Given : \(\mathrm{C}(\) diamond \()+\mathrm{O}_{2} \longrightarrow \mathrm{CO}_{2} ; \Delta H=-395 \mathrm{~kJ}\) \(\mathrm{C}\) (graphite) \(+\mathrm{O}_{2} \longrightarrow \mathrm{CO}_{2} ; \Delta H=-393 \mathrm{~kJ}\) The enthalpy of formation of diamond from graphite is (a) \(+2.0 \mathrm{~kJ}\) (b) \(-1.5 \mathrm{~kJ}\) (c) \(-788 \mathrm{~kJ}\) (d) \(788 \mathrm{~kJ}\)

Understanding Hess's Law is fundamental when endeavoring to calculate the enthalpy change during a chemical reaction, especially when it cannot be measured directly. The law asserts that the total change in enthalpy, which is the heat content of a system at constant pressure, is the same regardless of whether the reaction occurs in one step or multiple steps.

Hess's Law enables us to use known enthalpies of formation for certain chemical reactions to determine unknown enthalpies. The law is based on the premise that enthalpy is a state function, meaning it depends only on the initial and final states of a system, not on the path taken. For example, to find the enthalpy of formation of diamond from graphite, we can use the known enthalpies of CO2 formation from both diamond and graphite. By applying Hess's Law, we subtract one known reaction enthalpy from another to arrive at the enthalpy change for converting graphite into diamond.

Thermochemistry is the branch of chemistry that deals with the energy changes involved in chemical reactions. Fundamentally, it's concerned with the study of heat flow in chemical systems at constant pressure, known as enthalpy changes. Thermochemistry rests on the first law of thermodynamics, which states that energy cannot be created or destroyed, only transformed.

In the context of a chemical reaction, like the transformation of graphite to diamond, thermochemistry would analyze the heat absorbed or released. When we calculate the enthalpy of formation, we're essentially quantifying the heat required to form one mole of a substance from its constituent elements at their standard states. These measurements are crucial for scientists and engineers to design processes that are energy-efficient and environmentally benign.

Chemical thermodynamics is the area of chemistry that examines the relationship between chemical reactions and energy changes involving heat. It combines concepts from both thermochemistry and thermodynamics to predict the spontaneity of reactions, understand the energy changes involved, and assess the equilibrium properties of the systems.

Concerning our specific example, chemical thermodynamics would enable us to understand why diamond and graphite, although both are forms of carbon, have different enthalpies of formation. It would delve into the theory behind entropy, Gibbs free energy, and the second law of thermodynamics, which affirms that the total entropy of an isolated system can never decrease over time. It also helps in comprehending how energy is stored in chemical bonds and how it is affected by temperature and other conditions.