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: $$ 3 \mathrm{NO}_{2}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \longrightarrow 2 \mathrm{HNO}_{3}(\mathrm{aq})+\mathrm{NO}(\mathrm{g}) $$ (b) the industrial synthesis of boron trifluoride: $$ \mathrm{B}_{2} \mathrm{O}_{3}(\mathrm{~s})+3 \mathrm{CaF}_{2}(\mathrm{~s}) \longrightarrow 2 \mathrm{BF}_{3}(\mathrm{~g})+3 \mathrm{CaO}(\mathrm{s}) $$ (c) the formation of a sulfide by the action of hydrogen sulfide on an aqueous solution of a base: $$ \mathrm{H}_{2} \mathrm{~S}(\mathrm{aq})+2 \mathrm{KOH}(\mathrm{aq}) \longrightarrow \mathrm{K}_{2} \mathrm{~S}(\mathrm{aq})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) $$

The concept of enthalpies of formation is a fundamental aspect of chemical thermodynamics. It refers to the heat change that occurs when one mole of a compound is formed from its elements at standard conditions of 25 degrees Celsius and 1 atmosphere pressure.

For example, the enthalpy of formation of water, \( H_2O \), from hydrogen and oxygen gases is a measure of the energy released or absorbed when water is formed. These values are critically used to predict the heat exchanged in chemical reactions. They are tabulated as standard enthalpy change of formation, \( \Delta H_f^\circ \), and can be found in appendices in chemistry textbooks or databases.

To improve understanding, one should remember that the enthalpy of formation for an element in its standard state is zero. For instance, for diatomic oxygen, \( O_2 \), \( \Delta H_f^\circ = 0 \) because it is already in its standard state. This principle helps simplify calculations when using these enthalpies to gauge reaction enthalpies.

Chemical thermodynamics deals with the study of the interrelation of heat and work with chemical reactions or with physical changes of state within the confines of the laws of thermodynamics. It provides us with the toolkit to predict the feasibility and extent of chemical processes.

The reaction enthalpy, a part of this toolkit, tells us how much heat is absorbed or released during a chemical reaction. This is valuable because it helps predict not only the energy change but also the spontaneity of reactions under standard conditions. For example, an exothermic reaction, which releases heat, typically has a negative standard reaction enthalpy, \( \Delta H_rxn^\circ \), indicating that the reaction may be spontaneously favorable. In contrast, endothermic reactions absorb heat and often have positive reaction enthalpies.

Understanding the basics of thermodynamics can significantly enhance the comprehension of how reactions proceed and the significance of energy changes within those reactions.

Balanced chemical equations are the mathematical representations of chemical reactions that obey the Law of Conservation of Mass. This fundamental law states that mass can neither be created nor destroyed. In practical terms, this means that the number of atoms of each element must be the same on both sides of a chemical equation.

To balance a chemical equation, you may only adjust the coefficients (the numbers in front of the chemical formulas), never the subscripts within the formulas, as changing the subscripts would modify the actual compounds involved. For instance, adjusting the coefficient of \( H_2O \) to balance oxygen atoms would be appropriate, while changing the formula to \( H_2O_2 \) would not, since that represents a different compound (hydrogen peroxide).

Balancing equations is not only critical for understanding reaction stoichiometry but also for calculating reaction enthalpies. When using standard enthalpies of formation to determine the heat exchange in a reaction, as shown in the step-by-step solution, ensuring that the equation is balanced is the first step before any enthalpy calculations can be correctly performed.