To solve this problem, we need to leverage the given information about the enthalpy of formation and the bond dissociation energies. Here's the step-by-step solution:
Let's denote the bond dissociation energies of
A2,B2, and AB as
DA2,DB2, and
DAB, respectively. We are told that their bond dissociation energies are in the ratio 2:1:2. This means:
DA2:DB2:DAB=2:1:2If we let
DB2=x‌kJ∕mol, then:
‌DA2=2x‌DAB=2x Next, we can express the enthalpy change for the formation of the diatomic molecule AB from its constituent atoms. The formation reaction can be written as:
A2+B2⟶2‌ABThe enthalpy change for this reaction can be calculated using the bond dissociation energies:
∆H‌formation ‌=DA2∕2+DB2∕2−DABSubstitute the given enthalpy of formation and the relationships for bond dissociation energies into the equation:
−400‌kJ∕mol=‌+‌−2xSimplify the expression:
−400=x+‌−2x Combine like terms:
‌−400=x+‌−2x‌−400=−‌Multiply both sides by -2 :
800=x So, the bond dissociation enthalpy of
B2 is
800‌kJ∕mol. Therefore, the correct answer is:
Option A:
800‌kJ∕mol