Bond energies and heat of reaction

[brake4country]

Homework Statement

Given that the bond energy of hydrogen-hydrogen bonds is 436 KJ/mol, that of hydrogen-oxygen bonds is 464 KJ/mol, and those in oxygen molecules 496 KJ/mol, what is the approximate heat of reaction for 2H₂ + O₂→2H₂O

Homework Equations

H_products-H_reactants

The Attempt at a Solution

So, I understand that heats of reaction involving hydrogen gas and oxygen gas to liquid water is exothermic, so my answer must be negative. My book gives and answer of -488 KJ/mol but I keep ending up with -440 KJ/mol:

2(464) - [2(436) + 496] = -440 KJ/mol.

Calculation error? I went over the numbers twice. Thanks!

 

[Calaver]

How many molecules of water does the reaction yield, and how many hydrogen-oxygen bonds are in each molecule? I hope this helps.

 

[brake4country]

Actually, I looked up a video to see where my reasoning went astray. With the original equation, we have:

2H₂+ O₂→ 2H₂O

Bonds broken:
2H-H = 436 KJ/mol
0₂ = 496 KJ/mol

Bonds formed:
2H₂O

Using H_p-H_r, we get:
4(464)-[2(436) + 496)] = 488 KJ/mol but must be negative because g-->l is exothermic.

Since this is the right answer, I feel better now, but I prefer the experts here to make sure my work is valid. Thanks in advance!

 

[Calaver]

Your answer is correct, and your original answer had the right concept, it just looked like to me that you forgot to count one of the water molecules produced (or one of the hydrogen-oxygen bonds within each molecule).

 

[brake4country]

You are right. I had to draw out the bonds in the products to see what I did wrong. Thanks again!