Question

Calculate Use Hess's law to determine \(\Delta H\) for the reaction \({NO ({g})+{O}({g}) \rightarrow\) \({NO}_{2}({g}) \Delta H=?\) given the following reactions. Show your work. \({O}_{2}({g}) \rightarrow 20({g}) \Delta H=+495 {k}\) \(20_{3}({g}) \rightarrow 30_{2}({g}) \Delta H=-427 {kJ}\) \({NO}({g})+{O}_{3}({g}) \rightarrow {NO}_{2}({g})+\mathrm{O}_{2}({g}) \Delta H=-199 {kJ}\)

Short answer

The enthalpy change, ΔH, for the target reaction \(NO(g) + O(g) \rightarrow NO_{2}(g)\) is -446.5 kJ.

Step-by-step solution

Identify the target reaction components in the given reactions

We want the reaction \(NO(g) + O(g) \rightarrow NO_{2}(g)\). We can see O in reaction (1), NO and NO2 in reaction (3). To eliminate unwanted products and reactants, we will also need reaction (2).

Manipulate the given reactions to match the target reaction

To obtain the target reaction, we need to reverse reaction (1) and adjust the coefficients if needed. We will change the sign of the ΔH value for the reversed reaction. Reversing reaction (1) and dividing by 2: \[\frac{1}{2}O_{2}(g) \leftarrow O(g) \quad ΔH_{1r} = -\frac{1}{2} \times (+495kJ) = -247.5kJ\] Add reaction (3) to the reversed reaction (1): \[(3) + (1r): NO(g) + O(g) \rightarrow NO_{2}(g) \quad ΔH_T = ΔH_{1r} + ΔH_3\]

Calculate the enthalpy change for the target reaction

Now that we have the correct combination of reactions, we just need to sum the heats of reaction: \[\Delta H_T = ΔH_{1r} + ΔH_3 = -247.5kJ - 199kJ = -446.5kJ\] The enthalpy change, ΔH, for the target reaction is -446.5 kJ.

Key concepts

Enthalpy Change

Understanding enthalpy change is crucial in the field of thermochemistry, especially when dealing with chemical reactions involving heat energy. It represents the heat absorbed or released during a reaction at constant pressure. It's commonly denoted as \( \Delta H \), where a positive value indicates endothermic reactions (heat absorption), and a negative value suggests exothermic reactions (heat release).

In our exercise, we've calculated the enthalpy change of a specific reaction using Hess's Law, which states that the total enthalpy change of a reaction is the same, no matter how many steps it takes to get there. This is akin to saying that the total energy you use to climb a mountain is the same whether you hike straight up or take a longer, winding path. By manipulating given reactions and their respective enthalpy changes, we arrived at an aggregate enthalpy change for our targeted reaction, making Hess's Law a powerful tool for predicting the heat of reactions that can be hard to measure directly.

Thermochemistry

Thermochemistry is the branch of chemistry concerned with the energy changes that occur during chemical reactions, particularly the exchange of heat energy. It is based on the first law of thermodynamics, which states that energy cannot be created or destroyed, only transformed.

When studying thermochemistry, we often talk about the system, which is the part of the universe we are focusing on (usually the chemicals involved in the reaction), and the surroundings, which is everything else outside the system. The change in the system's enthalpy affects the surroundings, as heat is transferred between them. This transfer is what we call the enthalpy change, \( \Delta H \), which is also what we've calculated in our exercise using Hess's Law. Remarkably, this law helps us to indirectly measure enthalpy change by economically using data from related reactions and thus provides us with insight into the energetic demands of chemical processes.

Chemical Reactions

Chemical reactions involve reorganization of atoms and molecules to form new chemical substances. The starting substances, known as reactants, transform into products through bond formation and breakage, accompanied by energy changes. Understanding the flow of energy, particularly heat, during these transformations is essential. The enthalpy changes we calculate offer insights into whether a reaction will release heat into the surroundings or absorb it.

Moreover, the laws governing chemical reactions, such as conservation of mass and energy, enable chemists to predict products and the extent of reactions, as illustrated by our use of Hess's Law to determine the heat of formation for \(NO_{2}(g)\) from \(NO(g)\) and \(O(g)\). Our exercise exemplifies the predictive power of thermochemical principles and highlights the interconnected nature of chemical reactions, where the energy profile of one reaction can shed light on another related reaction.