Question

Determine \(\Delta H\) for the reaction $$ \mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3} \rightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}+3 \mathrm{SO}_{3} $$ given these data: \(4 \mathrm{Fe}+3 \mathrm{O}_{2} \rightarrow 2 \mathrm{Fe}_{2} \mathrm{O}_{3} \Delta H=-1,650 \mathrm{~kJ}\) \(2 \mathrm{~S}+3 \mathrm{O}_{2} \rightarrow 2 \mathrm{SO}_{3} \Delta H=-792 \mathrm{~kJ}\) \(2 \mathrm{Fe}+3 \mathrm{~S}+6 \mathrm{O}_{2} \rightarrow \mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3} \Delta H=-2,583 \mathrm{~kJ}\)

Short answer

To be continued...

Step-by-step solution

Write the Given Reactions

We are provided with three reactions and their corresponding enthalpy changes (\(\Delta H\)): 1) \(4 \mathrm{Fe} + 3 \mathrm{O}_{2} \rightarrow 2 \mathrm{Fe}_{2} \mathrm{O}_{3}, \Delta H = -1650\, \mathrm{kJ}\) 2) \(2 \mathrm{~S} + 3 \mathrm{O}_{2} \rightarrow 2 \mathrm{SO}_{3}, \Delta H = -792\, \mathrm{kJ}\) 3) \(2 \mathrm{Fe} + 3 \mathrm{~S} + 6 \mathrm{O}_{2} \rightarrow \mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}, \Delta H = -2583\, \mathrm{kJ}\)

Key concepts

Enthalpy Change

Enthalpy change, symbolized as \( \Delta H \), is an essential concept in chemistry that represents the heat absorbed or released in a chemical reaction. It indicates the difference between the enthalpy of the reactants and products. Understanding \( \Delta H \) helps predict whether a reaction is endothermic, absorbing heat, or exothermic, releasing heat. This change in enthalpy is crucial in the study of thermodynamics, as it indicates how energy is transformed during a reaction.
When a reaction releases heat, such as combustion, it has a negative \( \Delta H \), signaling that energy leaves the system. Conversely, a positive \( \Delta H \) suggests that the process is endothermic, with the system absorbing energy from its surroundings. In practical terms, knowing if a reaction absorbs or releases heat helps chemists design safer, more efficient processes.
In thermochemical calculations, Hess's Law is often used. This law states that the total enthalpy change for a chemical process is the same regardless of how many steps the process takes, as long as the initial and final conditions remain unchanged. This principle allows chemists to determine the enthalpy change for complex reactions by combining known reactions.

Chemical Reactions

Chemical reactions involve the transformation of substances, where reactants are converted into products. Their study involves understanding how the bonds in molecules are broken and new ones get formed, often involving shifts in energy and heat.
The provided chemical reactions illustrate an essential concept in chemistry—the transformation from one compound structure to another and determining the energy changes associated with these transformations. For instance, changing iron sulfate into iron oxide and sulfur trioxide involves balancing the conservation of atoms and using thermochemical data to find the overall energy change.
In the exercise, we are tasked with determining the enthalpy change for the transformation of \( \mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3} \) into \( \mathrm{Fe}_{2} \mathrm{O}_{3} \) and \( \mathrm{SO}_{3} \). By utilizing Hess's Law, which uses known \( \Delta H \) values for elementary steps, we can calculate the desired enthalpy change for the entire reaction by adding the appropriate scaled reactions to derive the reaction of interest. This demonstrates the application of theoretical knowledge to predict the behavior of chemical systems.

Thermochemistry

Thermochemistry is a branch of chemistry that focuses on the heat involved in chemical reactions. It plays a significant role in understanding how energy flows in reactions, which is vital for everything from industrial applications to biological processes.
This particular discipline allows chemists to calculate and predict the energy changes associated with chemical transformations. Understanding thermochemistry enables scientists to tailor energy-efficient reactions, crucial for applications such as battery development, food processing, and materials manufacturing.
Thermochemistry uses tools like calorimetry, the measurement of the heat of chemical reactions or physical changes, and concepts like \( \Delta H \), which help define the energetic landscape of reactions, connecting theoretical chemistry to real-world applications. In practice, knowing how much heat is exchanged in a reaction can inform whether additional steps or adjustments are needed to control reaction conditions, optimize yields, and ensure safety.