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 200 kJ/mol.

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An icosahedron (with 12 vertices and 20 faces) has E = V + F - 2 = 12 + 20 - 2 = 30 equivalent B-B bonds per B₁₂ unit. Forming this unit from 12 gaseous boron atoms evolves 30 × 200 = 6000 kJ per mole of B₁₂. This means 6000/12 = 500 kJ per mole of boron atoms. This corresponds to option (d).

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