Calculate the reaction enthalpy for the formation of anhydrous aluminum chloride, \(2 \mathrm{Al}(\mathrm{s})+3 \mathrm{Cl}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{AlCl}_{3}(\mathrm{~s})\), from the following data: $$ \begin{array}{ll} 2 \mathrm{Al}(\mathrm{s})+6 \mathrm{HCl}(\mathrm{aq}) \longrightarrow 2 \mathrm{AlCl}_{3}(\mathrm{aq})+3 \mathrm{H}_{2}(\mathrm{~g}) \\ & \Delta H^{\circ}=-1049 \mathrm{~kJ} \\ \mathrm{HCl}(\mathrm{g}) \longrightarrow \mathrm{HCl}(\mathrm{aq}) & \Delta H^{\circ}=-74.8 \mathrm{~kJ} \\ \mathrm{H}_{2}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{HCl}(\mathrm{g}) & \Delta H^{\circ}=-185 \mathrm{~kJ} \\ \mathrm{AlCl}_{3}(\mathrm{~s}) \longrightarrow \mathrm{AlCl}_{3}(\mathrm{aq}) & \Delta H^{\circ}=-323 \mathrm{~kJ} \end{array} $$

Thermochemistry is the study of heat and energy associated with chemical reactions and physical transformations. It is a sub-branch of thermodynamics, which deals more broadly with heat, work, and the properties of matter. One key principle of thermochemistry is that energy cannot be created or destroyed—it can only be changed from one form to another.

When a chemical reaction occurs, it can either release energy into the surrounding environment, known as an exothermic reaction, or absorb energy, known as an endothermic reaction. The amount of heat involved in a reaction at constant pressure is represented by the term enthalpy (\( \triangle H \)). Keeping track of enthalpy is crucial for predicting whether a reaction will occur spontaneously and for understanding how much energy is exchanged with the environment.

To calculate reaction enthalpies, scientists use specific measurement techniques like calorimetry. For educational and practical purposes, however, we often rely on tabulated standard enthalpies of formation and Hess's Law to find the enthalpy changes of reactions.

Enthalpy change, noted as \( \triangle H \), is the difference in enthalpy between the products and the reactants in a chemical reaction. It reflects the heat absorbed or released during the reaction at constant pressure. Enthalpy change can be measured directly or calculated using known values, such as those from standard enthalpies of formation and Hess's Law.

If a reaction is exothermic, the enthalpy change is negative because the system releases heat. Conversely, an endothermic reaction results in a positive enthalpy change as the system absorbs heat from its surroundings. Chemical equations often include the enthalpy change to indicate the heat involved.

Understanding enthalpy changes can help predict the direction and extent of a reaction. It also allows for the design of safer and more efficient industrial processes, as controlling heat release or absorption is vital in large-scale chemical manufacturing.

Hess's Law is a fundamental principle in thermochemistry that states the total enthalpy change of a chemical reaction is the same, regardless of the number of steps the reaction takes to go from reactants to products. This concept is based on the law of conservation of energy, which implies that enthalpy is a state function - its value is determined only by the current state of the system, not the path taken to reach that state.

Applying Hess's Law allows chemists to calculate the enthalpy change of complex reactions by breaking them down into simpler steps with known enthalpy changes. For instance, if a direct reaction's enthalpy change is difficult to measure or calculate, it can be found indirectly by adding or subtracting the enthalpy changes of multiple steps that lead to the same final products.

Understanding how to utilize Hess's Law is crucial because it provides a method for determining the energy changes in reactions that would otherwise be challenging to study due to their complexity or slow progression.

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It is the part of chemistry that involves the calculation of the amounts of substances involved in reactions. Stoichiometry is based on the law of conservation of mass, which states that during a chemical reaction, matter is neither created nor destroyed.

Stoichiometric calculations make use of the coefficients in a balanced chemical equation to relate the amounts of different substances. These relationships are crucial for determining the proportions of reactants needed and the amount of products that will be formed. For example, the stoichiometry of a reaction might show that two moles of hydrogen gas react with one mole of oxygen gas to produce two moles of water.

Understanding stoichiometry is essential for controlling and scaling up reactions for industrial production, ensuring reactions go to completion, and calculating yields. It also forms the basis for reaction enthalpy calculations, as it informs the chemist of the proportionate amount of heat involved for the various quantities of reactants and products in a reaction.