Using standard enthalpies of formation from Appendix \(2 \mathrm{~A}\), calculate the standard reaction enthalpy for each of the following reactions: (a) the final stage in the production of nitric acid, when nitrogen dioxide dissolves in and reacts with water: \(3 \mathrm{NO}_{2}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow 2 \mathrm{HNO}_{3}(\mathrm{aq})+\mathrm{NO}(\mathrm{g})\) (b) the formation of boron trifluoride, which is widely used in the chemical industry: \(\mathrm{B}_{2} \mathrm{O}_{3}(\mathrm{~s})+3 \mathrm{CaF}_{2}(\mathrm{~s}) \rightarrow 2 \mathrm{BF}_{3}(\mathrm{~g})+3 \mathrm{CaO}(\mathrm{s})\) (c) the formation of a sulfide by the action of hydrogen sulfide on an aqueous solution of a base: \(\mathrm{H}_{2} \mathrm{~S}(\mathrm{aq})+2 \mathrm{KOH}(\mathrm{aq}) \rightarrow \mathrm{K}_{2} \mathrm{~S}(\mathrm{aq})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})\)

The enthalpy of formation refers to the change in enthalpy when one mole of a compound is formed from its elements in their standard states. It provides a measure of the energy changes involved during the formation of a substance from its constituent elements. To understand this concept, visualize creating a compound in a process that takes each element from nature — such as hydrogen gas or solid carbon — to form a singular compound, for instance, water or carbon dioxide.

These enthalpy changes are so fundamental in chemistry that they are tabulated in reference books and used as benchmarks. The standard enthalpy of formation of an element in its most stable form is zero because there is no change involved in creating the element from itself. When these values are given for compounds, they enable us to calculate the overall energy changes, like reaction enthalpies, simply by combining these standard benchmarks.

Hess's Law is grounded in the principle that the total enthalpy change for a chemical reaction is the same, no matter how the reaction occurs, provided it happens under constant pressure. This law allows us to use known enthalpies of formation to determine unknown reaction enthalpies. Essentially, it's like a budget sheet for energy changes: you can add and subtract enthalpy changes from various steps of a reaction to find the total energy change.

Through Hess's Law, complex reactions that may be difficult to study directly can be broken down into simpler steps whose enthalpies are known or can be more easily determined. The power of Hess's Law lies in the fact that it transforms the calculation of enthalpies for complex chemical changes into an exercise of bookkeeping, carefully balancing the energy inputs and outputs.

Chemical thermodynamics involves the study of energy transformations and the accompanying changes in enthalpy and entropy within chemical reactions. Enthalpy is a measure of the total heat content in a system, while entropy expresses the degree of disorder or randomness.

The study of chemical thermodynamics provides deep insights into the balance of energy that occurs during chemical processes. For any given reaction, energy can be absorbed from or released into the surroundings, hinting at its endothermic or exothermic nature. The laws of thermodynamics set the stage for understanding these energy transformations and allow us to predict the feasibility and spontaneity of chemical reactions. An overarching theme in thermodynamics is the pursuit of states that present a lower energy and higher disorder, guiding the direction of natural processes.

Calculating enthalpy, specifically reaction enthalpy, involves using the standard enthalpies of formation for the reactants and products involved in a chemical process. The general formula to determine the standard reaction enthalpy is:
\[\fDelta H_{\text{rxn}}^{\text{o}} = \f(\fsum \fDelta H_f^\text{o}_{\text{products}}) - \f(\fsum \fDelta H_f^\text{o}_{\text{reactants}})\].
In this calculation, the enthalpies of formation for each product are multiplied by their respective stoichiometric coefficients and summed; the same is done for the reactants. Subtraction of the total reactants' enthalpy from the total products' enthalpy gives the reaction enthalpy. The precision of these calculations can be pivotal, for example, in predicting product yields or assessing safety in industrial settings, where the heat released or absorbed needs careful monitoring.