Calculate \(\Delta H_{\mathrm{rxn}}\) for the reaction. $$\mathrm{CH}_{4}(g)+4 \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{CCl}_{4}(g)+4 \mathrm{HCl}(g) $$ Use the following reactions and given \(\Delta H^{\prime}s\): $$\begin{array}{ll}{\mathrm{C}(s)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{CH}_{4}(g)} & {\Delta H=-74.6 \mathrm{kJ}} \\ {\mathrm{C}(s)+2 \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{CCl}_{4}(g)} & {\Delta H=-95.7 \mathrm{kJ}} \\ {\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{HCl}(g)} & {\Delta H=-92.3 \mathrm{kJ}}\end{array}$$

Understanding Hess's Law is crucial for piecing together how the heat energy of a chemical system changes during a reaction. 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 means that if you can split the overall reaction into several stages for which the enthalpy changes are known, you can calculate the enthalpy change for the whole reaction simply by adding these values together.

Envision that each chemical reaction is a path from A to B. Whether your journey is direct or goes through points C and D, the starting and ending locations remain the same. Hess's Law tells us that no matter the route, the total uphill and downhill will be the same - in chemistry, this 'ups and downs' are equivalent to the heat energy absorbed or released in the reaction. It's a powerful principle because it provides a method to determine the enthalpy change for reactions for which it's difficult to measure directly.

Using Hess's Law, we can manipulate known reactions (like flipping a reaction or scaling it to match the reactants and products) to mathematically construct our desired reaction. Then, we sum up all the enthalpy changes of these mini-reactions to find the total enthalpy change. Here, the 'mini-reactions' must, in the end, cancel out any unused reactants or products, leaving only the desired reaction equation. This method is especially valuable in educational contexts where direct measurement isn't possible.

Chemical reactions are transformations where one or more substances, the reactants, convert into different substances, known as products. How reactants interact and change into products can be depicted through chemical equations that also indicate the proportions in which the substances react and form products, reflecting the conservation of mass. In the context of enthalpy changes, understanding the stoichiometry of these chemical equations is key.

During a chemical reaction, bonds between atoms are broken and formed, which involves energy. If more energy is needed to break bonds than is released when new bonds form, the reaction is endothermic and absorbs heat from the surroundings. Conversely, if more energy is released than is consumed, the reaction is exothermic and the environment heats up. These heat exchanges are critical when considering reaction energetics and are represented by the sign of the enthalpy change (∆H), with positive values for endothermic and negative ones for exothermic reactions.

It's essential to recognize the importance of coefficients in a balanced equation, as they dictate the proportion of each substance involved. When applying Hess's Law or when performing calculations involving enthalpy changes, ignoring the stoichiometry could lead to incorrect results. These calculated enthalpy changes enable chemists to predict whether a reaction will release heat into the environment or absorb it, affecting reaction conditions and the feasibility of industrial processes.

The enthalpy of reaction, symbolized as ∆Hrxn, is a measure of the heat change during a chemical reaction at constant pressure. It's a vital concept in both thermodynamics and practical chemistry, as it helps determine the energy efficiency and safety of chemical processes. The enthalpy of reaction is calculated per mole of a reaction occurring under standard conditions, unless specified otherwise.

Enthalpy itself is a thermodynamic property that combines internal energy with pressure and volume to describe heat flow in a system. While we cannot measure enthalpy directly, we can calculate the changes in enthalpy. The ∆Hrxn is negative for exothermic reactions, indicating that the system is losing heat. For endothermic reactions, ∆Hrxn is positive, showing that heat is absorbed.

For the problem at hand, calculating the change in enthalpy involves manipulating the given reactions to model the target equation. By doing so, individual ∆H values are adjusted (for instance, reversing the equation changes the sign; multiplying it by a coefficient scales the ∆H proportionally). Adding these adjusted ∆H values for the reactions that model the desired process gives us the total energy change. Understanding how to apply these principles in calculations enables students to predict the energy demands or releases of chemical reactions, which is particularly important in large-scale industrial applications or environmentally sensitive chemical processes.