At \(25^{\circ} \mathrm{C}, 1\) mole of \(\mathrm{MgSO}_{4}\) was dissolved in water, the heat evolved was found to be \(91.2 \mathrm{~kJ}\). One mole of \(\mathrm{MgSO}_{4} \cdot 7 \mathrm{H}_{2} \mathrm{O}\) on dissolution gives a solution of the same composition accompanied by an absorption of \(13.8 \mathrm{~kJ}\). The enthalpy of hydration, i.e., \(\Delta H\) for the reaction $$ \mathrm{MgSO}_{4}(s)+7 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{MgSO}_{4} \cdot 7 \mathrm{H}_{2} \mathrm{O}(s) \text { is : } $$ (a) \(-105 \mathrm{~kJ} / \mathrm{mol}\) (b) \(-77.4 \mathrm{~kJ} / \mathrm{mol}\) (c) \(105 \mathrm{~kJ} / \mathrm{mol}\) (d) None of these

Hess's Law is a fundamental concept in thermochemistry, stating that the overall change in enthalpy for a chemical reaction is the same regardless of the number of stages in which the reaction occurs. This is because enthalpy is a state function, meaning it depends only on the initial and final states of the system, not on the path taken to get there.

In the case of our exercise, we apply Hess's Law to determine the enthalpy of hydration for magnesium sulfate. By using the data for the dissolution of anhydrous MgSO₄ and the hydration of MgSO₄·7H₂O, we can calculate the enthalpy change for combining anhydrous MgSO₄ with water to form the hydrated compound. This approach underlies the utility of Hess's Law in solving complex thermochemical problems by breaking them down into simpler steps.

The dissolution process involves a solute becoming incorporated into a solvent to form a solution. During this process energy changes occur, which can either be exothermic (releasing heat) or endothermic (absorbing heat). Understanding the dissolution process is vital for determining thermochemical values such as enthalpy changes.

In our exercise, we observed an exothermic process when anhydrous MgSO₄ dissolves in water, releasing heat, and an endothermic process when MgSO₄·7H₂O dissolves, absorbing heat. These observations are essential for calculating the enthalpy of hydration of MgSO₄, which involves the interaction of the solute with water during dissolution.

Thermochemistry is the branch of chemistry that deals with the relationships between chemical reactions and energy changes involving heat. The energy changes are often quantified in terms of enthalpy (H), which is the heat content of a system at constant pressure.

In the context of our exercise, thermochemistry allows us to understand and calculate the heat effect that accompanies the dissolution of anhydrous and hydrated magnesium sulfate. These calculations are integral to solving problems related to chemical reactions and processes involving heat exchange. The dissolution of MgSO₄ in water to form MgSO₄·7H₂O or vice versa is an excellent example of a thermochemical process.

Chemical energetics encompasses the study of energy changes in chemical reactions. Key to this study is the concept of enthalpy, which represents the heat change at constant pressure. Chemical energetics combines concepts of thermochemistry, kinetics, and thermodynamics to offer a comprehensive understanding of how and why chemical reactions occur, and how energy is transformed in the process.

For the exercise in question, the focus on chemical energetics is on how the energy is handled during the hydration and dissolution of magnesium sulfate. When explaining concepts like enthalpy of hydration, it becomes necessary to appreciate the conservation of energy and the ways in which it can be tracked through chemical processes, making chemical energetics an essential topic for anyone studying chemistry.