Calculation of bond energy of oxygen gas at 0K

[zenterix]

Homework Statement

For a diatomic molecule the bond energy is equal to the change in internal energy for the reaction

$$\mathrm{X_2(g)=2X(g)}$$

at 0K.

Of course, the change in internal energy and the change in enthalpy are the same at 0K.

Calculate the enthalpy of dissociation of $\mathrm{O_2(g)}$ at 0K.

The enthalpy of formation of $\mathrm{O(g)}$ at 298.15K is $249.173\mathrm{kJ\ mol^{-1}}$.

In the range $0-298.15\text{K}$, the average value of the heat capacity of $\mathrm{O_2(g)}$ is $\mathrm{29.1 J\ K^{-1}mol^{-1}}$ and the average heat capacity of $\mathrm{O(g)}$ is $22.7\mathrm{J\ K^{-1}mol^{-1}}$.

Relevant Equations

What is the value of the bond energy in electron volts?

We can compute the enthalpy of reaction of $\mathrm{O_2(g)\rightarrow 2O(g)}$ at 0K by heating reactant to 298.15K, doing the reaction and obtaining the product at this temperature, and then cooling the product down to 0K.

The result is

$$\Delta H_r=\mathrm{493.48kJ\ mol^{-1}}$$

According to the problem statement, this equals $\Delta U$ for the reaction.

How do we calculate the bond energy? The problem statement says that the bond energy equals the change in $U$ (equivalently the change in $H$).

When I convert $\Delta H$ to $\text{eV}$ I get $3.08\times 10^{24}\text{eV}$.

The back of the book says the answer is $5.115\text{eV}$.

What am I missing here?

 

[Borek]

6.02⋅10²³

(or, to be more precise: UNITS)

 

[zenterix]

Oh, right, I computed the change in enthalpy per mol which is bond energy per mol but I want per molecule.