\) are \(1.52 \times 10^{-8}\) for \(R=M e,\) and \(2.3 \times 10^{-4}\) for \(R=M e_{2} C H C H_{2} .(b)\) Describe the bonding in \(\mathrm{Al}_{2} \mathrm{Me}_{6}, \mathrm{Al}_{2} \mathrm{Cl}_{6}\) and \(\mathrm{Al}_{2} \mathrm{Me}_{4}(\mu-\mathrm{Cl})_{2}\).

Short answer

The low and high K values show steric/electronic impact on equilibrium. Al2Me6 and Al2Cl6 involve bridging bonds; Al2Me4(μ-Cl)2 has mixed ligand bonds.

Step-by-step solution

Understanding the Equilibrium

The equilibrium expression for the reaction \( \mathrm{Al}_{2} \mathrm{R}_{6} \rightleftharpoons 2 \mathrm{AlR}_{3} \) is given by the equilibrium constant \( K = \frac{[\mathrm{AlR}_{3}]^2}{[\mathrm{Al}_{2} \mathrm{R}_{6}]} \). The values of \( K \) indicate how far the reaction proceeds to form AlR₃ from Al₂R₆ in equilibrium.

Comparing K Values for Different R Groups

For \( R = Me \) (methyl group), \( K = 1.52 \times 10^{-8} \), while for \( R = Me_{2}CHCH_{2} \) (isobutyl group), \( K = 2.3 \times 10^{-4} \). The lower \( K \) value for \( R = Me \) suggests that the equilibrium heavily favors the formation of the dimer \( \mathrm{Al}_{2} \mathrm{Me}_{6} \), whereas the higher \( K \) for \( R = Me_{2}CHCH_{2} \) implies a greater tendency to favor the monomer \( \mathrm{AlR}_{3} \). This can be due to the greater steric requirements or electronic factors associated with larger \( R \) groups.

Bonding in Al2Me6

In \( \mathrm{Al}_{2} \mathrm{Me}_{6} \), the bonding involves dimerization where two AlMe₃ units are bonded together through shared Al-C (bridging) interactions. Here, two Al atoms each carry a partial positive charge and are coordinated by Me groups.

Bonding in Al2Cl6

The compound \( \mathrm{Al}_{2} \mathrm{Cl}_{6} \) forms dimeric structures where two \( \mathrm{Al} \) atoms are bridged by chlorine atoms. Each aluminum contributes two electrons, forming a \( 3c-4e \) (three-center, four-electron) bond with the bridging chloride ions. These are classic Lewis acid-base interactions.

Bonding in Al2Me4(μ-Cl)2

In \( \mathrm{Al}_{2} \mathrm{Me}_{4}(\mu-\mathrm{Cl})_{2} \), the compound comprises Al atoms coordinated by both methyl groups and bridging chloride atoms. The bonding involves \( 3c-4e \) bonds between Al, Cl, and the Al atoms, along with terminal Me attachments, reflective of a mixed ligand environment providing both steric and electronic properties.

Key concepts

Dimerization

Dimerization is a fascinating process where two identical molecules connect to form a single compound, known as a dimer. In the context of aluminum alkyl compounds, dimerization involves two units of aluminum alkyl bonding together. This reaction is represented as \( \mathrm{Al}_{2} \mathrm{R}_{6} \rightleftharpoons 2 \mathrm{AlR}_{3} \). Dimerization occurs due to specific interactions between the molecules, such as shared electron pairs. This process can be strongly affected by the size and nature of the substituent groups attached to the aluminum atoms. For example, methyl groups (small and simple) may lead to stable dimers like \( \mathrm{Al}_{2} \mathrm{Me}_{6} \). Larger substituents, like isobutyl, can exert steric pressure that encourages the formation of monomers (individual \( \mathrm{AlR}_{3} \) units). The balance between dimerization and staying as individual monomers is influenced by steric and electronic effects.

Equilibrium Constants

The equilibrium constant, \( K \), provides crucial insights into the position of equilibrium in chemical reactions. This constant reflects the balance between the products and reactants in a reversible reaction such as \( \mathrm{Al}_{2} \mathrm{R}_{6} \rightleftharpoons 2 \mathrm{AlR}_{3} \). Its value is calculated using the concentrations of the reactants and products: \[ K = \frac{[\mathrm{AlR}_{3}]^2}{[\mathrm{Al}_{2} \mathrm{R}_{6}]} \].

• A high \( K \) value signifies a reaction that strongly favors products at equilibrium.
• Conversely, a low \( K \) value indicates that the reactants are predominantly present in equilibrium.

For \( R = \mathrm{Me} \), the low \( K = 1.52 \times 10^{-8} \) suggests that the reaction mostly results in the formation of dimers, whereas for \( R = \mathrm{Me}_{2} \mathrm{CH} \mathrm{CH}_{2} \), a higher \( K = 2.3 \times 10^{-4} \) implies a shift toward the monomer form. This difference in \( K \) values illustrates how substituents alter the equilibrium by affecting either steric or electronic factors.

Aluminum Alkyl Bonding

In aluminum alkyls like \( \mathrm{Al}_{2} \mathrm{Me}_{6} \), bonding occurs through the interaction of aluminum atoms with methyl groups via shared electrons. These interactions form bridges between aluminum and carbon atoms, creating a stable dimer. This particular arrangement enables the formation of "three-center, four-electron" (\( 3c-4e \)) bonds, characterized by a pair of electrons shared across three centers.

• In \( \mathrm{Al}_{2} \mathrm{Cl}_{6} \), the dimer formation involves aluminum and chloride ions.
• The aluminum atoms bridge through chlorine, maintaining the \( 3c-4e \) bond.

Moreover, in \( \mathrm{Al}_{2} \mathrm{Me}_{4}(\mu-\mathrm{Cl})_{2} \), aluminum is bonded through both methyl and bridging chloride atoms, reflecting a mixed bonding environment. This showcases the complexity and versatility of aluminum alkyl bonding, influenced by the ligands involved.

Steric and Electronic Effects

While examining equilibrium reactions, steric and electronic effects play a pivotal role. Steric effects arise due to the physical size and shape of the substituents surrounding a reactive site. Large substituents can hinder the approach or proper alignment of reacting molecules, thereby affecting the stability of dimers like \( \mathrm{Al}_{2} \mathrm{R}_{6} \). In contrast, electronic effects are related to the presence and behavior of electrons in a molecule.

• These can influence the polarity of bonds and the ability of atoms to attract electrons.
• The electronic nature of substituents can stabilize or destabilize specific conformations of molecules.

For instance, molecules with electron-donating or withdrawing groups will affect bonding and reactivity, as seen in the variation of \( K \) values. These collective effects help in dictating whether a compound will prefer to stay as a monomer or dimer.