Problem 34 - Chemistry The Central Science

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, \(\Delta H\), equals the amount of heat transferred, \(q\), at constant pressure (\(\Delta H = q_P\)). (b) In a constant-pressure process with heat release, the enthalpy decreases, as both \(q\) and \(\Delta H\) are negative. (c) When \(\Delta H = 0\) in a constant-pressure process, the heat exchanged (\(q\)) is equal to the difference between the work done by the gas on its surroundings (\(w\)) and the pressure-volume work done (\(P\Delta V\)).

Step 1: (a) Condition when enthalpy change equals heat transferred

The enthalpy change of a process, \(\Delta H\), is equal to the amount of heat transferred into or out of the system (\(q\)), under the condition of constant pressure. Mathematically, this can be written as: \[ \Delta H = q_P, \] where \(q_P\) is the heat transferred at constant pressure.

Step 2: (b) Enthalpy change during a constant-pressure process with heat release

During a constant-pressure process, the system releases heat to the surroundings. This means that the heat transfer is negative (\(q < 0\)). According to the equation stated earlier, \(\Delta H = q_P\), the enthalpy change will also be negative (\((ΔH < 0)\)) during the process. Therefore, the enthalpy of the system decreases during the process.

Step 3: (c) Analysing the relationship between \(\Delta H\), \(\Delta E\), \(q\), and \(w\) when \(\Delta H=0\)

In a constant-pressure process, the enthalpy change is related to the internal energy change, heat, and work as follows: \[ \Delta H = \Delta E + P\Delta V, \] where \(\Delta E\) is the change in internal energy, \(P\) is the constant pressure, and \(\Delta V\) is the change in volume. When \(\Delta H = 0\), the equation becomes: \[ 0 = \Delta E + P\Delta V. \] Considering the first law of thermodynamics, which relates internal energy change, heat, and work, we have: \[ \Delta E = q - w, \] where \(w\) is the work done by the gas on its surroundings. By substituting this expression for \(\Delta E\) into the equation for constant pressure, we obtain: \[ 0 = (q - w) + P\Delta V. \] Solving for \(q\), we find: \[ q = w - P\Delta V. \] This indicates that when the enthalpy change is 0 during a constant-pressure process, the heat exchanged between the system and its surroundings (\(q\)) is equal to the difference between the work done by the gas on its surroundings (\(w\)) and the pressure-volume work done (\(P\Delta V\)).

Key Concepts

constant pressure

Constant pressure is a condition in thermodynamics where the pressure of a system does not change during a process. This situation is particularly useful when analyzing chemical reactions and physical changes because it simplifies the calculations involved. At constant pressure, the relationship between enthalpy change (\(\Delta H\)) and heat transfer is straightforward:

• Enthalpy change equals the heat transferred to or from the system.
• This relationship is expressed mathematically by the equation \(\Delta H = q_P\), where \(q_P\) is the heat transferred at constant pressure.

During a constant-pressure process, if the system releases heat to its surroundings, the heat transfer is negative (\(q < 0\)). This means the system's enthalpy decreases, as indicated by a negative enthalpy change (\(\Delta H < 0\)). It's a simple yet powerful concept often encountered in thermodynamic studies.

heat transfer

Heat transfer involves the movement of thermal energy from one object or system to another. This can occur in several ways, such as conduction, convection, and radiation. In the context of thermodynamics and constant pressure, understanding heat transfer is crucial.

• At constant pressure, the entire heat transfer during a process is equated to the change in enthalpy (\(\Delta H\)).
• When heat is released by the system, the value of \(q\) is negative, indicating energy flow out of the system.
• Conversely, when heat is absorbed, \(q\) is positive, and the system gains energy.

Heat transfer is a core concept in understanding how energy transactions affect the state and phase of a system. It is essential for analyzing processes in chemistry and engineering.

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. Mathematically, it is expressed as:\[\Delta E = q - w,\]where \(\Delta E\) is the change in internal energy, \(q\) is the heat transferred to the system, and \(w\) is the work done by the system.
In constant-pressure processes, this law interconnects with enthalpy changes:

• When \(\Delta H = 0\), energy balance becomes apparent: the heat added equals the work done minus any pressure-volume work.
• Substituting \(\Delta E = q - w\) into the enthalpy equation \(\Delta H = \Delta E + P\Delta V\), we find \(q = w - P\Delta V\).
• This showcases the intricate balance between heat, work, and internal energy in constant-pressure scenarios.

Understanding this law is crucial for grasping how energy conservation applies in real-world thermodynamic systems, ensuring energy changes are accurately accounted for across processes.