# Enthalpy Definition and Derivation

## What is Enthalpy?

Enthalpy is defined as the amount of internal energy and the output of a thermodynamic system's pressure and volume. Enthalpy is an energy-like property or state function that has energy dimensions (and is thus calculated in joules or erg units). The enthalpy H is equivalent to the sum of the internal energy E and the pressure P multiplied with volume V of the system i.e., H = E + PV, respectively.

Under the law of conservation of energy, the shift in internal energy is equal to the heat transmitted to the device, minus the work performed by it. If a change in volume at constant pressure is the only work performed, the change in enthalpy is exactly equal to the heat transferred to the device. The amount of energy is called the enthalpy (or latent heat of vaporization) and is expressed in units of joules per mole when energy needs to be applied to a substance to shift its phase from a liquid to a gas.

### Enthalpy Change

The name given to the amount of heat evolved or consumed in a reaction conducted at constant pressure is Enthalpy transition. The symbol of Enthalpy H is referred to as "delta H". At constant pressure, the equation for the change in internal energy, ∆U = q + w can be written as:

∆U = qP – p∆V

Where qP represents the heat absorbed by the system at constant pressure and – p∆V is the expansion work done due to the heat absorbed by the system. The above equation can be written in the terms of initial and final states of the system which is defined below:

UF – UI = qP –p(VF – VI)

Or qP = (UF + IVF) – (UI + pVI)

Enthalpy (H) can be written as H= U + PV. Putting the value in the above equation, we obtained:

qP = HF – HI = ∆H

Hence, change in enthalpy ∆H = qP, referred to as the heat consumed at a constant pressure by the system. At constant pressure, we can also write,

∆H = ∆U + p∆V

## Some Key Points

The heat from the device is lost to the surrounding atmosphere during exothermic reactions. ∆H is negative for such reactions. During endothermic reactions, heat is absorbed from the atmosphere by the system. ∆H is positive for such reactions.

### Enthalpy of Reactions:

Energy change (U) is equal to the amount of heat produced and the work carried out. Pressure-volume work is called work performed by an expanding gas (or just PV work). For instance, consider a gas-producing reaction, such as dissolving a piece of copper in concentrated nitric acid.

Cu(s)+4HNO3(aq)→Cu(NO3)2(aq)+2H2O(l)+2NO2(g)

The quantity of PV work performed by multiplying the external pressure P by the volume change induced by the piston movement (almost V) is found. At constant external pressure, (here, atmospheric pressure),

w=−PΔV

The negative sign associated with PV work performed means that when the volume increases, the device loses energy. The work performed by the system is negative if the volume increases at constant pressure (V> 0), implying that a system has lost energy by performing work on its surroundings. Conversely, the work performed by the system is positive if the volume decreases (almost V<0), which implies that the environment has worked on the system, thereby increasing its energy.

The internal energy U of a system is the sum of all its components' kinetic energy and potential energy. It is the inner energy shift that generates heat plus function. Chemists typically use a related thermodynamic quantity called enthalpy (H) to calculate the energy changes that occur in chemical reactions. Systems’ enthalpy is defined as the sum of their internal energy U plus the product of their pressure P and volume V:

H=U+PV

Since all state functions are internal energy, strain and volume, enthalpy is also a state function. We can therefore characterize a shift in enthalpy ('H) accordingly.

ΔH=Hfinal −Hinitial

If at constant pressure (i.e. for a given P, ΔP=0) a chemical shift occurs, the change in enthalpy ( ΔH) is

ΔH=Δ(U+PV)

=ΔU+ΔPV

=ΔU+PΔV

Substituting q+w for ΔU (First Law of Thermodynamics) and −w for PΔV we obtain

ΔH=ΔU+PΔ

=qp+w−w

=qp

The p subscript is used here to emphasize that this equation is only valid for a constant pressure phase. It is observed that the shift in enthalpy, the H of the system, is equal to the heat obtained or lost at constant pressure.

ΔH=Hfinal−Hinitial

=qp