Question

Find \(\Delta H^{\circ}\) in kilojoules for the reaction of nitric oxide with oxygen, \(2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{4}(g)\), given the following data: $$\begin{array}{ll}\mathrm{N}_{2} \mathrm{O}_{4}(g) \longrightarrow 2 \mathrm{NO}_{2}(g) & \Delta \mathrm{H}^{\circ}=55.3 \mathrm{~kJ} \\ \mathrm{NO}(g)+1 / 2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{NO}_{2}(g) & \Delta H^{\circ}=-58.1 \mathrm{~kJ} \end{array}$$

Short answer

\( \Delta H^{\circ} = -171.5 \, \mathrm{kJ} \)

Step-by-step solution

Understand the Given Reaction

The reaction for which we need to calculate \( \Delta H^{\circ} \) is given by: \[ 2 \mathrm{NO}(g) + \mathrm{O}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{4}(g) \]We are tasked to find the \( \Delta H^{\circ} \) for this entire reaction.

Utilize Given Thermochemical Equations

We are provided with the following thermochemical data:1. \( \mathrm{N}_{2} \mathrm{O}_{4}(g) \longrightarrow 2 \mathrm{NO}_{2}(g) \) with \( \Delta H^{\circ} = 55.3 \, \mathrm{kJ}\) 2. \( \mathrm{NO}(g) + \frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{NO}_{2}(g) \) with \( \Delta H^{\circ} = -58.1 \, \mathrm{kJ} \) These will be manipulated to find the overall \( \Delta H^{\circ} \) for our target reaction.

Rearrange and Calculate for Target Reaction

Firstly, reverse the first reaction since we want \( \mathrm{N}_{2} \mathrm{O}_{4}(g) \) as a product:\[ 2 \mathrm{NO}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{4}(g) \] with \( \Delta H^{\circ} = -55.3 \, \mathrm{kJ} \) (reverse the sign).Next, using the equation for \( \mathrm{NO} \):Double the second given reaction to match our reactants:\[ 2 \mathrm{NO}(g) + \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g) \] Doubling \( \Delta H^{\circ} = -58.1 \, \mathrm{kJ} \) gives:\[ \Delta H^{\circ} = 2(-58.1) = -116.2 \, \mathrm{kJ} \]

Add the Adjusted Equations

Combine the adjusted equations:\[ 2 \mathrm{NO}(g) + \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g) \] \( \Delta H^{\circ} = -116.2 \, \mathrm{kJ} \)\[ 2 \mathrm{NO}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{4}(g) \] \( \Delta H^{\circ} = -55.3 \, \mathrm{kJ} \)Adding these gives the overall reaction:\[ 2 \mathrm{NO}(g) + \mathrm{O}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{4}(g) \]\( \Delta H^{\circ} = -116.2 \, \mathrm{kJ} + (-55.3 \, \mathrm{kJ}) = -171.5 \, \mathrm{kJ} \)

Key concepts

thermochemistry

Thermochemistry is the branch of chemistry that deals with the relationship between chemical reactions and energy changes involving heat. In thermochemistry, we often focus on the enthalpy change, denoted as \( \Delta H \), which tells us whether a reaction absorbs or releases heat. If \( \Delta H \) is negative, it means the reaction releases heat and is exothermic. Conversely, if \( \Delta H \) is positive, the reaction absorbs heat, making it endothermic.
To better understand thermochemistry, think of it as the way chemistry and heat interact. Whenever there’s a chemical reaction, there's a detailed heat exchange process, which is crucial for various applications.

Key takeaways in this context include:

• Identifying the role of energy changes in chemical reactions.
• Learning how to calculate and understand enthalpy changes using given thermochemical data.
• Understanding how these heat changes impact the conditions under which a reaction takes place.

This knowledge is vital, especially when it comes to designing chemical processes or simply understanding how everyday chemical reactions occur.

Hess's Law

Hess’s Law is a powerful concept in chemistry that states that the total enthalpy change of a reaction is the same, regardless of the path taken from reactants to products. This means you can add or subtract multiple steps to find the overall \( \Delta H \) for a complex reaction. Because enthalpy is a state function, it depends only on the initial and final states, not on how the reaction proceeds.
Create a mental picture of a reaction occurring in one step directly or multiple steps indirectly. The energy exchange will be consistent, thanks to Hess's Law.

Using Hess’s Law effectively involves:

• Identifying intermediate reactions that converge on the desired outcome.
• Manipulating given equations by reversing or scaling them to fit the target reaction.
• Adding up the enthalpies of these steps to determine the total heat change.

In our scenario, using Hess’s Law allowed us to calculate the overall \( \Delta H \) for the reaction of nitric oxide and oxygen by combining known reactions to fit the desired chemical equation.

chemical reactions

Chemical reactions involve the rearrangement of atoms to transform reactants into products, often accompanied by energy changes. Understanding these reactions involves looking at the reactants, products, and the specific conditions under which they change.
When studying chemical reactions, breaking them down into simpler steps can clarify which bonds are broken and formed, where energy is consumed or released, and how these influence the reaction’s outcome.

Important aspects to consider in chemical reactions:

• Identifying balanced equations where the number of atoms for each element is the same on both sides of the reaction.
• Understanding how and why certain reactions absorb or release energy.
• Considering the implications of reaction conditions, such as temperature and pressure, on product stability and reaction rate.

In our example, the reaction of \( 2 \mathrm{NO}(g) + \mathrm{O}_{2}(g) \rightarrow \mathrm{N}_{2} \mathrm{O}_{4}(g) \) exemplifies how we harness knowledge of intermediate reactions and thermochemical data to find how much heat is involved, demonstrating the energy interplay within a chemical process.