Standard molar entropy
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In [[chemistry]], the '''standard molar entropy''' is the [[entropy]] content of one [[mole (unit)|mole]] of substance, under standard conditions (NOT STP).
The standard molar entropy is usually given the symbol ''S''<sup>o</sup>, and the units J mol<sup>−1</sup> K<sup>−1</sup> ([[joule]]s per mole [[kelvin]]). Unlike [[standard enthalpy change of formation|standard enthalpies of formation]], the value of ''S''<sup>o</sup> is an absolute. That is, an element in its standard state has a nonzero value of ''S''<sup>o</sup> at room temperature. The entropy of an element can be 0 J mol<sup>−1</sup> K<sup>−1</sup> 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 (unit)|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:
:<math>S^o = \sum_{k=1}^N \Delta S_k =\sum_{k=1}^N \int \frac{dq_k}{T} \, dT</math>
Here, '''dq<sub>k</sub>/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 (thermodynamics)|reversible]] process.
==Chemistry==
The standard molar entropy of a [[gas]] at [[STP]] includes contributions from:<ref>{{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 }}</ref>
* 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 structure]]s)
* 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:
<ref>{{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 }}</ref>
: ΔS°<sub>rxn</sub> = S<sup>o</sup>(products) - S<sup>o</sup> (reactants)
The standard entropy of reaction helps determine whether the reaction will take place [[spontaneous process|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:
: ΔS<sub>total</sub> = ΔS<sub>system</sub> + ΔS<sub>surroundings</b> > 0
==See also==
*[[Entropy]]
*[[Heat]]
*[[Gibbs free energy]]
*[[Third law of thermodynamics]]
==References==
{{reflist}}
==External links==
*[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)
[[Category:Chemical properties]]
[[Category:Thermodynamic entropy]]
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