Problem 66 - Chemistry The Central Science In Si Units

Question

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

Step-by-Step Solution

Answer

The \( \Delta H \) for \( \mathrm{N}_{2} \mathrm{O}(g) + \mathrm{NO}_{2}(g) \rightarrow 3\mathrm{NO}(g) \) is \( +457.0 \text{ kJ} \).

Step 1: Write Target Reaction

The target reaction to determine \( \Delta H \) for is \( \mathrm{N}_{2} \mathrm{O}(g) + \mathrm{NO}_{2}(g) \rightarrow 3\mathrm{NO}(g) \). Write this reaction clearly to keep the goal in mind.

Step 2: Reverse Necessary Reactions

We need the \( \mathrm{N}_{2} \mathrm{O}(g) \) on the reactant side. So, reverse the third given reaction: \( 2 \mathrm{N}_{2}(g) + \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{~N}_{2} \mathrm{O}(g) \), which changes \( \Delta H \) to \(+163.2 \; \text{kJ}\) (the opposite of the original).

Step 3: Use Remaining Reactions

The reaction \( \mathrm{N}_{2}(g) + \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}(g) \) will provide the \( \mathrm{NO} \). Use this reaction as it is with \( \Delta H = +180.7 \; \text{kJ} \).

Step 4: Reverse the Second Reaction

To use \( \mathrm{NO}_{2} \) as a reactant, reverse the second reaction: \( 2 \mathrm{NO}_{2}(g) \rightarrow 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \), which will change \( \Delta H \) to \(+113.1 \; \text{kJ}\).

Step 5: Combine Reactions

Combine the altered reactions to form the target equation. Balancing the oxygen atoms and nitrogen allows you to see that: \( \mathrm{N}_{2} \mathrm{O}(g) + \mathrm{NO}_{2}(g) \rightarrow 3 \mathrm{NO}(g) \).

Step 6: Calculate Total \( \Delta H \)

Add the \( \Delta H \) values: \( +163.2 \text{ kJ (reversed),} +180.7 \text{ kJ, and } +113.1 \text{ kJ (reversed)} \): \( 163.2 + 180.7 + 113.1 = 457.0 \text{ kJ} \).

Step 7: Final Answer

The overall \( \Delta H \) for the target reaction is \( +457.0 \text{ kJ} \). Note: The positive sign indicates the reaction is endothermic.

Key Concepts

Enthalpy Change

Understanding enthalpy change is crucial when analyzing chemical reactions. Enthalpy change, represented by \( \Delta H \), is the amount of heat absorbed or released during a reaction at constant pressure. This quantity tells us whether a reaction is endothermic (absorbing heat) or exothermic (releasing heat). In our example, we calculated the overall \( \Delta H \) for a reaction using Hess's Law, which ended up being +457.0 kJ.
The positive \( \Delta H \) value indicates an endothermic process, meaning heat is absorbed from the surroundings.

• A negative \( \Delta H \) would signal an exothermic reaction.
• Reversed reactions require reversing the sign of \( \Delta H \).
• Multiplying a reaction by a coefficient also scales \( \Delta H \) by that factor.

When applying Hess’s Law, rearranging and combining reaction equations with known enthalpy changes can help find \( \Delta H \) for complex reactions.

Chemical Reactions

Chemical reactions involve the transformation of reactants into products. This process often involves breaking and forming bonds, requiring varying amounts of energy. In the context of our problem, we used known reactions to form a new desired reaction. Consider these key points about chemical reactions:

• They are governed by conservation of mass and energy.
• Reactants must balance with products in terms of atoms involved.
• Hess's Law allows for indirect calculation of \( \Delta H \) using several simpler reactions.

Utilizing known reactions, we strategically reversed or combined them to align with our target equation. This strategic manipulation allows us to indirectly calculate the enthalpy change for reactions which might not be straightforward to measure directly.

Reaction Energetics

Reaction energetics refers to the study of energy changes during chemical reactions. It's important to understand how energy is exchanged and what factors influence these exchanges. In the exercise, the focus is on using Hess's Law to determine how energy is handled in a complex reaction.
Essential points about reaction energetics are:

• Endothermic reactions absorb energy, often requiring heat input to proceed.
• Exothermic reactions release energy, which may be in the form of heat or light.
• Hess's Law and enthalpy change help quantify these energy changes.

In our calculation, we found the target reaction required 457.0 kJ of energy input. This information is valuable for understanding whether a reaction will need additional energy to proceed or not, and it helps chemists design processes that consider energy efficiency and safety. These concepts are vital in fields such as thermochemistry and chemical engineering.