# Enthalpy

Enthalpy (H) is equal to the internal energy of a system (U) plus the work (w), pressure times volume ($w=PV$), needed to displace the environment to produce the components of the system: $H=U+PV$.

A system is the part of the universe that is under consideration. In a thermodynamic system, the sum of all kinetic energy and potential energy of the particles in the system is internal energy (U). Kinetic energy is the energy in the motion and vibration of particles. Potential energy arises from particle interactions such as chemical bonds or lattice energy in solids. Internal energy is often difficult to calculate as an absolute value. For most systems, chemists are not interested in absolute internal energy, but change in the internal energy of the substances in the system. The first rule of thermodynamics states that the change in internal energy of the system (U) is equal to heat into and out of a system (q) plus the work (w) done on or by the system: $\Delta U=q+w$. Work (w) is the energy that is transformed when a force acts on an object over a distance.

Work (w) is equal to $-P_{\rm{out}}\cdot\Delta V$. It is possible to write the equation for internal energy as:
$\begin{gathered}\Delta U=q+w\\{\Delta U=q-P_{\rm{out}}\cdot\Delta V}\end{gathered}$
If the chemical reaction occurs under constant volume, then the $\Delta V$ term will equal 0. This makes $-P_{\rm{out}}\cdot\Delta V$ equal to 0. The system does no work, and no work is done on the system. In this case $\Delta U$ is equal to the heat term, q.

#### First Law of Thermodynamics

A chemical reaction performed under constant volume is rare. Most chemical reactions are performed under constant atmospheric pressure, where the volume varies. If the pressure is constant, it is possible to write $-P_{\rm{out}}\cdot\Delta V$ as $\Delta(PV)$. This changes the equation for internal energy:
$\Delta U=q-\Delta(PV)$
For chemical reactions, the heat released or absorbed during the reaction is of special interest. This equation can be rearranged to solve for heat:
$q=\Delta U+\Delta(PV)$
The heat released or absorbed during a reaction is partly due to the changes in internal energy of the substances involved. The $\Delta(PV)$ term relates the heat to a change in volume. This means that if the total volume of the substances in the reaction increases, typically by formation of a new gas during a reaction, then the new gas must push against the atmospheric pressure to exist. Similarly, if a gas is consumed and the total volume goes down, then the atmospheric pressure pushes against the substances. The equation can be further simplified by moving the $\Delta$ term outside the parentheses.
$q=\Delta(U+PV)$
The term $U+PV$ indicates enthalpy. Enthalpy (H) is the internal energy of a system plus the work needed to displace the environment to produce the components of the system. Enthalpy is useful in thermodynamics because it accounts for pressure-volume differences. If enthalpy is added to the equation, the equation for the heat absorbed or released at constant pressure (qp) is:
$q_{\rm{p}}=\Delta H\;\;\;\;\;\text{(at constant pressure)}$
At constant pressure, the change in enthalpy is equal to the heat released or absorbed during a chemical reaction. Holding the pressure constant is vital; this relation does not hold true if the pressure varies. Enthalpy has the same unit as energy, joules.