Question

Does \(\Delta H_{\mathrm{rxn}}\) for the reaction represented by the following equation equal the standard enthalpy of formation for \(\mathrm{CH}_{3} \mathrm{OH}(l) ?\) Why or why not? [Section 5.7] $$ \mathrm{C}(\text { graphite })+4 \mathrm{H}(\mathrm{g})+\mathrm{O}(\mathrm{g}) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(l) $$

Short answer

No, the enthalpy change of the given reaction (ΔHrxn) does not equal the standard enthalpy of formation for CH₃OH (liquid) because the elements on the reactant side are not in their standard states, specifically Hydrogen and Oxygen have different forms (H₂(g) and O₂(g)) in the standard enthalpy of formation definition.

Step-by-step solution

Write down the definition of the standard enthalpy of formation for CH3OH(l)

The standard enthalpy of formation for CH₃OH is the enthalpy change that occurs when 1 mole of CH₃OH (liquid) is formed from its elements in their standard states. The reaction can be represented by the following equation:$$ \mathrm{C}(\text { graphite })+\frac{2}{1}\mathrm{H}_{2}(\mathrm{g})+\frac{1}{2}\mathrm{O}_{2}(\mathrm{g})\longrightarrow \mathrm{CH}_{3} \mathrm{OH}(l) $$

Compare the given reaction to the standard enthalpy of formation definition for CH3OH(l)

Now, we compare the given reaction:$$ \mathrm{C}(\text { graphite })+4 \mathrm{H}(\mathrm{g})+\mathrm{O}(\mathrm{g})\longrightarrow \mathrm{CH}_{3} \mathrm{OH}(l) $$with the standard enthalpy of formation definition:$$ \mathrm{C}(\text { graphite })+\frac{2}{1}\mathrm{H}_{2}(\mathrm{g})+\frac{1}{2}\mathrm{O}_{2}(\mathrm{g})\longrightarrow \mathrm{CH}_{3} \mathrm{OH}(l) $$

Determine if ΔHrxn for the given reaction equals the standard enthalpy of formation for CH3OH(l)

Upon comparing the two reactions, we can see that they are not identical, mainly because the types of Hydrogen and Oxygen in the given reaction are not in their standard states (H₂(g) and O₂(g)). Consequently, the enthalpy change of the given reaction (ΔHrxn) does not equal the standard enthalpy of formation for CH₃OH (liquid). Answer: No, the enthalpy change of the given reaction (ΔHrxn) does not equal the standard enthalpy of formation for CH₃OH (liquid) because the elements on the reactant side are not in their standard states, as required for the standard enthalpy of formation definition.