Free energy-dependent phase transfer of water

What does ‘Free mean’

[Purposely the right up kept simple. However, questions are open]

The basic definition of "energy" is it is a measure of a body's (in thermodynamics, the system's) ability to cause change. We need the energy to perform mechanical work. Our energy converts to work. This energy conversion, however, is not straightforward: while some internal energy is consumed to perform the work, some is diverted away (lost) in the form of heat (transferred thermal energy). The difference between the change in internal energy, which is ΔU, and the energy lost in the form of heat is what is called the "useful energy" of the body, or the work of the body performed on an object. In thermodynamics, this is what is known as "free energy".

The Gibbs free energy is given by G = H − TS, where H is the enthalpy.

What does free energy mean?

The free energy change 

 G associated with a chemical process tells whether or not the process will occur under the specified conditions. For a chemical process to occur spontaneously (that is, without the net addition of energy) the free energy change at the specified conditions must be negative. The three factors that play a role in determining the spontaneity of a process (that is, the sign of (- G) are: (1) whether the process is exothermic,

 (H < 0), (2) the temperature at which it is proposed to run the process reaction, and (3) the entropy change 

 S associated with the process. These factors are related by the equation given earlier:

∆G = H - TS

General rules of free energy

If a reaction is exothermic ( H is negative) and the entropy 

 S is positive (more disorder), the free energy change is always negative and the reaction is always spontaneous.

If a reaction is endothermic ( H positive) and the entropy change S is negative (less disorder), the free energy change is always positive and the reaction is never spontaneous.

If the enthalpy change  H and the entropy change 

 S are both positive or both negative, the spontaneity of the reaction depends on the temperature.

Water

When ∆G<0, the process is spontaneous, ∆G=0, a process in equilibrium, ∆G>0 process is reversible. The solid lines separating are phase boundary lines in the phase diagram where two phases are in thermal equilibrium, ∆G=0. A phase can only transit to another phase spontaneously when ∆G<0

Free energy-dependent phase transfer of water

∆G = H − T∆S

Melting of ice

When ice melts, the change is endothermic (H is positive), and entropy increases (S is positive) as the water molecules lose the ordered arrangement of ice crystals. Therefore, ∆G>0. melting of ice as it is therefore not spontaneous. 

However, the T∆ S factor for melting ice at 298 K is numerically larger than H; the free energy change G is then negative, so melting is spontaneous at that temperature, 25 degc.

Freezing of water

It is an exothermic process. H is negative. S is also negative because of liquid freezing to solid. The freezing of water is therefore spontaneous.

Evaporation of water at room temperature

Usually "standard" conditions for gases correspond to one bar of partial pressure for that gas. But the partial pressure of water in our atmosphere is usually much lower than this. Assuming water vapor is an ideal gas, then the free energy change as a function of partial pressure is given by G=G∘ + RT lnp/p∘. If the atmosphere were perfectly 100% dry, then the water vapor partial pressure would be 0, so lnp/p∘ would be negative infinity. That would translate to an infinitely negative -- i.e., highly spontaneous. That stands for - ΔG for the water evaporation process.

Vaporization of water

The evaporation of water is spontaneous even though this change is endothermic ΔH = +44 kJ mol–1). When water changes from liquid to a gas there is a considerable increase in disorder and entropy (ΔS = +118.8 J K–1 mol–1). As a result, evaporation is spontaneous because TΔS > ΔH, enabling ΔG<0.