Enthalpy — Core Principles

Core Principles

Enthalpy ($H$) is a fundamental thermodynamic property defined as the sum of a system's internal energy ($U$) and the product of its pressure ($P$) and volume ($V$), i.e., $H = U + PV$. It is a state function, meaning its value depends only on the current state of the system, not the path taken.

The change in enthalpy, $\Delta H$, is particularly significant in chemistry because it represents the heat absorbed or released by a system during a process carried out at constant pressure ($Q_p$). This makes $\Delta H$ a direct measure of heat flow in most chemical reactions.

The relationship between $\Delta H$ and $\Delta U$ is given by $\Delta H = \Delta U + P\Delta V$. For reactions involving gases, this can be further expressed as $\Delta H = \Delta U + \Delta n_g RT$, where $\Delta n_g$ is the change in the number of moles of gaseous species.

A negative $\Delta H$ indicates an exothermic reaction (heat released), while a positive $\Delta H$ indicates an endothermic reaction (heat absorbed). Various types of enthalpy changes exist, such as standard enthalpy of formation, combustion, and neutralization, each describing specific chemical or physical transformations under standard conditions.

Important Differences

vs Internal Energy (U)

Aspect	This Topic	Internal Energy (U)
Definition	Enthalpy ($H = U + PV$): Total heat content of a system at constant pressure, including internal energy and PV work.	Internal Energy ($U$): Total energy contained within a system, including kinetic and potential energies of its molecules.
Measurement Condition	Change in enthalpy ($\Delta H$) is measured at constant pressure ($Q_p$).	Change in internal energy ($\Delta U$) is measured at constant volume ($Q_v$). (From First Law: $\Delta U = Q_v$ when $W=0$).
Relation to Heat	$\Delta H = Q_p$ (Heat exchanged at constant pressure).	$\Delta U = Q_v$ (Heat exchanged at constant volume).
PV Work Inclusion	Explicitly includes the energy associated with pressure-volume work ($PV$).	Does not explicitly include $PV$ work in its definition; $PV$ work is a form of energy transfer that contributes to $\Delta U$ via $W$ in $\Delta U = Q + W$.
Relevance	More relevant for chemical reactions and biological processes occurring in open systems (constant pressure).	More relevant for processes occurring in closed, rigid containers (constant volume).

Enthalpy and internal energy are both state functions representing energy within a system, but they differ in how they account for pressure-volume work. Enthalpy ($H$) is defined as $U + PV$, making its change ($\Delta H$) directly equivalent to the heat exchanged at constant pressure ($Q_p$). Internal energy ($U$) represents the sum of kinetic and potential energies of molecules, and its change ($\Delta U$) is equivalent to the heat exchanged at constant volume ($Q_v$). For reactions involving significant volume changes, especially with gases, $\Delta H$ and $\Delta U$ can differ substantially, with $\Delta H$ being more practically useful for open-system chemical reactions.