Given that ΔHf^∘[H(g)] =218.0 kJ ·mol^-1 .ΔHf^∘ C(g)] =716.7 k J ·mol^-1 ΔHf^∘[CH4(g

step 1 For us to answer this question, let's first of all look into the standard enthalpy change of thi

Given that ΔHf^∘[H(g)] =218.0 kJ ·mol^-1 .ΔHf^∘ C(g)]...

Given that $$ \begin{aligned} \Delta H_{f}^{\circ}[\mathrm{H}(g)] &=218.0 \mathrm{~kJ} \cdot \mathrm{mol}^{-1} \\ \left.\Delta H_{\mathrm{f}}^{\circ} \mathrm{C}(g)\right] &=716.7 \mathrm{k} J \cdot \mathrm{mol}^{-1} \\ \Delta H_{\mathrm{f}}^{\circ}\left[\mathrm{CH}_{4}(g)\right] &=-74.6 \mathrm{~kJ} \cdot \mathrm{mol}^{-1} \end{aligned} $$ calculate the average molar bond enthalpy of a carbon-hydrogen bond in a $\mathrm{CH}_{4}$ molecule. Why is there a slight difference between this value and the molar bond enthalpy of a carbon-hydrogen bond listed in Table $14.5$ ?

Given that
$$
\begin{aligned}
\Delta H_{f}^{\circ}[\mathrm{H}(g)] &=218.0 \mathrm{~kJ} \cdot \mathrm{mol}^{-1} \\
\left.\Delta H_{\mathrm{f}}^{\circ} \mathrm{C}(g)\right] &=716.7 \mathrm{k} J \cdot \mathrm{mol}^{-1} \\
\Delta H_{\mathrm{f}}^{\circ}\left[\mathrm{CH}_{4}(g)\right] &=-74.6 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}
\end{aligned}
$$
calculate the average molar bond enthalpy of a carbon-hydrogen bond in a $\mathrm{CH}_{4}$ molecule. Why is there a slight difference between this value and the molar bond enthalpy of a carbon-hydrogen bond listed in Table $14.5$ ?

Key Concepts

Enthalpy of Formation

Enthalpy of formation is the standard energy change that occurs when one mole of a compound is formed from its elements in their reference states. It serves as a basis for calculating reaction energetics and is crucial in determining bond energies through Hess’s law by relating the energy content of compounds to the energies of individual atoms or simpler molecules.

Bond Enthalpy

Bond enthalpy, or bond energy, refers to the amount of energy required to break one mole of a specific type of bond in a gaseous molecule. It provides insight into the strength of chemical bonds and is typically derived as an average value when bonds of the same type exist in different environments within a molecule.

Average Bond Enthalpy Calculation

The average bond enthalpy is calculated using Hess's law by combining standard enthalpies of formation and dissecting a chemical reaction into steps, such as atomization and recombination of molecules. This approach estimates the energy required to break all similar bonds, divided by the number of bonds, acknowledging that the energy may vary slightly from bond to bond due to environmental differences.

Molecular Environment Effects

The slight difference between the calculated average bond enthalpy and the tabulated value arises because bond enthalpies are influenced by the molecular environment. In a molecule like methane, while all C–H bonds may be nearly equivalent, subtle electronic and steric effects can alter their individual energies, and the tabulated values average these differences from numerous measurements and compounds.

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