Molecular Orbital Theory -- Diatomics -- Bond Order?

Question

An unknown gas, X2(g), which behaves much like N2(g) (NN), is analysed and the following enthalpies of formation are obtained:
Gas
X(g) 376 kJ/mol
H(g) 217 kJ/mol
X2H4(g) 442 kJ/mol


We also know that the X-H bond energy is 267 kJ/mol.
Use this information to estimate the X-X (single-)bond energy in the X2H4 molecule

Please do explain the proper method and the various steps used to solve this problem.
Thank you.

Answer 1

442 kJ mol-1 is heat of formation of X2H4 from X2 and H2.

Find heat of the reaction

2 X + 4 H = X2H4

by the usual procedure ({products} - {reactants})

The heat given out by the formation of X2H2 from atoms is just the required X-X bond energy + 4 x H-X bond energy (why?).

In all these problems (bond energy, lattice energy etc) you are using Hess's Law (a special case of conservation of energy) to say that you get the same result when you make a compound from given ingredients, whatever the path chosen, and that gves you enough information to find the missing link.