Editing Standard molar entropy

{{Layman|date=February 2025}}{{short description|Standard entropy content of one mole of a substance under a standard state}}
In [[chemistry]], the '''standard molar entropy''' is the [[entropy]] content of one [[mole (unit)|mole]] of pure substance at a [[standard state]] of pressure and any temperature of interest. These are often (but not necessarily) chosen to be the [[standard temperature and pressure]].

The standard molar entropy at pressure = <math>P^0</math> is usually given the symbol {{mvar|S°}}, and has units of [[joule]]s per [[Mole (unit)|mole]] per [[kelvin]] (J⋅mol<sup>−1</sup>⋅K<sup>−1</sup>). Unlike [[Standard enthalpy of formation|standard enthalpies of formation]], the value of {{mvar|S°}} is absolute. That is, an element in its standard state has a definite, nonzero value of {{mvar|S}} at [[room temperature]]. The entropy of a pure [[crystalline]] structure can be 0{{nbsp}}J⋅mol<sup>−1</sup>⋅K<sup>−1</sup> only at 0{{nbsp}}K, according to the [[third law of thermodynamics]]. However, this assumes that the material forms a '[[perfect crystal]]' without any [[residual entropy]]. This can be due to [[crystallographic defect]]s, [[dislocations]], and/or incomplete rotational quenching within the solid, as originally pointed out by [[Linus Pauling]].<ref>{{cite book |last1=Pauling |first1=Linus |title=The Nature of the Chemical Bond |date=1960 |publisher=Cornell University Press |location=Ithaca, NY |edition=3rd}}</ref> These contributions to the entropy are always present, because crystals always grow at a finite rate and at temperature. However, the residual entropy is often quite negligible and can be accounted for when it occurs using [[statistical mechanics]]. 

==Thermodynamics==
If a [[mole (unit)|mole]] of a solid substance is a perfectly ordered solid at 0{{nbsp}}K, then if the solid is warmed by its surroundings to 298.15{{nbsp}}K without melting, its absolute molar entropy would be the sum of a series of {{mvar|N}} stepwise and reversible entropy changes. The limit of this sum as <math>N \rightarrow \infty </math> becomes an integral:
:<math>S^\circ = \sum_{k=1}^N \Delta S_k = \sum_{k=1}^N \frac{dQ_k}{T} \rightarrow \int _0 ^{T_2} \frac{dS}{dT} dT = \int _0 ^{T_2} \frac {C_{p_k}}{T} dT</math>
In this example, <math>T_2 =298.15 K </math> and <math>C_{p_k}</math> is the [[molar heat capacity]] at a constant pressure of the substance in the [[reversible process (thermodynamics)|reversible process]] {{mvar|k}}. The molar heat capacity is not constant during the experiment because it changes depending on the (increasing) temperature of the substance. Therefore, a table of values for <math>\frac{C_{p_k}}{T}</math> is required to find the total molar entropy. The quantity
<math>\frac{dQ_{k}}{T}</math> represents the ratio of a very small exchange of heat energy to the temperature {{mvar|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 [[Standard temperature and pressure|STP]] includes contributions from:<ref>{{cite book|last=Kosanke|first=K.|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{{nbsp}}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|last1=Chang|first1=Raymond|last2=Cruickshank|first2=Brandon|title=Chemistry|publisher=[[McGraw-Hill Higher Education]]|year=2005|isbn=0-07-251264-4|chapter=Entropy, Free Energy and Equilibrium|page=765}}</ref>
:<math>{\Delta S^\circ}_{rxn} = S^\circ_{products} - S^\circ_{reactants}</math>

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:
:<math>(\Delta S_{total} = \Delta S_{system} + \Delta S_{surroundings})>0</math>
Molar entropy is not the same for all gases. Under identical conditions, it is greater for a heavier gas.

==See also==
*[[Entropy]]
*[[Heat]]
*[[Gibbs free energy]]
*[[Helmholtz free energy]]
*[[Standard state]]
*[[Third law of thermodynamics]]

==References==
{{reflist}}

==External links==
*[https://chem.libretexts.org/Bookshelves/General_Chemistry/Chemistry_1e_(OpenSTAX)/Appendices/Standard_Thermodynamic_Properties_for_Selected_Substances Table of Standard Thermodynamic Properties for Selected Substances]

[[Category:Chemical properties]]
[[Category:Thermodynamic entropy]]
[[Category:Molar quantities]]