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 $$\mathrm{N}_{2} \mathrm{O}(g)+\mathrm{NO}_{2}(g) \longrightarrow 3 \mathrm{NO}(g)$$

Short answer

The overall enthalpy change (∆H) for the target reaction, \( N2O(g) + NO2(g) \rightarrow 3NO(g) \), is \( +212.2 \, kJ \).

Step-by-step solution

Analyze the given reactions and the target reaction

First, let's take a closer look at the given reactions and the target reaction. We need to find a way to combine the given reactions to obtain the target reaction. In order to do this, we may need to reverse and/or multiply the given reactions by a suitable factor to align with the stoichiometry of the target reaction. Given reactions: 1. N2(g) + O2(g) → 2NO(g) (∆H = +180.7 kJ) 2. 2NO(g) + O2(g) → 2NO2(g) (∆H = -113.1 kJ) 3. 2N2O(g) → 2N2(g) + O2(g) (∆H = -163.2 kJ) Target reaction: N2O(g) + NO2(g) → 3NO(g)

Manipulate the given reactions

We want to have N2O and NO2 on the left side and 3NO on the right side of the target reaction. Observe that: - In reaction 1, there are 2NO on the right side, which can contribute to forming 3NO in the target reaction. - In reaction 2, there are 2NO2 on the right side. We can reverse this reaction to have one NO2 on the left side. - In reaction 3, there is 2N2O on the left side. We can divide this reaction by 2 to have one N2O on the left side. Manipulated reactions: 1. N2(g) + O2(g) → 2NO(g) (∆H = +180.7 kJ) 2. NO2(g) → NO(g) + 1/2O2(g) (∆H = +113.1 kJ) [reversed] 3. N2O(g) → N2(g) + 1/2O2(g) (∆H = -81.6 kJ) [divided by 2]

Combine manipulated reactions and add enthalpy changes

Now, we can combine the manipulated reactions to form the target reaction and add up their enthalpy changes to get the overall enthalpy change for the target reaction. Sum of manipulated reactions: N2(g) + O2(g) + NO2(g) + N2O(g) → 2NO(g) + NO(g) + 1/2O2(g) + N2(g) + 1/2O2(g) Cancelling out terms: N2O(g) + NO2(g) → 3NO(g) Sum of enthalpy changes: ∆H = (+180.7 kJ) + (+113.1 kJ) + (-81.6 kJ) = +212.2 kJ

Write the final answer

The overall enthalpy change (∆H) for the target reaction, N2O(g) + NO2(g) → 3NO(g), is +212.2 kJ.

Key concepts

Enthalpy Change Calculation

When we talk about enthalpy change calculation, we refer to the measurement of the total heat content in a chemical system during a reaction, usually represented by \( \Delta H \) for a particular equation. This value is a critical component of thermochemistry, for it denotes whether a reaction is exothermic (releases heat) or endothermic (absorbs heat).

To calculate \( \Delta H \) for a reaction not directly observed, as seen in the exercise, we can utilize known enthalpy changes of related reactions and apply Hess's Law. This law states that the total enthalpy change of a reaction is the same, no matter how many steps or stages the reaction is carried out in. Put simply, enthalpy is a state function—it only depends on the initial and final states, not on the path taken.

The exercise demonstrates the importance of reaction stoichiometry alignment when using Hess's Law. We analyze and sometimes manipulate given reactions to match the stoichiometry of the target reaction. In our specific example, the target reaction's enthalpy change was found by reversing and halving given reactions, then summing up their enthalpy changes. The clear presentation of each manipulation step is crucial for students to follow along and understand the enthalpy calculation process.

Chemical Reaction Stoichiometry

Understanding chemical reaction stoichiometry is essential for successfully applying Hess's Law and calculating enthalpy changes. Stoichiometry involves the quantitative relationship between reactants and products in a chemical reaction. Knowing how many moles of each substance react and form allows scientists and students to predict the amounts of products resulting from a given amount of reactants.

In the context of the example given, the stoichiometry of the target reaction and the provided reactions had to be carefully analyzed to ensure the correct alignment. For instance, we observe that, by adjusting coefficients and reversing reactions, we're able to effectively 'cancel out' molecules on opposite sides of the reaction equation, leaving the desired target reaction.

Stoichiometry and Hess's Law

This approach emphasizes the importance of correct stoichiometric coefficients for both reactants and products. Failure to consider this could lead to incorrect calculations of the enthalpy change. Accessible explanations of these concepts can help students appreciate the meticulous nature required in stoichiometric calculations and how it directly impacts the results in thermochemical equations.

Thermochemistry

Thermochemistry is the branch of chemistry that studies the energy and heat associated with chemical reactions and physical transformations. The law of conservation of energy, which states that energy cannot be created or destroyed, is fundamental to thermochemistry and underpins principles like Hess's Law.

The enthalpy change (\( \Delta H \)) of a reaction indicates whether the reaction is exothermic, releasing energy to its surroundings, or endothermic, absorbing energy from its surroundings. Thermochemistry visually captures this energy exchange with graphs and models, often plotting the enthalpies of reactants and products and showing the energy released or absorbed.

Real-World Relevance

In practical terms, thermochemistry is involved in energy production, such as in burning fuels, and in everyday processes like cooking and refrigeration. By understanding concepts such as enthalpy, students can better grasp how energy transformations are critical to both natural and engineered processes. The straightforward breakdown of complex chemical reactions into comprehensible concepts is invaluable for students to confidently approach and solve thermochemical problems.