Problem 33 - Chemistry The Central Science In Si Units

Question

(a) Why is the change in internal energy \(\Delta E\) usually harder to measure than the change in enthalpy \(\Delta H ?\) (b) \(E\) is a state function, but \(q\) is not a state function. Explain. (c) For a given process at constant pressure, \(\Delta H\) is negative. Is the process endothermic or exothermic?

Step-by-Step Solution

Answer

(a) 94E involves measuring both heat and work, which complicates measurement; 94H involves only heat at constant pressure. (b) E depends only on state, while q depends on the process path. (c) Exothermic.

Step 1: Understanding Internal Energy vs Enthalpy

The change in internal energy, 94E, involves measuring both heat transferred (94q) and work done (94w) on or by the system: 94E = q + w. Directly measuring work can be complex, as it involves changes in volume and external pressure. In contrast, enthalpy, 94H, at constant pressure, simplifies to just measuring the heat absorbed or released, making 94H easier to measure.

Step 2: State Function vs Path Function

A state function describes a property that depends only on the current state of the system, not the path taken to reach that state. Internal energy (E) is a state function because its value depends only on the system's current condition. In contrast, heat (q) is not a state function because the amount of heat exchanged depends on the specific process path taken between two states.

Step 3: Interpreting a Negative 94H

Enthalpy change (94H) is negative in processes where the system releases heat to the surroundings. At constant pressure, a negative 94H indicates an exothermic process, where heat exits the system, transferring energy out.

Key Concepts

Internal Energy Measurement

In thermodynamics, measuring changes in a system's internal energy, denoted as \( \Delta E \), often presents challenges. This is because \( \Delta E \) encompasses two components: the heat transferred \( q \) and the work performed \( w \). Specifically, the formula \( \Delta E = q + w \) highlights this relationship.

• Heat transfer \( q \): This involves measuring the heat exchanged with the surroundings, depending on various factors like temperature change and specific heat capacity.
• Work \( w \): This involves calculating the work done by or on the system, which may include factors such as volume changes or pressure exertion.

Calculating work can be complex, especially when dealing with variables such as changing volumes and external pressures. In contrast, measuring a change in enthalpy \( \Delta H \) at constant pressure is simpler. This is because \( \Delta H \) focuses primarily on the heat component alone, thereby avoiding the intricacies associated with work calculations.

State Functions

In thermodynamics, understanding state functions is crucial. A state function is a property whose value depends only on the current state of the system, not the path used to reach that state. Internal energy \( E \) is an example of a state function.

• Internal energy \( E \): Marks the total energy contained within a system and is solely reliant on the system's current conditions such as temperature and pressure.

On the flip side, some properties are path-dependent and not considered state functions.

• Heat \( q \): Is a classic example of a path function, since the amount of heat exchanged can vary widely based on the specific path or conditions leading from one state to another.

Therefore, while \( E \) can reliably indicate the energy status of a system, \( q \) cannot provide the same consistency, as it varies depending on how the process is carried out.

Exothermic Process

An exothermic process is a type of reaction or change where the system releases heat to its surroundings. In practical thermodynamics terms, this shows as a negative change in enthalpy \( \Delta H \) at constant pressure.

• The system loses heat: As the heat exits the system, it results in a drop in the system's internal energy.
• Surroundings gain energy: The energy is transferred to the environment, typically increasing the temperature of the surroundings.

Therefore, when \( \Delta H \) is negative, it directly indicates an exothermic process. This implies that the system is energetically favorable, often requiring less input to maintain the process, and is commonly seen in processes like combustion or many chemical reactions.