Can you remember your organic chemistry experiments? You (sloppily?) added all your reagents to a flask, heated it up for a few hours under reflux and the products formed spontaneously. Then, the hard work began-getting the pure product. This usually involved some tedious operation like distillation, recrystallization or chromatography (the separation or purification step). This example illustrates that separations are difficult. They are difficult because they are thermodynamically unfavorable. The root cause of the problem is that all separations are entropically disfavored.
If the final volume is larger than the initial volume, then the
log term is positive and the entropy of the system is favorable
(+). So, in general terms, dilution is always a thermodynamically
favored process.
How about the entropy of mixing. The mixing process is one of
dilution. A compound is diluted when it is mixed with other compounds.
Therefore, the art of separations requires that separated materials
become unmixed, which means that the unfavorable entropy change
must be overcome.
Example: Mix 50 mL of EtOH with 50 mL of water. View the system
as ethanol. The final volume is twice the initial volume. So:
The entropy of mixing is positive and therefore favorable. To
separate the ethanol into 50 mL of water and 50 mL of ethanol
requires just the reverse (a negative entropy change). Thus, energy
must be added to the system to perform a separation.