Given these data $$\begin{array}{c}\mathrm{C}_{2} \mathrm{H}_{4}(g)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) \\\\\Delta H^{\circ}=-1411 \mathrm{~kJ} / \mathrm{mol} \\\2 \mathrm{C}_{2} \mathrm{H}_{2}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) \\\\\Delta H^{\circ}=-2599 \mathrm{~kJ} / \mathrm{mol} \\\\\mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l) \\\\\Delta H^{\circ}=-285.8 \mathrm{~kJ} / \mathrm{mol}\end{array}$$ calculate the heat of hydrogenation for acetylene: $$\mathrm{C}_{2} \mathrm{H}_{2}(g)+\mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4}(g)$$

Understanding the concept of enthalpy change is crucial to grasping the energy dynamics of chemical reactions. Enthalpy change, denoted as \( \Delta H \), refers to the heat change during a chemical reaction at constant pressure. It's an essential parameter in thermodynamics, serving as a measure of the energy exchanged between the system and its surroundings.

Exothermic reactions, where energy is released into the surroundings, exhibit a negative \( \Delta H \), indicating that the potential energy of the products is lower than that of the reactants. Conversely, endothermic reactions absorb energy, resulting in a positive \( \Delta H \). The heat of hydrogenation—an exothermic process involving the addition of hydrogen to an unsaturated compound—can be thought of as a specific kind of enthalpy change where the energy released is due to the conversion of multiple bonds into single bonds.

When calculating the enthalpy change for a reaction, Hess's Law can be employed. This law states that the total change in enthalpy for a chemical reaction is the same, regardless of the steps taken to perform the reaction. Hence, we can use known enthalpy values from related reactions and manipulate them to find the enthalpy change for the reaction in question, as was done in our exercise to calculate the heat of hydrogenation for acetylene.

Chemical reactions involve the transformation of substances into one or more different substances through breaking and forming chemical bonds. Each reaction is characterized by its reactants—the starting materials—and products—the end result of the reaction.

In the given exercise, we explored three different chemical reactions, each with their own unique reactants and products. By understanding how to manipulate these given reactions, such as reversing the first reaction or doubling the third, we create a path to the ultimate target reaction, which in this case was the hydrogenation of acetylene. This process of chemical reaction manipulation exemplifies the power of stoichiometry and conservation of mass, allowing us to predict the outcome when substances interact chemically.

Moreover, in any chemical reaction, it's important to ensure that the reaction is balanced, meaning the number of atoms for each element on the reactant side equals the number of atoms on the product side. This principle is a cornerstone of chemistry and allows us to construct and deconstruct reaction pathways logically and accurately move forward with calculations.

Stoichiometry is the branch of chemistry that deals with the quantitative relationship between reactants and products in a chemical reaction. It allows chemists to predict the amounts of substances consumed and produced in a given reaction.

To solve stoichiometric problems, it is fundamental to understand and work with the mole concept. A mole is a unit that represents \(6.022 \times 10^{23}\) entities, whether they are atoms, ions, molecules, or electrons. In calculating the heat of hydrogenation for acetylene, we used stoichiometry to manipulate the equations to reflect the mole ratios of the reactants and products needed to reach the final reaction.

Through stoichiometry, we were able to combine modified reactions and cancel out substances appearing on both the reactant and product sides. This step conforms to the Law of Conservation of Mass which states that matter is neither created nor destroyed in a chemical reaction. Therefore, stoichiometry is not just about counting molecules but ensuring that the physical law of mass conservation is upheld throughout the process.