103 . When we estimate ΔH^∘ from bond enthalpies we assume that all bonds of the same type (sing

step 1 Let's do this problem about bond energies today. And before I get started, I recommend that you

103 . When we estimate ΔH^∘ from bond enthalpies we assume...

$103 .$ When we estimate $\Delta H^{\circ}$ from bond enthalpies we assume that all bonds of the same type (single, double, triple) 106 between the same two atoms have the same energy, regardless of the molecule in which they occur. The purpose of this problem is to show you that this is only an approximation. You will need these standard enthalpies of formation: $$ \begin{array}{ll} \mathrm{C}(\mathrm{g}) & \Delta H_{f}^{0}=716.7 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{CH}(\mathrm{g}) & \Delta H_{f}^{\circ}=596.3 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{CH}_{2}(\mathrm{~g}) & \Delta H_{f}^{0}=392.5 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{CH}_{3}(\mathrm{~g}) & \Delta H_{f}^{\circ}=146.0 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{H}(\mathrm{g}) & \Delta H_{f}^{\circ}=218.0 \mathrm{~kJ} / \mathrm{mol} \end{array} $$ (a) What is the average $\mathrm{C}-\mathrm{H}$ bond energy in methane, $\mathrm{CH}_{4}$ ? (b) Using bond enthalpies, estimate $\Delta H^{\circ}$ for the reaction 107 $$ \mathrm{CH}_{4}(\mathrm{~g}) \longrightarrow \mathrm{C}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{~g}) $$ (c) By heating $\mathrm{CH}_{4}$ in a flame it is possible to produce the reactive gaseous species $\mathrm{CH}_{3}, \mathrm{CH}_{2}, \mathrm{CH}$, and even carbon atoms, $\mathrm{C}$. Experiments give these values of $\Delta H^{\circ}$ for the reactions shown:

$103 .$ When we estimate $\Delta H^{\circ}$ from bond enthalpies we assume that all bonds of the same type (single, double, triple) 106
between the same two atoms have the same energy, regardless of the molecule in which they occur. The purpose of this problem is to show you that this is only an approximation. You will need these standard enthalpies of formation:
$$
\begin{array}{ll}
\mathrm{C}(\mathrm{g}) & \Delta H_{f}^{0}=716.7 \mathrm{~kJ} / \mathrm{mol} \\
\mathrm{CH}(\mathrm{g}) & \Delta H_{f}^{\circ}=596.3 \mathrm{~kJ} / \mathrm{mol} \\
\mathrm{CH}_{2}(\mathrm{~g}) & \Delta H_{f}^{0}=392.5 \mathrm{~kJ} / \mathrm{mol} \\
\mathrm{CH}_{3}(\mathrm{~g}) & \Delta H_{f}^{\circ}=146.0 \mathrm{~kJ} / \mathrm{mol} \\
\mathrm{H}(\mathrm{g}) & \Delta H_{f}^{\circ}=218.0 \mathrm{~kJ} / \mathrm{mol}
\end{array}
$$
(a) What is the average $\mathrm{C}-\mathrm{H}$ bond energy in methane, $\mathrm{CH}_{4}$ ?
(b) Using bond enthalpies, estimate $\Delta H^{\circ}$ for the reaction 107
$$
\mathrm{CH}_{4}(\mathrm{~g}) \longrightarrow \mathrm{C}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{~g})
$$
(c) By heating $\mathrm{CH}_{4}$ in a flame it is possible to produce the reactive gaseous species $\mathrm{CH}_{3}, \mathrm{CH}_{2}, \mathrm{CH}$, and even carbon atoms, $\mathrm{C}$. Experiments give these values of $\Delta H^{\circ}$ for the reactions shown:

Key Concepts

Limitations of Bond Enthalpy Approximations

While bond enthalpies provide a convenient method for estimating reaction enthalpies, they are inherently approximate due to the assumption that bonds of the same type have identical energies regardless of their molecular context. In reality, factors such as molecular geometry, electronic effects, and the presence of other substituents can lead to variations in bond strengths. Recognizing these limitations is important when using bond energies for quantitative thermochemical predictions.

Standard Enthalpy of Formation

The standard enthalpy of formation is defined as the enthalpy change accompanying the formation of one mole of a compound from its elements in their most stable form under standard conditions. These values serve as reference points in thermochemistry and are crucial for alternative methods of calculating reaction enthalpies, such as using Hess's law, which can then be compared with bond enthalpy calculations.

Average Bond Energy

Average bond energy refers to the mean energy required to break similar types of bonds in different molecules. Although individual bonds of the same type might have slightly different energies due to their molecular environment, averaging provides a useful simplification to estimate reaction enthalpies. This approximation is often employed when specific bond energies are not available for every different chemical context.

Bond Enthalpy

Bond enthalpy, or bond dissociation energy, is the energy required to break one mole of a specific bond in a gaseous molecule. It represents the strength of a chemical bond and is used as an approximation of the energy needed to break bonds during reactions. This concept is fundamental in thermochemistry and helps in estimating the energetic changes accompanying chemical reactions.

Enthalpy Change of Reaction Estimation

The enthalpy change of a reaction can be estimated by applying the concept of bond energies. This involves calculating the total energy required to break all bonds in the reactants and subtracting the total energy released upon formation of bonds in the products. This method, often used alongside Hess's law, provides an approximate value for the reaction enthalpy based on the energetic contributions of individual bonds.

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