free energy or Gibbs free energy, quantity derived from the relationships between heat and work studied in thermodynamics and used as a measure of the relative stability of a physical or chemical system, i.e., the tendency of the system to react or change. If the change in free energy, Δ G, is negative, the transformation of the system will occur spontaneously, since transitions in which the energy decreases are favored, whereas those in which it increases (Δ G positive) are not. The change in free energy for a given process at a particular temperature depends on three factors, as seen from the equation Δ G = Δ H - T Δ S, where Δ H is the change in the enthalpy of the system, T is the temperature in degrees Kelvin, and Δ S is the change in entropy. A negative value of the enthalpy change indicates a decrease in the heat content of the system and contributes to a favorable value of the free energy; a positive entropy change indicates a decrease in the orderliness of the system and also contributes to a favorable value of the free energy, since a system tends to go from more ordered to less ordered states. It may happen that the change in enthalpy for the reaction is favorable but that of the entropy is unfavorable, or vice versa; in such a case the temperature is the deciding factor since it determines how much weight is given to the entropy change. For example, in the transition of liquid water to ice, the enthalpy change is favorable because heat is released in the process but the entropy change is unfavorable because the transition is to the more ordered, crystalline state. Below a temperature of 32°F (273°K) the enthalpy term, Δ H, is larger and the process is spontaneous, but at higher temperatures the entropy term, T Δ S, predominates, and the transition does not occur. Although the free energy indicates whether or not a given reaction will occur, it gives no information about the speed of such a reaction. The reaction of hydrogen with oxygen to form water has a favorable, negative, free energy, but the reaction rate is so slow that without the presence of a catalyst it is not observable. Scientists use tables listing the standard free energy, Δ G °, of various compounds; the standard free energy is the change in free energy when one mole of the compound is formed at 25°C and 1 atmospheric pressure.
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