`BCl_(3)` is trigonal planr while `AlCl_(3)` is tetrahedral in dimeric state. Explain.

Answer

To explain why \( \text{BCl}_3 \) is trigonal planar while \( \text{AlCl}_3 \) is tetrahedral in its dimeric state, we need to analyze the molecular geometry and hybridization of both compounds.

### Step 1: Understanding the structure of \( \text{BCl}_3 \)
- **Molecular Geometry**: \( \text{BCl}_3 \) has a trigonal planar geometry. This is because the boron atom is surrounded by three chlorine atoms.
- **Hybridization**: The boron atom undergoes \( sp^2 \) hybridization. This means that one \( s \) orbital and two \( p \) orbitals mix to form three \( sp^2 \) hybrid orbitals, which are arranged in a plane at 120-degree angles.
- **Reason for Trigonal Planarity**: Due to the small size of boron, it cannot accommodate more than three chlorine atoms, leading to a stable trigonal planar structure.

### Step 2: Understanding the structure of \( \text{AlCl}_3 \)
- **Molecular Geometry**: \( \text{AlCl}_3 \) exists as a dimer \( \text{Al}_2\text{Cl}_6 \) in the solid state, which has a tetrahedral geometry.
- **Hybridization**: The aluminum atom is larger than boron, allowing it to accept electron pairs from chlorine atoms. In the dimeric state, aluminum undergoes \( sp^3 \) hybridization, which allows for the formation of four hybrid orbitals.
- **Dative Bond Formation**: In the dimeric structure, each aluminum atom forms two dative bonds with chlorine atoms, leading to a tetrahedral arrangement of the chlorine atoms around the aluminum atoms.

### Conclusion
- **Comparison**: The key difference lies in the size and electronic configuration of boron and aluminum. Boron, being smaller, can only accommodate three chlorine atoms, resulting in a trigonal planar structure. In contrast, aluminum, being larger, can form additional bonds and thus adopts a tetrahedral geometry in its dimeric form.

### Summary
- \( \text{BCl}_3 \) is trigonal planar due to \( sp^2 \) hybridization and the inability of boron to accommodate more than three chlorine atoms.
- \( \text{AlCl}_3 \) forms a tetrahedral dimer \( \text{Al}_2\text{Cl}_6 \) due to \( sp^3 \) hybridization and the ability of aluminum to accept electron pairs from chlorine.