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The standard molar entropy is usually given the symbol S°, and as units of joules per mole kelvin (J mol−1 K−1). Unlike standard enthalpies of formation, the value of S° is an absolute. That is, an element in its standard state has a nonzero value of S° at room temperature. The entropy of a pure crystalline structure can be 0 J mol−1 K−1 only at 0 K, according to the third law of thermodynamics. However, this presupposes that the material forms a 'perfect crystal' without any frozen in entropy (defects, dislocations), which is never completely true because crystals always grow at a finite temperature. This residual entropy is often quite negligible.
If a mole of substance were at 0 K, then warmed by its surroundings to 298 K, its total molar entropy would be the addition of all N individual contributions:
Here, dqk/T represents a very small exchange of heat energy at temperature T. The total molar entropy is the sum of many small changes in molar entropy, where each small change can be considered a reversible process.
Changes in entropy are associated with phase transitions and chemical reactions. Chemical equations make use of the standard molar entropy of reactants and products to find the standard entropy of reaction:
The standard entropy of reaction helps determine whether the reaction will take place spontaneously. According to the second law of thermodynamics, a spontaneous reaction always results in an increase in total entropy of the system and its surroundings: