Question

(a) Why is the change in internal energy \(\Delta E\) usually harder to measure than the change in enthalpy \(\Delta H ?(\mathbf{b}) E\) 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?

Short answer

(a) Measuring ΔE is harder than measuring ΔH because both heat exchange (q) and work done (w) need to be determined for ΔE, while only heat exchange at constant pressure (q_p) needs to be measured for ΔH. (b) Internal energy (E) is a state function because it depends solely on the initial and final states of the system, but heat (q) is not a state function because it depends on the path taken by the system during a process. (c) If ΔH is negative at constant pressure, the process is exothermic because the system is releasing heat to the surroundings.

Step-by-step solution

(a) Difficulty in measuring ΔE and ΔH

(a) The change in internal energy (ΔE) of a system depends on the heat exchange with the surroundings (q) and the work done by/on the system (w). Mathematically, it can be represented as: \( \Delta E = q + w \) On the other hand, the change in enthalpy (ΔH) of a system at constant pressure is related to the heat exchange and is given by: \( \Delta H = q_p \) (where q_p is the heat exchange at constant pressure) Measuring ΔE is usually harder than measuring ΔH because both heat exchange (q) and work done (w) need to be determined for ΔE. In contrast, only heat exchange at constant pressure (q_p) needs to be measured for ΔH which is relatively simpler.

(b) State function

(b) A state function is a property that depends only on the current state of the system and not on the path taken to reach that state. Internal energy (E) is a state function because it depends solely on the initial and final states of the system. Heat (q), however, depends on the path taken by the system during a process. Different processes involving different paths can result in the same change of state, but in general, the amount of heat exchanged (q) would not be the same. Therefore, heat (q) is not a state function.

(c) Endothermic or exothermic process

(c) If the change in enthalpy (ΔH) is negative for a given process at constant pressure, it means that the system is releasing heat to the surroundings. This release of heat implies that the process is exothermic. In contrast, a process would be endothermic if it absorbs heat from the surroundings, which would result in a positive ΔH value.

Key concepts

Internal Energy

Internal energy, denoted by the symbol \(E\), is a fundamental concept in thermodynamics. It represents the total energy contained within a system, which includes both kinetic and potential energy types. The change in internal energy, expressed as \(\Delta E\), can be calculated using the formula \( \Delta E = q + w \), where \(q\) is the heat exchanged and \(w\) is the work done by or on the system.

Measurement of \(\Delta E\) is intricate because it requires knowledge of both heat exchange and work done, each a process-dependent variable. This complexity is why directly measuring \(\Delta E\) is often more difficult compared to enthalpy changes.

In various chemical reactions, studying internal energy aids in understanding energy conservation, as it must account for all forms of energy entering or leaving the system.

Enthalpy

Enthalpy, symbolized as \(H\), is another important thermodynamic quantity. It reflects the heat content of a system at constant pressure. The variation in enthalpy, \(\Delta H\), is defined primarily and directly through heat exchange under constant pressure, making it a simpler parameter to measure than \(\Delta E\).

Mathematically, enthalpy change is given as \( \Delta H = q_p \) where \(q_p\) is the heat absorbed or released at constant pressure. Because it links directly to the practical aspect of heat transfer, enthalpy is widely used in chemistry and engineering.

Understanding enthalpy allows one to evaluate energetic changes in reactions, predict reaction behavior, and assess whether a process is endothermic or exothermic. It helps in gauging energy efficiency and in designing processes for optimal energy usage.

State Functions

State functions are essential concepts in thermodynamics. They are properties of a system that depend only on the present state of the system, not how it came to be in that state. Examples of state functions include internal energy \(E\), enthalpy \(H\), pressure, volume, and temperature.

Unlike these, heat \(q\) and work \(w\) are path functions because they depend on the process through which the system changes from one state to another.

The significance of state functions lies in their predictability and path independence, allowing calculations with only the initial and final states information. This makes them powerful tools for determining thermodynamic properties and changes.

In chemical processes, knowing that internal energy \(E\) is a state function means focusing on the substance's energy at the start and end, offering efficiency in determining energy changes.

Exothermic Process

An exothermic process is a type of chemical change where the system releases energy, typically in the form of heat, to its surroundings. Such processes are characterized by a negative change in enthalpy, \(\Delta H < 0\).

Common examples include combustion reactions, like burning fuel, where the energy released exceeds the energy input, making them energetically favorable.

Exothermic reactions are crucial in energy applications, like heating systems and engines. Understanding them is essential for harnessing their potential safely and efficiently.

Recognizing whether a reaction is exothermic involves observing temperature increase in the environment, indicating that the system has released heat.

Endothermic Process

An endothermic process is one where the system absorbs energy from its surroundings. This absorption results in a positive change in enthalpy, \(\Delta H > 0\).

Endothermic reactions include processes like photosynthesis and the melting of ice, where energy input is essential for the reaction to progress.

These reactions are vital in areas like cooling technologies and in biological systems where energy is stored for future use.

The ability to identify endothermic processes helps in managing processes that require energy input, crucial for understanding energy flow in natural and industrial settings.

Detection of endothermic reactions often involves a cooling effect in the environment, as the system pulls in heat to support the reaction.