# Reaction energy of oxygen and hydrogen

From the bonding energy of following bonds that I found in a Wikipedia article, I calculated the reaction energy that would be released when oxygen and hydrogen are reacted to produce water. The phase of each component is unknown.

$$\begin{array}{lc} \hline \text{Bond} & D_0/\pu{kJ mol-1} \\ \hline \ce{H-H} & 436 \\ \ce{O-H} & 497 \\ \ce{O=O} & 498 \\ \hline \end{array}$$

Therefore,

$$\ce{2 H2 + O2 -> 2 H2O} + \pu{618 kJ}$$

However, this Wikipedia article suggests that $$\pu{241.8 kJ}$$ of energy is released for every mole of hydrogen, which is $$\pu{483.6 kJ}$$ per $$\pu{2 mol}$$ for the context of the equation above.

Even when I consider the vaporization of water, which is $$\pu{40.65 kJ mol-1}$$, the total energy will amount to $$\pu{536.7 kJ}$$ per $$\pu{2 mol}$$, which is still far away from $$\pu{483.6 kJ}$$ per $$\pu{2 mol}$$ that is suggested in the Wikipedia article.

Where could this extra energy be going?

• Bond energies are a great deal less universal than you seem to be thinking. – Ivan Neretin Jan 20 '19 at 2:10
• The catch may be the cleavage of OH in water. Also, you need to be careful with signs, vaporization is endothermic. – Buck Thorn Jan 20 '19 at 11:28
• I am aware that it is endothermic. Therefore I have performed the following calculation: 2H2 + O2 = 2H2O(liquid) + 618kJ = (2H2O(gas) - 40.65kJ*2) + 618kJ = 2H2O(gas) + 536.7kJ – Y. Yoshii Jan 20 '19 at 16:16
• Please tell me. If my way is unconventional, what method is normally used to solve thermochemical equations in chemistry? – Y. Yoshii Jan 20 '19 at 16:24
• @Y.Yoshii Maybe this is useful: pubs.acs.org/doi/10.1021/jp013909s – Buck Thorn Jan 20 '19 at 20:23

Part of the discrepancy appears to be due to the need for two $$\ce{O-H}$$ dissociation energy terms to compute the $$\ce{OH}$$ bond energy for water: one for the $$\ce{OH}$$ bond in water (i.e. $$\ce{H-OH}$$), and another for the $$\ce{OH}$$ bond in the $$\ce{OH}$$ radical (i.e. $$\ce{^.O-H}$$). Values for these are reported by Ruscic et al. [1]. Using the average value of $$\ce{D_0}$$ for $$\ce{H2O}$$ (the $$\ce{OH}$$ bond energy for water), namely $$\pu{459 kJ/mol}$$, gives
$$\ce{2H2 + O2 -> 2H2O} \quad \Delta H = \pu{-466 kJ/mol}$$
This point is addressed in the Wikipedia page for "bond dissociation energy", the reference cited therein providing a slightly different bond energy for water of $$\pu{461.5 kJ/mol}$$.