Problem 61 - Chemistry: The Central Science in SI Units, Global Edition

Question

Can you use an approach similar to Hess's law to calculate the change in internal energy, \(\Delta E,\) for an overall reaction by summing the \(\Delta E\) values of individual reactions that add up to give the desired overall reaction?

Step-by-Step Solution

Answer

An approach similar to Hess's law can be used to calculate the change in internal energy, \(\Delta E\), for an overall reaction by summing the internal energy values of individual reactions only in cases when the work done on or by the system is negligible and there are no significant pressure, volume, or temperature changes during the reaction. In situations where the work done on or by the system is significant, we cannot use such an approach, as internal energy is influenced by the specific path taken during the reaction.

Step 1: Understanding the difference between internal energy and enthalpy

Enthalpy (\(\Delta H\)) is the heat content of a system at constant pressure. It is a state function, which means its value depends only on the current state of the system and not on the path taken to reach that state. Given this property, we can use Hess's law to find the change in enthalpy for a reaction by summing the changes in enthalpy for individual reactions that add up to the overall reaction. However, internal energy (\(\Delta E\)) is not a solely state function. It also depends on the path taken by the system during a reaction due to the presence of work done on or by the system. This means that internal energy is influenced by factors such as pressure, volume, and temperature changes in addition to the heat content of the system.

Step 2: Evaluating the applicability of Hess's law for internal energy calculations

Since internal energy is a path-dependent quantity and influenced by factors other than heat content, we must consider whether an approach similar to Hess's law can be used for finding the change in internal energy for an overall reaction. In situations where the work done on or by the system is negligible, the internal energy change can be considered as a state function. This generally occurs when there are no significant pressure, volume, or temperature changes during the reaction. In such cases, we can adopt an approach similar to Hess's law and calculate the change in internal energy for an overall reaction by summing the internal energy changes of individual reactions. However, in situations where the work done on or by the system cannot be neglected and leads to significant pressure, volume, or temperature changes, we cannot use an approach analogous to Hess's law for calculating the change in internal energy for an overall reaction.

Step 3: Conclusion

An approach similar to Hess's law can be used to calculate the change in internal energy, \(\Delta E\), for an overall reaction by summing the internal energy values of individual reactions ONLY in cases when the work done on or by the system is negligible and there are no significant pressure, volume, or temperature changes during the reaction. In situations where the work done on or by the system is significant, we cannot use such an approach, as internal energy is influenced by the specific path taken during the reaction.

Key Concepts

Hess's Law

Hess's Law is a powerful concept in chemistry that allows us to simplify the calculation of enthalpy changes in reactions. It is based on the idea that enthalpy, a state function, depends only on the initial and final states of a system, regardless of the steps or path taken between those states. This means we can split a complex reaction into simpler steps whose enthalpy changes are known and sum them to find the total enthalpy change.
Understanding Hess's Law is especially useful because it lets us calculate the change in enthalpy even if the direct measurement is challenging. By using a series of reactions that add up to the desired overall reaction, we apply Hess's Law to find the total change in enthalpy with ease and accuracy.
In simple terms:

• Identify smaller known reactions whose sum equals the overall reaction.
• Calculate the sum of their enthalpy changes.

By doing so, you take advantage of the state function nature of enthalpy, making complex calculations simpler.

State Function

A state function is a property of a system that depends only on the current state of the system and not on how that state was reached. This means that for any process, if you know the initial and final states, you can determine the changes in state functions like enthalpy and internal energy without needing any information about the path taken.
Common state functions in thermodynamics include:

• Enthalpy ( \(\Delta H \) )
• Internal Energy ( \(\Delta E \) )
• Entropy ( \(\Delta S \) )

State functions are crucial in simplifying thermodynamic calculations, as they allow us to use principles like Hess's Law to add or subtract quantities directly.
When dealing with reactions, remember that state functions provide consistency, regardless of the different ways or paths reactions might occur.

Path Dependency

Path dependency refers to processes or functions where the outcome depends on the route taken to reach the final state, not just on the final and initial states themselves. Unlike state functions, path-dependent properties can vary widely based on the specific steps or path involved in a process.
While enthalpy is a state function and not path-dependent, internal energy can be influenced by the path when considering the work done on or by the system. This is because:

• Work done depends on variables like volume and pressure changes.
• Heat exchange also affects the internal energy.

Understanding path dependency helps clarify why internal energy calculations may not always follow the straightforward addition used for enthalpy under Hess's Law.
In situations where work and heat changes are non-negligible, the total internal energy will be path-dependent, requiring detailed knowledge of all steps in the process.

Thermodynamics

Thermodynamics is the study of energy transformation and how these transformations affect matter. It's a broad field encompassing several laws and principles that explain how energy moves and changes in isolated and open systems.
Key principles of thermodynamics include:

• The First Law of Thermodynamics, which is the conservation of energy. It states that energy cannot be created or destroyed, only transformed.
• The different types of energy, such as internal energy, potential energy, and kinetic energy, and how these may be converted from one to another.

In thermodynamics, understanding the distinction between state functions and path-dependent functions is vital for solving energy change problems.
This discipline focuses on how elements like pressure, temperature, and volume interact with energy changes, making it essential for exploring both path-dependent processes and applications of Hess's Law where simplified calculations are needed.