1.1. Internal Energy vs. Enthalpy

Internal Energy (E)

• Definition: The internal energy of a system (symbol E, sometimes denoted U) is the sum of all kinetic energies (motion of atoms or molecules) and potential energies (interactions between particles) inside that system.

• Change in internal energy (ΔE): When a system undergoes a process (such as a chemical reaction), its internal energy may change. The first law of thermodynamics states that:

ΔE = q + w

• Here, q is positive when heat flows into the system; w is positive when work is done on the system (for example, compressing a gas).

• Limitations of ΔE in chemistry: Most chemical reactions occur at (or near) constant atmospheric pressure. In that context, it is more convenient to focus on a quantity that directly tracks heat flow at constant pressure—namely, enthalpy (H).

Internal energy (E) is essentially the total energy contained in a system due to the motion and interaction of its atoms and molecules. Every time a chemical reaction occurs, energy is either absorbed or released, which results in a change in internal energy (ΔE). This concept is based on the first law of thermodynamics, which states that energy cannot be created or destroyed, only transformed from one form to another.

In the equation ΔE = q + w, 'q' represents the heat added to or lost by the system, and 'w' represents the work done on or by the system. A positive 'q' indicates heat entering the system, whereas a positive 'w' indicates work being done on the system. However, in most chemical reactions, because they typically occur at constant pressure, changing internal energy is not as useful as enthalpy (H), which is more applicable for these scenarios.

Imagine a sealed container of gas. When you compress the gas by pushing down on the piston, you're doing work on the system, increasing its energy. If the gas heats up, that heat represents energy entering the system. Now consider cooking: when you heat food in a pan, you're adding energy (heat) to the food, leading to changes in taste and texture—this is an observable effect of changes in internal energy that occur during cooking.

Enthalpy (H)

• Definition: Enthalpy, denoted H, is defined as the internal energy E plus the product of pressure (P) and volume (V):

H = E + P·V

• Enthalpy is a state function; its value depends only on the current state (for example, temperature, pressure, and composition), not on the path taken to reach that state.

• Change in enthalpy (ΔH) at constant pressure: When a chemical reaction or physical process occurs at constant pressure, the change in enthalpy equals the heat flow to or from the surroundings (assuming no non-PV work, such as electrical work). In equation form, for constant external pressure P:

ΔH = q_p

• Interpretation of ΔH:

  • If ΔH is negative (ΔH < 0), the system releases heat into the surroundings; we call that an exothermic process.
  • If ΔH is positive (ΔH > 0), the system absorbs heat from the surroundings; we call that an endothermic process.

• Key Point: For reactions carried out at atmospheric pressure (a constant pressure condition), measuring the heat flow q_p directly gives the enthalpy change ΔH.

Enthalpy (H) is a concept that combines internal energy (E) with work done by or on a system due to volume changes under constant pressure (P·V). It is defined by the equation H = E + P·V. Because enthalpy is a state function, it is determined by the state of the system (like temperature and pressure) and not how the system got there.

During a chemical reaction, if the reaction occurs at constant pressure, the change in enthalpy (ΔH) reflects the heat that is absorbed or released. A negative ΔH means that the reaction is exothermic (releasing heat), while a positive ΔH means it is endothermic (absorbing heat). This helps chemists understand how a reaction interacts thermally with its surroundings.

Think about making ice water. When you add ice to water, the water absorbs energy (heat) from the surroundings to melt the ice, making it colder. This is an endothermic process. Conversely, when you burn wood, it releases heat into the environment, warming a room, which is an exothermic process. Both examples illustrate how enthalpy changes indicate the energy flow associated with chemical reactions or physical processes.

This section outlines the differences and limitations:

1. System Conditions: ΔE is useful for closed systems and changes involving work and heat flow, whereas ΔH is more relevant for reactions at constant pressure.
2. Application: In practical chemistry, ΔH generally provides a clearer insight into heat transfers during reactions at constant pressure, making it a central focus in thermochemistry.
3. Limitations: ΔE may not accurately reflect the energy changes for systems undergoing constant pressure conditions, hence the preference for ΔH (enthalpy) under such circumstances.

The differences between ΔE (internal energy change) and ΔH (enthalpy change) primarily revolve around the conditions under which they are measured and their practical applications. While ΔE can be calculated for closed systems where work might be done as energy is added or removed, ΔH focuses specifically on systems with constant pressure—where many chemical reactions occur.

Because most reactions in laboratories and industries are at constant atmospheric pressure, using ΔH provides a more straightforward understanding of the heat transfer involved. Thus, chemists prefer to work with enthalpy as it relates directly to energy flow under the conditions in which they are most concerned.

Consider climbing a hill. The energy you exert (work done) can be compared to ΔE, as it accounts for your effort regardless of how steep the hill is. When you reach the top (constant elevation) and look at the view (corresponding to ΔH), you’re interested in the energy you invested relative to the atmospheric conditions (constant pressure), such as how hard it feels to breathe at that height. It's about understanding the energy in relation to the surrounding pressure and conditions.

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