Boron exists in different allotropic forms. All allotropic form contains icosahedral units (icosahedral is a regular shape with 12 corners and 20 faces) with boron atoms at all 12 corners and all bond

Question

Boron exists in different allotropic forms. All allotropic form contains icosahedral units (icosahedral is a regular shape with 12 corners and 20 faces) with boron atoms at all 12 corners and all bonds are equivalent. Calculate the heat evolved at constant pressure (in kJ/mole) of boron atom undergoing the above change if the bond dissociation enthalpy of B-B bond is 300 kJ/mol.

TestHub · Accepted Answer

An icosahedron (12 vertices, 20 faces) has E = V + F - 2 = 12 + 20 - 2 = 30 edges. This means there are 30 equivalent B-B bonds per B ₁₂ unit. Forming this unit from 12 gaseous boron atoms evolves 30 × 300 = 9000 kJ per mole of B ₁₂ . Therefore, the energy evolved per mole of boron atoms is 9000/12 = 750 kJ. This corresponds to option (b).

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