# Standard molar entropy

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Standard molar entropy

In chemistry, the standard molar entropy is the entropy content of one mole of substance, under standard conditions (not standard temperature and pressure STP).

The standard molar entropy is usually given the symbol "S"o, and the units joules per mole kelvin (J mol−1 K−1). Unlike standard enthalpies of formation, the value of "S"o is an absolute. That is, an element in its standard state has a nonzero value of "S"o at room temperature. The entropy of an element 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. Fortunately this residual entropy is often quite negligible.

Thermodynamics

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:

:$S^o = sum_\left\{k=1\right\}^N Delta S_k =sum_\left\{k=1\right\}^N int frac\left\{dq_k\right\}\left\{T\right\} , dT$

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.

Chemistry

The standard molar entropy of a gas at STP includes contributions from: [cite book | last = Kosanke| first = K. | coauthors = | title = Pyrotechnic chemistry | publisher = Journal of Pyrotechnics | year = 2004| id = ISBN 1-889526-15-0 | chapter = Chemical Thermodynamics | page = 29 ]

* The heat capacity of one mole of the solid from 0 K to the melting point (including heat absorbed in any changes between different crystal structures)
* The latent heat of fusion of the solid.
* The heat capacity of the liquid from the melting point to the boiling point.
* The latent heat of vaporization of the liquid.
* The heat capacity of the gas from the boiling point to room temperature.

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:

[cite book | last = Chang| first = Raymond | coauthors = Brandon Cruickshank | title = Chemistry | publisher = McGraw-Hill Higher Education | year = 2005 | id = ISBN 0-07-251264-4 | chapter = Entropy, Free Energy and Equilibrium | page = 765 ]

: ΔS°rxn = So(products) - So (reactants)

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:

: ΔStotal = ΔSsystem + ΔSsurroundings > 0

ee also

*Entropy
*Heat
*Gibbs free energy
*Third law of thermodynamics

References

* [http://www.ualberta.ca/~jplambec/che/data/index.htm Compendium of Chemical Data] - Chemical properties of various substances (James A. Plambeck, University of Alberta)
* [http://www.humboldt.edu/~rap1/C110/C110Notes/C110_lec06.htm Free Energy and Chemical Reactions] - Course notes for General Chemistry (R. Paselk, Humboldt State University)

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