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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 standard temperature and pressure [[Standard conditions for temperature and pressure|STP]]).


The standard molar entropy is usually given the symbol ''S''°, and as units of [[joule]]s per mole [[kelvin]] (J mol<sup>−1</sup> K<sup>−1</sup>). Unlike [[standard enthalpy change of formation|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<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.  This residual entropy is often quite negligible.


==Thermodynamics==
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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^\circ = \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 [[Standard conditions for temperature and pressure|STP]] includes contributions from:<ref>{{cite book | last = Kosanke| first =  K. | coauthors =  | title = Pyrotechnic chemistry | publisher =  Journal of Pyrotechnics | year = 2004| 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 [[Product (chemistry)|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 | isbn = 0-07-251264-4 | chapter = Entropy, Free Energy and Equilibrium | page = 765 }}</ref>
 
: Δ''S''°<sub>rxn</sub> = ''S''°<sub>products</sub> – ''S''°<sub>reactants</sub>
 
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:
 
: Δ''S''<sub>total</sub> = Δ''S''<sub>system</sub> + Δ''S''<sub>surroundings</sub> > 0
 
==See also==
*[[Entropy]]
*[[Heat]]
*[[Gibbs free energy]]
*[[Helmholtz free energy]]
*[[Third law of thermodynamics]]
 
==References==
{{reflist}}
 
==External links==
*[http://users.humboldt.edu/rpaselk/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]]

Latest revision as of 15:29, 27 December 2014


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