Thermochemical equation help?

Question

Consider the thremochemical equation :
2 A-A + B-B ~~> 2 A-B-A DH0 = - 200.0 kJ./mol
If the A-A and A-B bond energies are respectively 250.0 and 225..0
kJ/mol. calculate the B-B bond energy.

How is the answer 200KJ? Can't seem to figure it out

Answer 1

2 A-A + B-B ----> 2 A-B-A

Breaking two A-A bonds = +2(250.0) = +500.0 kJ / mole

Forming four A-B bonds = 4(-225.0) = - 900 kJ / mole

X = Energy to break one B-B bond

DH =(Energy to break 2 A-A bonds) + (Energy to break one B-B bond) + (Energy to form four A-B bonds)

-200 = +500 + X -900

X = 200


Answer: 200.0 kJ/mole

Answer 2

Break the process into steps. First dissociate A-A:

2A-A ===> 4A 2 x 250 = +500.0 kJ

Next dissociate B-B:

B-B ===> 2B +x kJ

Finally, combine 4A's with 2 B's:

4A + 2B ===> A-B-A 4 x -225.0 kJ = -900.0 kJ

Add them all up:

500 + x - 900 = -200

x = 200 kJ