COMEDK 2024 Shift 1 Paper

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=2:1:2
If we let DB2=x‌kJ∕mol, then:
‌DA2=2x
‌DAB=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⟶2‌AB
The enthalpy change for this reaction can be calculated using the bond dissociation energies:
∆H‌formation ‌=DA2∕2+DB2∕2−DAB
Substitute the given enthalpy of formation and the relationships for bond dissociation energies into the equation:

−400‌kJ∕mol=‌

2x

2

+‌

x

2

−2x
Simplify the expression:
−400=x+‌

x

2

−2x

Combine like terms:
‌−400=x+‌

x

2

−2x
‌−400=−‌

x

2

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