The structure of \(Al_{2}Cl_{6}\) is given below. The correct order of bond angles X, Y and Z is
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In bridged structures, the bridge-angle is always the smallest due to the rigid geometry of the cyclic structure, whereas terminal angles expand to minimize steric interference.
Concept:
Aluminum chloride (\(AlCl_3\)) exists as a dimer (\(Al_2Cl_6\)) in the vapor phase. The structure consists of two aluminum atoms bridged by two chlorine atoms. This creates a specific geometry for the bond angles between the bridging atoms and the terminal atoms.
Step 1: Identify the geometric constraints.
The two aluminum atoms are linked by a four-membered \(Al_2Cl_2\) ring. The bond angles inside this ring (specifically the bridge angle Y) are constrained by the ring structure, which usually forces the angle to be smaller than the ideal tetrahedral angle.
Step 2: Examine terminal versus bridge angles.
The terminal chlorine atoms are bonded to the aluminum atoms outside the bridge. Due to the repulsion between the lone pairs and the lack of ring-closure constraints, the terminal \(Cl-Al-Cl\) angles (like angle Z) are significantly wider and less constrained than those within the bridge.
Step 3: Compare angles X, Y, and Z.
Experimental and computational structural analysis shows that the angle Z (terminal) is the largest, followed by X, and finally Y (the bridge angle) which is the most compressed. This establishes the trend: \(Z > X > Y\).
