system will change until it has obtained the lowestGibbs energy:
G:HTS ð 2 : 4 ÞUnless mentioned otherwise, we will always mean the Gibbs energy when
speaking about free energy.
The free energy is thus the property determining what will happen. If
we add some sugar to water, it will dissolve and the sugar molecules will
distribute themselves evenly throughout the liquid, because that gives the
lowest free energy. In this case the increase in entropy has a greater effect
than the increase in enthalpy (in crystalline sugar, the molecules attract each
other and the enthalpy is thus lower than in solution). If we have pure oil
droplets in water, they will rise to the surface (lower potential energy) and
then coalesce into one layer (lower interfacial area and thus lower surface
free energy). If we bring water to a temperature of 20 C, it will crystallize
(lower enthalpy, which in this case more than compensates for the decrease
in entropy). If we have a solution of ethanol in water with air above it, the
ethanol will divide itself in such a way over the phases that its partial free
energy (or chemical potential: Section 2.2.1) is the same in both; the same
applies for the water. All these processes occur spontaneously, and they will
never reverse if the external conditions (temperature, pressure, volume
available) are left unaltered.
All this applies, however, only to macroscopic amounts of matter.
Thermodynamics is valid only for large numbers of molecules. If small
numbers are considered, say less than a few times 100, exceptions to the rule
stated above may occur; even at 10 8 C, a few water molecules may
temporarily become oriented as in an ice crystal, just by chance, but
macroscopically ice will never form at that temperature.
Another remark to be made is that the absolute values of enthalpy and
entropy are generally unknown. (Only a perfect crystal of one component at
zero absolute temperature has zero entropy.) Quantitative results therefore
mostly refer to some standard state (usually 0 8 C and 1 bar), where these
parameters are taken to be zero. One always considers the change in
thermodynamic properties, and that is quite sufficient. At constant pressure
and temperature, the basic equation thus is
DG¼DHTDS ð 2 : 5 Þ*The change may be from one state to another, say water plus crystalline
sugar to a sugar solution, etc. If the change considered is reversible, we have
at equilibriumDG¼0 and thusDH¼TeDS. For example, at 273.15 K
(0 8 C) and 1 bar there is equilibrium between (pure) water and ice.DHis here
the enthalpy of fusion, which can readily be measured by calorimetry and