Given the following reactions, $$ \begin{aligned} \mathrm{N}_{2} \mathrm{H}_{4}(l)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) & \Delta H^{\circ} &=-534.2 \mathrm{~kJ} \\ \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(g) & \Delta H^{\circ} &=-241.8 \mathrm{~kJ} \end{aligned} $$ calculate the heat of formation of hydrazine.

Enthalpy change is a measure of the heat energy absorbed or released in a chemical reaction at constant pressure, symbolized by \( \Delta H \) and is expressed in kilojoules per mole (kJ/mol). It's an essential concept in thermodynamics and tells us whether a reaction is exothermic (releasing heat) or endothermic (absorbing heat).

For instance, when hydrazine (\( \mathrm{N}_2\mathrm{H}_4 \) ) reacts with oxygen to form nitrogen and water, the enthalpy change can be negative or positive. If \( \Delta H \) is negative, as in the given exercise, this indicates that the reaction releases energy, making it exothermic. In more straightforward terms, we can think of the enthalpy change as the difference in energy between the products and reactants, a value that can be determined through experiments or calculated using Hess's Law.

Hess's Law states that the total enthalpy change for a chemical reaction is the same, regardless of the number of steps the reaction is carried out in. This law relies on the principle of conservation of energy, meaning that if you start with certain reactants and end with certain products, the energy change will be the same, no matter the pathway taken.

Using Hess's Law, we can calculate enthalpy changes (\( \Delta H \) ) for reactions that are difficult to study directly. As seen in the exercise, by reversing and scaling existing reactions with known enthalpy values, we can determine the \( \Delta H \) for a target reaction, like the formation of hydrazine. It's like piecing together a puzzle — by rearranging and combining pieces that we understand well (standard reactions), we construct a new picture (target reaction) and deduce its associated energy changes.

Chemical reaction stoichiometry involves the quantitative relationship between reactants and products in a chemical reaction. It's like a recipe that tells you how much of each reactant you need to produce a certain amount of product.

In the context of the exercise, stoichiometry tells us how many moles of each substance react and the proportion in which they combine to form new substances. For example, to create hydrazine, the correct number of moles of nitrogen gas (\( \mathrm{N}_2 \) ) and hydrogen gas (\( \mathrm{H}_2 \) ) must react. Adjusting reactions to ensure the correct stoichiometry is essential. It ensures that all atoms from the reactants are accounted for in the products, and no atom is lost or gained in the process, following the Law of Conservation of Mass. By understanding stoichiometry, we can manipulate and combine reactions using Hess's Law to find out the enthalpy change of reactions that are too complicated to observe directly.