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Example 5.11: Evaluating an Enthalpy of Formation

Ozone, \(\ce{O3(g)}\), forms from oxygen, \(\ce{O2(g)}\), by an endothermic process. Ultraviolet radiation is the source of the energy that drives this reaction in the upper atmosphere. Assuming that both the reactants and products of the reaction are in their standard states, determine the standard enthalpy of formation, \(\mathrm{ΔHf°}\) of ozone from the following information:

Solution

\(ΔH_{\mathrm{298°}}\) \(= 286\ \frac{\mathrm{kJ}}{\mathrm{mol}}\)


\(ν_{\mathrm{\ce{O3}}}\) \(= 2\)


\(\mathrm{ΔHf°}_{\mathrm{\ce{O3}}}\) = ?


\(\mathrm{ΔHf°}\) is the enthalpy change per one mole of a substance formed (in its standard state from the elements in their standard states). In the chemical equation, we are making 2 moles of ozone, so we have to divide the enthalpy of reaction by the stoichiometric coefficient of ozone to account for that.

\(\mathrm{ΔHf°}_{\mathrm{\ce{O3}}}\) \(= \dfrac{ΔH_{\mathrm{298°}}}{ν_{\mathrm{\ce{O3}}}}\)

\(\ \ \ =\dfrac{286\ \frac{\mathrm{kJ}}{\mathrm{mol}}}{2}\)

\(\ \ \ =143\ \frac{\mathrm{kJ}}{\mathrm{mol}}\)


In other words, \(\mathrm{ΔHf°}\) for \(\ce{O3(g)}\) is the enthalpy change for the reaction: