\begin{aligned} &\text { The heat of dissociation of } \mathrm{H}_{2} \text { is } 435 \mathrm{~kJ} \mathrm{~mol}^{-1} \text { . If } \mathrm{C}_{(\mathrm{s})} \longrightarrow \mathrm{C}_{(\mathrm{g})} \text { ; }\\\ &\Delta H=720 \mathrm{~kJ} \mathrm{~mol}^{-1}, \text { calculate the bond energy per mol of the } \mathrm{C}-\mathrm{H} \text { bond }\\\ &\text { in } \mathrm{CH}_{4} \text { molecule. } \Delta H_{\mathrm{f}} \text { for } \mathrm{CH}_{4}=-75 \mathrm{~kJ} \mathrm{~mol}^{-1} \text { . } \end{aligned}

When we talk about the heat of dissociation, we are referring to the amount of energy required to break a particular chemical bond in a molecule to form separate atoms. This is a fundamental concept in thermochemistry and crucial for understanding how molecules interact. In the context of the given exercise, the heat of dissociation pertains to the energy needed to split molecular hydrogen (H_{2}) into individual hydrogen atoms. Calculating this heat for diatomic molecules like H_{2}, which have only one type of bond, is relatively straightforward. This information is pivotal when we examine more complex molecules and need to understand the individual bond energies to predict reactions' behavior.

For instance, if the heat of dissociation for H_{2} is given as 435 kJ/mol, as in our example, this value indicates the energy required to break the bonds in one mole of H_{2} molecules. In thermochemical calculations such as those for IIT-JEE exams, students need to pay attention to the stoichiometry of the reaction, where calculating the energy for forming or breaking multiple bonds becomes necessary.

Enthalpy of formation, denoted as Delta H_{f}, is another key concept in thermochemistry that represents the change in enthalpy when one mole of a compound is formed from its elements in their standard states. It's a measure of the energy change during the formation of a substance from its constituent elements. A negative Delta H_{f} is indicative of an exothermic reaction, where energy is released when the compound forms. Conversely, a positive Delta H_{f} would signify an endothermic process, requiring energy input to occur.

In our exercise, the enthalpy of formation for methane (CH_{4}) is provided as -75 kJ/mol. This implies that forming methane from its elements - carbon and hydrogen - releases energy, making the reaction exothermic. This energy must be taken into consideration when calculating bond energies within a molecule because it affects the total energy needed to break the molecule down into its atomic constituents.

Sublimation energy is the amount of energy required to convert a substance from the solid phase directly into the gas phase without passing through the liquid phase. This is an important concept in thermochemistry, especially when studying elements like carbon, which sublimate at standard pressure conditions. The sublimation energy plays a pivotal role when calculating the overall energy changes in reactions involving elements that sublimate.

In the given problem, the exercise states that the sublimation energy of carbon, converting from solid (C_{(s)}) to gas (C_{(g)}), is 720 kJ/mol. This amount of energy is significant when calculating the bond energy for the C-H bond in CH_{4} because it represents the energy investment required to free the carbon atoms into a gaseous state where they can then bond with hydrogen atoms.

Thermochemistry is a branch of physical chemistry that involves the study of heat evolved or absorbed in chemical reactions. It's a key topic for competitive exams like IIT-JEE, where a deep understanding of energetic aspects of chemical reactions is essential. Mastering concepts such as the ones discussed here - heat of dissociation, enthalpy of formation, and sublimation energy - is crucial for success in IIT-JEE and other similar exams.

As it pertains to thermochemistry questions in IIT-JEE, students are often required to perform calculations involving these concepts to predict the possible outcomes of reactions or to determine the feasibility of a reaction under given conditions. It involves a careful balance and understanding of various types of energies, including bond energies and the energy changes associated with phase changes. To excel in thermochemistry, one must practice manipulating these energy values and applying the laws of thermodynamics in a wide range of chemical scenarios.