Calculate \(\Delta H\) for $$2 \mathrm{NOCl}(g) \rightarrow \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)+\mathrm{Cl}_{2}(g)$$given the following reactions:$$\begin{array}{ll}\frac{1}{2} \mathrm{~N}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{NO}(g) & \Delta H=90.3 \mathrm{~kJ} \\\ \mathrm{NO}(g)+\frac{1}{2} \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{NOCl}(g) & \Delta H=-38.6 \mathrm{~kJ}\end{array}$$

Reaction enthalpy, denoted as \(\Delta H\), is the heat change associated with a chemical reaction at constant pressure. It indicates whether a reaction is endothermic (absorbing heat) or exothermic (releasing heat). For example, in the given exercise, the enthalpy changes for the reactions are provided. For the first reaction, \(\frac{1}{2} \text{N}_2(g) + \frac{1}{2} \text{O}_2(g) \rightarrow \text{NO}(g)\), the enthalpy change is +90.3 kJ, indicating an endothermic process. On the other hand, for the reaction \(\text{NO}(g) + \frac{1}{2} \text{Cl}_2(g) \rightarrow \text{NOCl}(g)\), the enthalpy change is -38.6 kJ, indicating an exothermic process.

Understanding these values helps in calculating the overall enthalpy change when combining reactions.

Hess's law states that the total enthalpy change in a chemical reaction is the same regardless of the number of steps the reaction takes. This means you can add up the enthalpy changes of individual steps to find the overall enthalpy change. In the exercise, to find the enthalpy change for \(\text{2 NOCl}(g) \rightarrow \text{N}_2(g) + \text{O}_2(g) + \text{Cl}_2(g)\), we combined two reactions:

• \frac{1}{2} \text{N}_2(g) + \frac{1}{2} \text{O}_2(g) \rightarrow \text{NO}(g): \Delta H_1 = 90.3 \text{kJ}
• \text{NO}(g) + \frac{1}{2} \text{Cl}_2(g) \rightarrow \text{NOCl}(g): \Delta H_2 = -38.6 \text{kJ}

By reversing the second reaction and adding the enthalpy changes, we obtained a new reaction: \(\text{NOCl}(g) \rightarrow \text{NO}(g) + \frac{1}{2} \text{Cl}_2(g)\) with an enthalpy change of +38.6 kJ.

Thermochemistry is the study of the heat involved in chemical processes and reactions. It involves concepts like reaction enthalpy, calorimetry, and Hess's law. For students, it's important to understand how energy is exchanged during reactions.

In the provided exercise, we employed thermochemistry principles to calculate the overall enthalpy change for a complex reaction using given data, showcasing its practical application. By understanding thermochemistry, students can predict how heat transfer influences reaction spontaneity and equilibrium. This field bridges the gap between abstract concepts and real-world chemical reactions, providing insights into both theoretical and practical aspects of chemistry.