Question

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

Short answer

The enthalpy change, ΔH, for the target reaction \( \mathrm{N}_{2} \mathrm{O}(g)+\mathrm{NO}_{2}(g) \rightarrow 3\mathrm{NO}(g) \) can be calculated using Hess's law. By manipulating the given reactions and performing the necessary operations, we find that the target ΔH value is -318.9 kJ.

Step-by-step solution

Identify the target reaction

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

Manipulate the given reactions to match the target reaction

We have the following three given reactions: \[ \begin{aligned} 1.)\quad\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow 2\mathrm{NO}(g) & \quad\Delta H=+180.7\: \mathrm{kJ}\\ 2.)\quad 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightarrow 2\mathrm{NO}_{2}(g) & \quad\Delta H=-113.1\: \mathrm{kJ}\\ 3.)\quad 2\mathrm{N}_{2}\mathrm{O}(g) \rightarrow 2\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) & \quad\Delta H=-163.2\: \mathrm{kJ} \end{aligned} \] To match the target reaction, we need to: - Reverse reaction 1 to get 2 NO (g) to the left side of the equation. - Multiply reaction 2 by 1/2 to balance the number of NO2 (g) involved. - Multiply reaction 3 by 1/2 to balance the number of N2O (g) involved. Upon doing these operations, we get the following equations: \[ \begin{aligned} 1'.)\quad 2\mathrm{NO}(g) \rightarrow \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) & \quad\Delta H=-180.7\: \mathrm{kJ}\\ 2'.)\quad \mathrm{NO}(g)+\frac{1}{2}\mathrm{O}_{2}(g) \rightarrow \mathrm{NO}_{2}(g) & \quad\Delta H=-56.6\: \mathrm{kJ}\\ 3'.)\quad \mathrm{N}_{2}\mathrm{O}(g) \rightarrow \mathrm{N}_{2}(g)+\frac{1}{2}\mathrm{O}_{2}(g) & \quad\Delta H=-81.6\: \mathrm{kJ} \end{aligned} \]

Sum the modified reactions to form the target reaction and their enthalpy changes to find the target ΔH value

Now, adding the modified reactions 1', 2', and 3', we get the target reaction: \[ \mathrm{N}_{2}\mathrm{O}(g)+\mathrm{NO}_{2}(g) \rightarrow 3\mathrm{NO}(g) \] Now, we can add the corresponding enthalpy changes of the modified reactions to find the target ΔH value: \[ \Delta H_\text{target} = (-180.7) + (-56.6) + (-81.6) = -318.9\: \mathrm{kJ} \] The ΔH for the target reaction is -318.9 kJ.

Key concepts

Enthalpy Change

When it comes to chemical reactions, the concept of enthalpy change (\(\Delta H\)) is pivotal. This represents the heat absorbed or released during a reaction at constant pressure. It's like a snapshot of the energy change, showing us how much energy is needed or released.
In our exercise, we are focusing on calculating the \(\Delta H\) for a target reaction involving gases like \(\text{N}_2\text{O}\), \(\text{NO}_2\), and \(\text{NO}\).
This enthalpy change can be determined using Hess's Law, which lets us understand energy transformations in steps:

• Each step of a reaction, such as combining \(\text{NO}\) and \(\text{O}_2\) to form \(\text{NO}_2\), has a specific \(\Delta H\).
• The total \(\Delta H\) is just the sum of these steps.
• By knowing the \(\Delta H\) of standard reactions, we can deduce unknown enthalpy changes.

Understanding \(\Delta H\) is crucial. It helps predict whether a reaction releases energy (exothermic) or requires energy (endothermic), thus informing us of its spontaneity and potential impact.

Target Reaction

In this problem, our focus is to calculate the \(\Delta H\) for a specific target reaction. The target reaction is:
\[\mathrm{N}_{2}\mathrm{O}(g)+\mathrm{NO}_{2}(g) \rightarrow 3\mathrm{NO}(g)\]
This target reaction isn't standalone; instead, it's connected to other reactions through Hess's Law.
To achieve our goal, we aim to modify a set of known reactions to resemble the target one:

• We reverse or adjust given reactions so their sum equals the target.
• This involves flipping equations or changing coefficients, affecting \(\Delta H\).

For instance, reversing a reaction inverts \(\Delta H\). Multiplying reactions alters \(\Delta H\) proportionally.
By precisely maneuvering these equations, we shape them to match our target reaction, allowing us to calculate its \(\Delta H\) efficiently. This precise control over reaction manipulation is a hallmark of using Hess's Law.

Thermodynamic Calculations

Thermodynamic calculations are essential for understanding the energy changes and feasibility of chemical reactions. In our exercise, we utilized techniques from thermodynamics to compute the \(\Delta H\) for a given target reaction:

• Thermodynamics offers tools to predict and quantify energy transfers in reactions.
• Hess's Law is particularly powerful, providing a method to calculate enthalpy changes by summing stepwise stages.
• These incremental calculations break down complex reactions into simpler segments.

Once the modified reactions mirror the target equation, as demonstrated in our exercise, we simply sum their \(\Delta H\) values. Calculating this summed \(\Delta H\) gives us insights into how much energy the target reaction involves.
These calculations inform us about the potential endothermic or exothermic nature of the reaction. By breaking down processes into thermodynamic steps, we craft a clearer picture of chemical behavior, crucial for fields like chemistry and engineering.