Barium metal is produced by the reaction of aluminum metal with barium oxide. From the standard reaction enthalpies $$ \begin{array}{ll} 2 \mathrm{Ba}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{BaO}(\mathrm{s}) & \Delta H^{\circ}=-1107 \mathrm{~kJ} \\ 2 \mathrm{Al}(\mathrm{s})+\frac{3}{2} \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{~s}) & \Delta H^{\circ}=-1676 \mathrm{~kJ} \end{array} $$ calculate the reaction enthalpy for the production of metallic barium in the reaction: $$ 3 \mathrm{BaO}(\mathrm{s})+2 \mathrm{Al}(\mathrm{s}) \stackrel{\Delta}{\longrightarrow} \mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{~s})+3 \mathrm{Ba}(\mathrm{s}) $$

Thermochemistry is a branch of thermodynamics that focuses on the energy changes occurring during chemical reactions, particularly the exchange of heat energy. It helps us understand how much energy is absorbed or released, in the form of heat, when a substance reacts chemically. One of the most fundamental concepts in thermochemistry is the reaction enthalpy, which quantifies the heat change at constant pressure. This is vital in predicting the feasibility and spontaneity of chemical reactions and in designing industrial processes, such as the production of barium metal.
Thermochemical equations provide insight into whether a reaction is endothermic (absorbs heat) or exothermic (releases heat), as well as how energy changes can affect reaction conditions and product yield. For example, in the production of barium, the enthalpy change associated with the reaction of aluminum and barium oxide will determine the amount of energy needed or the usability of the heat produced during the process.

Chemical reactions involve the rearrangement of atoms and molecules to form new substances. These transformations are governed by the laws of conservation of mass and energy, meaning that atoms and energy are neither created nor destroyed, but simply redistributed. Every chemical reaction is characterized by a chemical equation that represents reactants converting into products. In the case of barium production, aluminum metal reacts with barium oxide to produce aluminum oxide and barium metal. Understanding how to balance chemical equations and relate the reactants to the products allows chemists to predict the outcomes of reactions and calculate vital parameters such as reaction enthalpy.
To ensure clear communication and accuracy in the study of chemistry, it's crucial for students to grasp the skill of writing and interpreting these equations. Comprehending the stoichiometry involved in these equations is equally critical, since it determines the proportions of reactants and products involved in the reactions.

Enthalpy change, denoted as \( \Delta H \), is a term in thermochemistry that refers to the heat absorbed or released in a chemical reaction at constant pressure. It is an essential indicator of the energy dynamics within a chemical process. The enthalpy change can be either positive, indicating that a reaction is endothermic and heat is absorbed from the surroundings, or negative, indicating an exothermic reaction where heat is released.
In the given textbook problem, calculating the enthalpy change of the reaction for producing barium metal requires an understanding of how to manipulate equations and apply Hess's Law. Hess's Law states that the overall enthalpy change for a reaction is the same, no matter how many steps the reaction is carried out in. This allows us to determine the enthalpy change for a reaction that might be difficult to measure directly by using known enthalpies for related reactions, as illustrated in the step-by-step solution.

Barium is a soft, silvery metal that is used in various industrial applications, such as the production of alloys and in the removal of residual gases from electronic vacuum tubes. The production of barium involves complex chemical reactions where a more reactive metal, like aluminum, is used to displace barium from its oxide. This method is a part of a group of reactions known as single displacement reactions or replacement reactions.
In the textbook solution, we see the process for calculating the reaction enthalpy associated with the production of metallic barium from barium oxide using aluminum. By providing clear explanations and breaking down each step, we ensure that students can follow the logical progression of the solution and apply similar reasoning to other chemical reactions involved in the production of different metals or chemical substances. Such knowledge is not only applicable in academic settings but also fundamental for those pursuing careers in fields such as materials science, chemical engineering, and metallurgy.