Question

Given the data $$ \begin{aligned} \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \cdots-\rightarrow 2 \mathrm{NO}(g) & \Delta H=+180.7 \mathrm{~kJ} \\ 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)-\cdots 2 \mathrm{NO}_{2}(g) & \Delta H=-113.1 \mathrm{~kJ} \\ 2 \mathrm{~N}_{2} \mathrm{O}(g)-\cdots 2 \mathrm{~N}_{2}(g)+\mathrm{O}_{2}(g) & \Delta H=-163.2 \mathrm{~kJ} \end{aligned} $$ use Hess's law to calculate \(\Delta H\) for the reaction $$ \mathrm{N}_{2} \mathrm{O}(g)+\mathrm{NO}_{2}(g)-\cdots 3 \mathrm{NO}(g) $$

Short answer

The enthalpy change, ΔH, for the reaction \(\mathrm{N}_{2} \mathrm{O}(g)+\mathrm{NO}_{2}(g) \rightarrow 3 \mathrm{NO}(g)\) is \( +262.3 \mathrm{~kJ} \).

Step-by-step solution

Identify the desired reaction

We are asked to find the enthalpy change for the following chemical reaction: \[ \mathrm{N}_{2} \mathrm{O}(g)+\mathrm{NO}_{2}(g) \rightarrow 3 \mathrm{NO}(g) \]

Manipulate the given reactions

In order to achieve the desired reaction, we need to manipulate the given reactions in such a way that they cancel out the undesired reactants and products while keeping the desired ones. First, we'll reverse the third reaction and multiply it by a factor of \(\frac{1}{2}\): \[ \mathrm{N}_{2}(g)+\frac{1}{2}\mathrm{O}_{2}(g) \rightarrow \frac{1}{2}2\mathrm{N}_{2} \mathrm{O}(g) \] Now, the enthalpy change for this reaction will be multiplied by the same factor and have the opposite sign, resulting in: \[ \Delta H = \frac{1}{2} \times (+163.2 \mathrm{~kJ}) = +81.6 \mathrm{~kJ} \]

Add the manipulated reactions

Now, we can add the first reaction and the manipulated third reaction to get the desired reaction: 1. \(\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \cdots-\rightarrow 2 \mathrm{NO}(g)\) \(\Delta H=+180.7 \mathrm{~kJ}\) 2. reversed and multiplied: \(\mathrm{N}_{2}(g)+\frac{1}{2}\mathrm{O}_{2}(g) \rightarrow \frac{1}{2}2\mathrm{N}_{2} \mathrm{O}(g) \) \(\Delta H=+81.6 \mathrm{~kJ}\) Now add the reactions: \[ \begin{aligned} &(\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)) + (\mathrm{N}_{2}(g)+\frac{1}{2}\mathrm{O}_{2}(g))\\ &\quad\,\rightarrow (2 \mathrm{NO}(g)) +(\mathrm{N}_{2} \mathrm{O}(g) ) \end{aligned} \] This simplifies to the desired reaction: \[ \mathrm{N}_{2} \mathrm{O}(g)+\mathrm{NO}_{2}(g) \rightarrow 3 \mathrm{NO}(g) \]

Add the corresponding enthalpy changes

Since we have added the reactions, we can now add their corresponding enthalpy changes to calculate ΔH for the desired reaction: \( \Delta H_{new} = \Delta H_1 + \Delta H_3' \) \( \Delta H_{new} = +180.7 \mathrm{~kJ} + 81.6 \mathrm{~kJ} = +262.3 \mathrm{~kJ} \)

State the result

The enthalpy change, ΔH, for the desired reaction \[ \mathrm{N}_{2} \mathrm{O}(g)+\mathrm{NO}_{2}(g) \rightarrow 3 \mathrm{NO}(g) \] is \( +262.3 \mathrm{~kJ} \).

Key concepts

Enthalpy Change

Enthalpy change, denoted as \( \Delta H \), is a critical concept in thermodynamics and chemistry. It represents the heat change at constant pressure during a chemical reaction. In simple terms, it helps us understand whether a reaction absorbs or releases energy as heat.

Understanding \( \Delta H \) is crucial as it guides us in predicting the energy requirements or releases of reactions. If \( \Delta H \) is positive, the reaction absorbs heat and is called endothermic. If \( \Delta H \) is negative, the reaction releases heat and is exothermic.

Energy plays a vital role in determining if products will form. A known \( \Delta H \) can help us determine reaction feasibility and safety. Enthalpy is a state function, meaning it depends only on the initial and final states, not on the path taken. This property simplifies calculations especially when using Hess's Law.

Chemical Reactions

Chemical reactions involve the transformation of reactants to products. Each reaction has its specific chemical equation, which shows the substances involved and the ratios in which they react. In the given problem, we see reactions like \( \mathrm{N}_2(g) + \mathrm{O}_2(g) \rightarrow 2 \mathrm{NO}(g) \).

These equations must be balanced to conserve mass and atoms, meaning the number of each type of atom in the reactants must match that in the products. This ensures adherence to the Law of Conservation of Mass.

Each chemical reaction also has an associated enthalpy change \( \Delta H \), indicating the heat absorbed or released. This helps assess energy changes during a reaction. Chemistry utilizes a variety of reaction types, each serving different purposes in scientific and industrial processes. Practice and understanding of these transformations are fundamental for solving complex problems.

Manipulating Reactions

Manipulating reactions is a powerful tool for chemists. It involves altering given reactions to derive a desired reaction and its enthalpy change. This process is key when applying Hess's Law.

To manipulate reactions, we may need to reverse, multiply, or divide chemical equations. Reversing a reaction changes the sign of \( \Delta H \). Multiplying or dividing reactions by a coefficient affects \( \Delta H \) proportionally.

• Reversing: Changes the sign of \( \Delta H \).
• Multiplying by a factor: Scales \( \Delta H \) by that factor.

By adding and manipulating reactions, Hess's Law allows calculation of enthalpy for reactions difficult to measure directly. It essentially says that \( \Delta H \) of the overall process is the sum of \( \Delta H \) of individual steps. This underlines the importance of correctly handling reactions to ensure accurate enthalpy calculations. Mastery of this concept can simplify complex reaction pathways.