Problem 34 - Chemistry: The Central Science in SI Units, Global Edition

Question

(a) Under what condition will the enthalpy change of a process equal the amount of heat transferred into or out of the system? (b) During a constant-pressure process, the system releases heat to the surroundings. Does the enthalpy of the system increase or decrease during the process? (c) In a constant-pressure process, \(\Delta H=0\). What can you conclude about \(\Delta E, q,\) and \(w ?\)

Step-by-Step Solution

Answer

(a) The enthalpy change of a process will equal the amount of heat transferred into or out of the system under the condition of constant pressure, represented as: \(\Delta H = q_P\). (b) In a constant-pressure process where the system releases heat to the surroundings, the enthalpy of the system decreases as \(\Delta H\) will be negative. (c) If \(\Delta H = 0\) in a constant-pressure process, this implies \(q_P = 0\). Based on the first law of thermodynamics, we can conclude that the change in internal energy (\(\Delta E\)) is equal to the negative of the work done by the system (\(w\)), i.e., \(\Delta E = -w\).

Step 1: Condition for enthalpy change equal to heat transferred

For the enthalpy change to equal the amount of heat transferred into or out of the system, the process needs to happen at a constant pressure. Mathematically, this can be represented as: \[ \Delta H = q_P \] Where \(\Delta H\) is the change in enthalpy, and \(q_P\) is the heat transferred at constant pressure. #b#

Step 2: Enthalpy Change during Constant-Pressure Process

In a constant pressure process, the enthalpy change is given by: \[ \Delta H = q_P \] Since the system is releasing heat to the surroundings, the heat transfer \(q_P\) will be negative, which implies that \(\Delta H\) will also be negative. Therefore, the enthalpy of the system decreases during the process. #c#

Step 3: Conditions for Constant-Pressure Process with no Enthalpy Change

If \(\Delta H = 0\) during a constant-pressure process, the heat transferred at constant pressure must also be zero, i.e., \(q_P = 0\). Now, we can use the first law of thermodynamics which states that the change in internal energy (\(\Delta E\)) is equal to the heat added to the system (\(q\)) minus the work done by the system (\(w\)): \[ \Delta E = q - w \] Under constant pressure, \(q_P = q\), so in this case, \(q = 0\). This simplifies the equation to: \[ \Delta E = -w \] Since \(\Delta H = 0\), we can conclude that the change in the internal energy (\(\Delta E\)) is equal to the negative of the work done by the system (\(w\)).

Key Concepts

Constant-Pressure Process

In thermodynamics, a constant-pressure process is one where the pressure remains unaltered throughout the process. This is particularly significant because, under these conditions, the change in enthalpy (\( \Delta H\) can be directly equated to the heat exchanged, denoted as \( q_P \).

• Equational Representation: The enthalpy change at constant pressure is mathematically expressed as \( \Delta H = q_P \). This means that under constant pressure, we don't have to account separately for heat and enthalpy change, because they are equivalent.
• Practical Implications: Many real-world processes, such as boiling water at atmospheric pressure, occur under constant pressure, making this concept vital for understanding everyday thermodynamics.

When analyzing a constant-pressure process, recognizing that any change in enthalpy directly correlates with the heat exchange simplifies the calculation of heat and energy changes in the system.

First Law of Thermodynamics

The First Law of Thermodynamics is a fundamental principle stating that energy cannot be created or destroyed, only transferred or transformed. When applied to constant-pressure processes, this law plays a pivotal role in evaluating the energy dynamics involved.

• Formula: The law is expressed as \( \Delta E = q - w \), where \( \Delta E \) represents the change in internal energy, \( q \) is the heat added to the system, and \( w \) is the work done by the system.
• Connection to Enthalpy: At constant pressure, the heat exchanged \( q \) corresponds to \( q_P \), making it straightforward to determine changes in internal energy. If \( q_P \) is known, and the work done is measured, one can easily find the internal energy change.

This law ensures that all energy changes in a system are balanced by the heat introduced or taken from the system and the work completed by or on the system. Hence, it reinforces the underpinning of energy conservation in physical and chemical processes.

Internal Energy Change

Internal energy change is a central theme in thermodynamics, representing the total change in energy within a system. This concept is essential when analyzing processes at constant pressure.

• Calculation: For a process where \( \Delta H = 0 \) and \( q_P = 0 \), we apply the simplified equation from the first law: \( \Delta E = -w \). This indicates that any change in internal energy is countered by the work done by the system.
• Significance of Zero Enthalpy Change: When the enthalpy remains unchanged, it signifies a perfect balance between heat exchange and work done. Such a scenario implies that the system transforms energy primarily through work without any net external heat transfer.

Understanding the nuances of internal energy change, especially under constant pressure, provides deeper insights into the energy interactions within a system, aiding in comprehensive energy management and analysis.