Question

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

Short answer

(a) The change in enthalpy (\( \Delta H \)) is usually easier to measure than the change in internal energy (\( \Delta U \)) because it involves directly observable quantities like heat flow (q) and work (w) under constant pressure conditions. This allows for a simpler relationship: \( \Delta H = q_p \). (b) Enthalpy (H) is a state function because it depends only on the state of the system (U, P, and V), while heat (q) is a path function, depending on the particular process taken between two states. (c) If \( \Delta H > 0 \) at constant pressure, the process is endothermic, meaning that heat is being absorbed by the system from the surroundings.

Step-by-step solution

(a) Easier measurement of enthalpy change

Enthalpy is a thermodynamic property, defined as the sum of the internal energy (U) of a system and the product of the pressure (P) and volume (V) of that system (H = U + PV). The change in enthalpy for a given process (\( \Delta H \)) can be mathematically expressed as: \( \Delta H = \Delta U + P \Delta V \). The change in enthalpy is usually easier to measure than the change in internal energy because it involves directly observable quantities in a typical constant pressure experiment (e.g. in a laboratory). Essentially, one can measure the heat flow (q) and work (w) involved under constant pressure conditions, such as an open beaker or container. Then, as the work performed can be calculated as \( w = - P \Delta V \), one can relate the change in enthalpy with the heat transfer as follows: \( \Delta H = q_p \) (under constant pressure). Since the heat transfer is easier to measure, the change in enthalpy is also easier to determine compared to internal energy.

(b) State functions and path functions

A state function is a property that solely depends on the initial and final states of a system, without being affected by the path (process) taken to reach these states. Examples of state functions include enthalpy (H), internal energy (U), and entropy (S). On the other hand, a path function depends on the particular process taken between two states, which means that the property is not uniquely determined by the initial and final states. Heat (q) and work (w) are examples of path functions. Since enthalpy (H) is defined as the sum of internal energy and the product of pressure and volume (H = U + PV), it only depends on the state of the system (U, P, and V are all state functions). Therefore, enthalpy (H) is a state function. However, heat (q) is not a state function because it depends on the path taken by the system during the process and can vary for different paths between the same initial and final states.

(c) Endothermic or exothermic process?

If the given process has a positive change in enthalpy (\( \Delta H > 0 \)) at constant pressure, this means that the heat is being absorbed by the system from the surroundings. The absorbing of heat is the definition of an endothermic process. Therefore, the process is endothermic. In contrast, if the change in enthalpy (\( \Delta H \)) were negative at constant pressure, the process would release heat from the system to the surroundings, and it would be considered exothermic.

Key concepts

Thermodynamics and Enthalpy

When studying thermodynamics, one frequently encounters enthalpy, a core concept in this field. It is essential for describing heat changes during chemical reactions or physical transformations. Thermodynamics is primarily concerned with energy, work, and heat, and how these quantities are transferred and transformed. Enthalpy, symbolized by H, is particularly useful because it accounts for heat flow in processes occurring at constant pressure, which is a common condition in most laboratory settings.

Understanding enthalpy as a combination of a system's internal energy and the product of its pressure and volume (\(H = U + PV\)) simplifies the task of quantifying energy changes in many scenarios. Since enthalpy can be directly measured through heat under constant pressure conditions, it provides a convenient way of tracking how energy enters or leaves a system, making it a pivotal term in the study of thermodynamics.

State Function Explained

A state function, such as enthalpy (\(H\)), internal energy (\(U\)), volume (\(V\)), or pressure (\(P\)), solely depends on the state of the system at a given point, not the path taken to reach that state. These functions are essential individuals in the realm of thermodynamics because they allow us to describe a system's characteristics with definitive respect to its equilibrium state.

Enthalpy is particularly significant as it is invariant regardless of the journey between two equilibrium points, reflecting a principal fact that, in a closed system, the total change in enthalpy equals the sum of heat added to the system and the work done on it at constant pressure, assuming no non-PV work takes place. This facet makes it a reliable measure and widely applicable for scientists and engineers calculating energy changes without detailing the specific process involved.

Endothermic Process Indicators

A process is described as endothermic if it absorbs heat from its surroundings, as indicated by a positive change in enthalpy (\( \triangle H > 0 \)). These processes are fundamental in thermodynamics and chemistry, as they indicate a system's requirement for energy input to proceed, such as in the melting of ice or photosynthesis in plants. The absorbed energy often leads to breaking bonds within reactants or creating higher energy states.

A practical understanding of endothermicity allows students and researchers to predict and control reactions and processes. Recognizing an endothermic process helps in energy management and in the design of systems such as chemical reactors, where controlling temperature and energy flow is critical. By linking the sign of enthalpy change to the nature of energy exchange, learners can develop a stronger grasp of chemical thermodynamics and better anticipate the behavior of systems under various conditions.