Editing Entropy (section)

=== Entropy in chemical thermodynamics ===
Thermodynamic entropy is central in [[chemical thermodynamics]], enabling changes to be quantified and the outcome of reactions predicted. The [[second law of thermodynamics]] states that entropy in an [[isolated system]] — the combination of a subsystem under study and its surroundings — increases during all spontaneous chemical and physical processes. The [[Clausius theorem|Clausius equation]] introduces the measurement of entropy change which describes the direction and quantifies the magnitude of simple changes such as heat transfer between systems — always from hotter body to cooler one spontaneously.

Thermodynamic entropy is an [[Intensive and extensive properties|extensive]] property, meaning that it scales with the size or extent of a system. In many processes it is useful to specify the entropy as an [[Intensive and extensive properties|intensive property]] independent of the size, as a specific entropy characteristic of the type of system studied. Specific entropy may be expressed relative to a unit of mass, typically the kilogram (unit: J⋅kg<sup>−1</sup>⋅K<sup>−1</sup>). Alternatively, in chemistry, it is also referred to one [[Mole (unit)|mole]] of substance, in which case it is called the ''molar entropy'' with a unit of J⋅mol<sup>−1</sup>⋅K<sup>−1</sup>.

Thus, when one mole of substance at about {{val|0|u=K}} is warmed by its surroundings to {{val|298|u=K}}, the sum of the incremental values of <math display="inline">q_\mathsf{rev} / T</math> constitute each element's or compound's standard molar entropy, an indicator of the amount of energy stored by a substance at {{val|298|u=K}}.<ref name="ctms">{{Cite book|last=Moore|first=J. W.|author2=C. L. Stanistski|author3=P. C. Jurs|title=Chemistry, The Molecular Science|publisher=Brooks Cole|year=2005|isbn=978-0-534-42201-1|url-access=registration|url=https://archive.org/details/chemistrymolecul0000moor}}</ref><ref name="Jungermann">{{cite journal|last1=Jungermann|first1=A.H.|s2cid=18081336|year=2006|title=Entropy and the Shelf Model: A Quantum Physical Approach to a Physical Property|journal=Journal of Chemical Education|volume=83|issue=11|pages=1686–1694|doi=10.1021/ed083p1686|bibcode = 2006JChEd..83.1686J}}</ref> Entropy change also measures the mixing of substances as a summation of their relative quantities in the final mixture.<ref>{{Cite book|last=Levine|first=I. N.|title=Physical Chemistry, 5th ed.|url=https://archive.org/details/physicalchemistr00levi_1|url-access=registration|publisher=McGraw-Hill|year=2002|isbn=978-0-07-231808-1}}</ref>

Entropy is equally essential in predicting the extent and direction of complex chemical reactions. For such applications, <math display="inline">\Delta S</math> must be incorporated in an expression that includes both the system and its surroundings: <math display="block">\Delta S_\mathsf{universe} = \Delta S_\mathsf{surroundings} + \Delta S_\mathsf{system}</math>Via additional steps this expression becomes the equation of [[Gibbs free energy]] change <math display="inline">\Delta G</math> for reactants and products in the system at the constant pressure and temperature <math display="inline">T</math>:<math display="block">\Delta G = \Delta H - T\ \Delta S</math>where <math display="inline">\Delta H</math> is the [[enthalpy]] change and <math display="inline">\Delta S</math> is the entropy change.<ref name="ctms" />
{| class="wikitable"
!'''ΔH'''
!'''ΔS'''
!'''Spontaneity'''
!'''Example'''
|-
| +
| +
|Spontaneous '''at high ''T'''''
|Ice melting
|-
|–
|–
|Spontaneous '''at low ''T'''''
|Water freezing
|-
|–
| +
|Spontaneous '''at all ''T'''''
|Propane combustion
|-
| +
|–
|'''Non-spontaneous''' at all ''T''
|Ozone formation
|}
The spontaneity of a chemical or physical process is governed by the [[Gibbs free energy]] change (ΔG), as defined by the equation ΔG = ΔH − TΔS, where ΔH represents the enthalpy change, ΔS the entropy change, and T the temperature in Kelvin. A negative ΔG indicates a thermodynamically favorable ([[Spontaneous process|spontaneous]]) process, while a positive ΔG denotes a non-spontaneous one. When both ΔH and ΔS are positive ([[Endothermic process|endothermic]], entropy-increasing), the reaction becomes spontaneous at sufficiently high temperatures, as the TΔS term dominates. Conversely, if both ΔH and ΔS are negative (exothermic, entropy-decreasing), spontaneity occurs only at low temperatures, where the enthalpy term prevails. Reactions with ΔH < 0 and ΔS > 0 ([[Exothermic process|exothermic]] and entropy-increasing) are spontaneous at all temperatures, while those with ΔH > 0 and ΔS < 0 (endothermic and entropy-decreasing) are non-spontaneous regardless of temperature. These principles underscore the interplay between energy exchange, disorder, and temperature in determining the direction of natural processes, from phase transitions to biochemical reactions.
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