Calculate the standard enthalpy of formation of \(\mathrm{PCl}_{5}(\mathrm{~s})\) from the standard enthalpy of formation of \(\mathrm{PCl}_{3}(\mathrm{l})\) (see Appendix \(2 \mathrm{~A}\) ) and \(\mathrm{PCl}_{3}(\mathrm{l})+\mathrm{Cl}_{2}(\mathrm{~g}) \longrightarrow \mathrm{PCl}_{5}(\mathrm{~s}), \Delta H^{\circ}=-124 \mathrm{~kJ}\).

Understanding Hess's Law is crucial when it comes to assessing the heat evolution or consumption in chemical reactions. In a nutshell, Hess's Law states that the total change in enthalpy, a measure of heat energy, for a chemical reaction is the same regardless of the pathway the reaction takes. This principle allows chemists to infer the enthalpy change of a reaction by summing the enthalpy changes of individual steps that lead to the final reaction.

For instance, if you cannot directly determine the enthalpy of reaction for a process, you could find this information by adding up the enthalpy changes of related reactions that, when combined, yield the overall process. This enables you to work with thermochemical equations algebraically, just like mathematical equations. The key is ensuring that the reactants and products are the same on both sides, and then the enthalpy changes can be summed or subtracted accordingly.

Chemical thermodynamics deals with the study of energy and work of a system. It's a segment of thermodynamics, the science that considers heat transfer between different environments. In chemical thermodynamics, we specifically look at the enthalpy changes associated with the breaking and forming of chemical bonds. Understanding this domain is essential for predicting the feasibility of reactions, estimating the energy needed to start a reaction, or the energy released during a reaction.

Enthalpy, denoted by the symbol H, is the thermodynamic quantity representing the heat content of a system. It accounts for internal energy of the system plus the energy needed to make room for the system by displacing its environment and establishing its volume and pressure. The standard enthalpy of formation is a special case where it indicates the change in enthalpy when one mole of a compound is formed from its elements under standard conditions.

Enthalpy change, represented by the symbol \( \Delta H \) is a central term in the discussion of chemical reactions. It's defined as the heat absorbed or released in a chemical process under constant pressure. The standard enthalpy change refers to this value under standard conditions, which generally means 1 atmosphere of pressure and a common reference temperature, usually 25 degrees Celsius.

The standard enthalpy of formation \( \Delta H^\circ_f \) of a compound is a specific kind of enthalpy change. It's the heat change that occurs when one mole of a substance in its standard state is formed from its elements in their standard states. If the value of \( \Delta H^\circ_f \) is negative, it indicates that the formation of the compound is exothermic, releasing heat to the surroundings. On the other hand, a positive value means that the reaction is endothermic and that energy is absorbed from the surroundings during the formation of the compound. Calculating these values is fundamental for understanding the energy aspects of chemical reactions, including their spontaneity and thermal effects.