The Entropy of Vaporisation

Entropy is the degree of disorder of a system. A higher value of entropy means there is a high value of disorder. It is denoted by ‘S’. The disorder of a system is related to the phase it is in.

For a crystalline solid substance, the entropy should be the lowest (most ordered), and the gaseous state is the state of the highest entropy.

Entropy changes are expressed as heat divided by temperature, so the units of entropy are calories per degree (cal deg-1) or Joules per Kelvin (JK-1).

Kinetic Molecular theory

 The temperature of a substance is proportional to the average kinetic energy of its particles. Increasing the temperature of a substance will result in more movements of the particles in solids and more rapid movements of the particles in liquids and gases. When the temperature is high, the kinetic energies of atoms are also higher than at lower temperatures. So, we can say that the entropy for any substance increases with temperature.

The Second Law of Thermodynamics in Terms of Entropy 

As per the second law of thermodynamics, the total entropy of the system and its surroundings (universe) increases spontaneously.

It can be thermodynamically written as:

∆ S Universe = ∆ S Total = ∆ S Sys + ∆ S Surr > 0.

The Entropy of Vaporisation

The entropy of vaporisation is the increase in entropy upon the vaporisation of a liquid. 

As the degree of the disorder increases in the transition, from a liquid having a small volume to a vapour having a larger volume, the entropy of vaporisation is always positive.

 At standard pressure (Po = 1 bar), the entropy of vaporisation is denoted as ΔSovap, and it has unit J/(mol·K). 

Enthalpy of Vaporisation (ΔvapH)

The standard enthalpy of vaporisation is the amount of heat required to vaporise one mole of a liquid at certain conditions such as constant temperature and standard pressure (1bar). It is also called the molar enthalpy of vaporisation.

Water requires heat for evaporation. At a constant temperature of its boiling point Tb and at constant pressure,

H2O(l) ⎯→ H2O(g); ΔvapH= + 40.79kJ mol-1

ΔvapH is the standard enthalpy of vaporisation.

We can express the entropy of vaporisation as:

∆Svap=∆HvapTvap

From the above formula we can say that the entropy of vaporisation is equal to the heat of vaporisation divided by the boiling point.

Hydrogen bonded liquids (like water) have a higher value of the entropy of vaporisation.

Molar enthalpy (ΔvapH) and entropy of vaporisation (∆Svap) and boiling point(Tb) of some liquids are given below: 

Since the gas state has higher entropy than the liquid state, the entropy change for the vaporisation of water is always found to be positive.

Gibbs Free Energy of a System

Gibbs free energy of a system is defined as the maximum amount of energy available to a system during a process that can be converted into useful work.

Gibbs free energy is denoted by G.

G= H – TS

Changes in Gibbs energy at constant temperature and pressure is defined as 

∆G= ∆H – T∆S

The SI unit of Gibbs energy is Jmol-1 or kJmol-1.

When ΔG is zero, the process is already in equilibrium, with no net change taking place over time.

A phase change can be noted to occur always at constant pressure and temperature. During the phase change, both the phases exist at equilibrium. The free energy, thus, for a phase change is zero (∆G = 0).

So, we can write the above formula at equilibrium as: 

∆Gvap= ∆Hvap – Tvap ∆Svap =0

Here,

T= Absolute thermodynamic temperature which is measured in Kelvin (K)

∆Svap= Entropy of vaporisation.

∆Hvap= Enthalpy of vaporisation

Trouton’s Rule

According to this rule, the entropy of vaporisation is similar for different kinds of liquids at their boiling point, i.e., the value is about 85-88J/(K-mol).

Trouton’s rule can be presented as a function of the gas constant R.

∆Svap10.5R

Trouton’s ratio can also be expressed as follows:

LvapTboiling85-88JK.mol

Trouton’s rule is valid for many liquids as given below:

Trouton’s rule is used to determine the enthalpy of vaporisation of those liquids with known boiling points.

Exceptions to Trouton’s rule

1. The entropies of vaporisation of water (H2O), ethanol (C2H5OH), formic acid (HCOOH), and hydrogen fluoride are very far from the expected values. The entropy of vaporisation of water and ethanol shows positive deviance from Trouton’s rules because of the presence of hydrogen bonds in them that lessen the entropy of these liquids. In the gaseous phase, formic acid forms a dimer; hence, it shows negative deviance.
2. The entropy of vaporisation of xenon hexafluoride (XeF6) at its boiling point has a very high value, i.e., 136.9 J/(K·mol). 

Conclusion

 The temperature of a substance is proportional to the average kinetic energy of its particles. Increasing the temperature of a substance will result in more movements of the particles in solids and more rapid movements of the particles in liquids and gases. At higher temperatures, the kinetic energies of the atoms is also higher than at lower temperatures. So, we can say that the entropy for any substance increases with temperature.