From the following heats of combustion, CH3 OH(l)+(3)/(2)...

From the following heats of combustion, $$\mathrm{CH}_{3} \mathrm{OH}(l)+\frac{3}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)$$ $$\begin{array}{l} \Delta H_{\mathrm{rxn}}^{\circ}=-726.4 \mathrm{kJ} / \mathrm{mol} \\ \Delta H_{\mathrm{rxn}}^{\circ}=-393.5 \mathrm{kJ} / \mathrm{mol} \\ \Delta H_{\mathrm{rxn}}^{\circ}=-285.8 \mathrm{kJ} / \mathrm{mol} \end{array}$$ $$\begin{aligned} \mathrm{C}(\mathrm{graphite})+\mathrm{O}_{2}(g) & \longrightarrow \mathrm{CO}_{2}(g) \\ \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) & \longrightarrow \mathrm{H}_{2} \mathrm{O}(l) \end{aligned}$$ calculate the enthalpy of formation of methanol $\left(\mathrm{CH}_{3} \mathrm{OH}\right)$ from its elements: $$\text { C(graphite) }+2 \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(l)$$

From the following heats of combustion,
$$\mathrm{CH}_{3} \mathrm{OH}(l)+\frac{3}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)$$
$$\begin{array}{l}
\Delta H_{\mathrm{rxn}}^{\circ}=-726.4 \mathrm{kJ} / \mathrm{mol} \\
\Delta H_{\mathrm{rxn}}^{\circ}=-393.5 \mathrm{kJ} / \mathrm{mol} \\
\Delta H_{\mathrm{rxn}}^{\circ}=-285.8 \mathrm{kJ} / \mathrm{mol}
\end{array}$$
$$\begin{aligned}
\mathrm{C}(\mathrm{graphite})+\mathrm{O}_{2}(g) & \longrightarrow \mathrm{CO}_{2}(g) \\
\mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) & \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)
\end{aligned}$$
calculate the enthalpy of formation of methanol $\left(\mathrm{CH}_{3} \mathrm{OH}\right)$ from its elements:
$$\text { C(graphite) }+2 \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(l)$$

Key Concepts

Hess's Law

Hess’s Law states that the total enthalpy change for a reaction is the same, no matter how many steps or intermediates occur during the reaction. This principle allows one to add, subtract, or reverse multiple thermochemical equations in order to calculate unknown enthalpy changes, such as the enthalpy of formation for a compound.

Standard Enthalpy of Formation

The standard enthalpy of formation is defined as the enthalpy change when one mole of a compound is formed from its elements in their standard states. It provides a baseline for comparing the energy changes in various chemical reactions and is used extensively in thermodynamic calculations.

Standard Enthalpies of Combustion

Standard enthalpies of combustion refer to the enthalpy changes when substances burn completely in oxygen under standard conditions. These values are often employed as reference data in thermochemical calculations and can be combined using Hess’s Law to derive other enthalpy changes, such as the enthalpy of formation.

Thermochemical Equation Manipulation

Thermochemical equation manipulation involves reversing, scaling, and combining chemical equations while appropriately adjusting the corresponding enthalpy changes. This process is essential when using experimental data from related reactions, like combustion reactions, to deduce the enthalpy change of a target reaction.

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