Rising energy costs have renewed interest in energy efficient separations. Such efficiencies can be defined as the free energy of unmixing divided by the free energy that must be added to the process. The greatest efficiencies occur when the energy cost far exceeds any capital cost. In this limit, rate processes are not important, and efficiency is governed by thermodynamics. Even for isothermal processes, these efficiencies are constrained by the second law of thermodynamics. For example, we show that the maximum possible efficiency η for dilute gas absorption and stripping is η=2/-lnHS/H Ay0 where HA and HS are the Henry's law constants in the absorber and stripper, respectively; and y0 is the mole fraction of this dilute gas exiting the absorber. Similar results for extraction, adsorption, crystallization, and membranes seem consistent with earlier estimates for distillation. The global recognition that fossil fuels are a limited resource has caused many to think about the energy used in chemical manufacture and, especially, of chemical separations. These separations, usually felt to consume 30-80% of the energy used in making chemicals, are often targeted for improvement. They are a tempting target: distillation alone is estimated to consume about one million barrels of crude oil in North America alone, with an efficiency of around 11%. Here would seem to be a major opportunity for energy saving. Estimates like this have prompted us to look at how chemical separations could possibly be more efficient. Each of us has done research on separations for decades; and each of us has authored a text codifying what is known about such separations. However, neither we nor many others have carefully considered how efficient separation processes could possibly be. In this paper, we want to explore the maximum possible efficiency possible for separations like gas absorption, liquid-liquid extraction, adsorption, and crystallization. We are especially concerned with the constraints of the second law of thermodynamics on these efficiencies. We also want to compare these maximum possible efficiencies with those possible for distillation. The results should help us to identify the greater opportunities for chemical manufacture with less energy use.