View source for Standard state

{{Short description|Reference point (°) used to calculate the properties of a material under different conditions}}
{{distinguish|Standard conditions for temperature and pressure|Standard sea-level conditions}}

The '''standard state''' of a material (pure [[chemical substance|substance]], mixture or [[Solution (chemistry)|solution]]) is a reference point used to calculate its properties under different conditions. A degree sign (°) or a superscript [[Plimsoll line|Plimsoll]] symbol (<sup>⦵</sup>) is used to designate a thermodynamic quantity in the standard state, such as change in [[enthalpy]] (Δ''H''°), change in [[entropy]] (Δ''S''°), or change in [[Gibbs free energy]] (Δ''G''°).<ref name="Toolbox">{{cite web | last = Toolbox | first = Engineering | title = Standard state and enthalpy of formation, Gibbs free energy of formation, entropy and heat capacity| work = Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications! | publisher = www.EngineeringToolBox.com   | date = 2017 | url = https://www.engineeringtoolbox.com/standard-state-enthalpy-formation-definition-value-Gibbs-free-energy-entropy-molar-heat-capacity-d_1978.html  | access-date = 2019-12-27 }}</ref><ref name="Thought">{{cite web | last = Helmenstine, PhD | first = Ann Marie | title = What Are Standard State Conditions? - Standard Temperature and Pressure | work = Science, Tech, Math > Science | publisher = thoughtco.com | date = March 8, 2019 | url = https://www.thoughtco.com/standard-state-conditions-overview-609256  | access-date = 2019-12-27 }}</ref> The degree symbol has become widespread, although the Plimsoll is recommended in standards, see discussion about typesetting [[#Typesetting|below]].

In principle, the choice of standard state is arbitrary, although the [[International Union of Pure and Applied Chemistry]] (IUPAC) recommends a conventional set of standard states for general use.<ref name="GB1">{{GoldBookRef| file=S05925 | title = standard state}}</ref> The standard state should not be confused with [[standard temperature and pressure]] (STP) for gases,<ref>{{GoldBookRef | file = S05910 | title = standard conditions for gases}}</ref> nor with the [[standard solution]]s used in [[analytical chemistry]].<ref>{{GoldBookRef | file=S05924 | title = standard solution}}</ref> STP is commonly used for calculations involving gases that approximate an [[ideal gas]], whereas standard state conditions are used for [[Thermodynamics|thermodynamic]] calculations.<ref name="Thought2">{{cite web | last = Helmenstine, PhD | first = Ann Marie | title = Standard Conditions Versus Standard State | work = Science, Tech, Math > Science | publisher = thoughtco.com | date = July 6, 2019 | url = https://www.thoughtco.com/difference-between-standard-conditions-state-607534  | access-date = 2020-09-06 }}</ref>

For a given material or substance, the standard state is the '''reference state''' for the material's thermodynamic state properties such as [[enthalpy]], [[entropy]], [[Gibbs free energy]], and for many other material standards. The [[standard enthalpy change of formation]] for an element in its standard state is zero, and this convention allows a wide range of other thermodynamic quantities to be calculated and tabulated. The standard state of a substance does not have to exist in nature: for example, it is possible to calculate values for [[steam]] at 298.15&nbsp;K and {{val|e=5|ul=Pa}}, although steam does not exist (as a gas) under these conditions. The advantage of this practice is that tables of thermodynamic properties prepared in this way are self-consistent.

== Conventional standard states ==
Many standard states are non-physical states, often referred to as "hypothetical states". Nevertheless, their thermodynamic properties are well-defined, usually by an extrapolation from some limiting condition, such as zero pressure or zero concentration, to a specified condition (usually unit concentration or pressure) using an ideal extrapolating function, such as ideal solution or ideal gas behavior, or by empirical measurements. Strictly speaking, temperature is not part of the definition of a standard state. However, most tables of thermodynamic quantities are compiled at specific temperatures, most commonly [[Room temperature#Definitions in science and industry|room temperature]] ({{convert|298.15|K|C F|0|disp=comma}}), or, somewhat less commonly, the [[freezing point]] of [[water]] ({{convert|273.15|K|C F|0|disp=comma}}).<ref name="Thought2" />

=== Gases ===
The standard state for a gas is the hypothetical state it would have as a pure substance obeying the [[ideal gas equation]] at standard pressure. IUPAC recommends using a standard pressure ''p''<sup>⦵</sup> or P° equal to {{val|e=5|u=Pa}}, or 1 bar.<ref>{{GoldBookRef| file=S05921 | title = standard pressure}}</ref><ref name="libretext">{{cite web |title=Activities and their Effects on Equilibria |url=https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Physical_Properties_of_Matter/Solutions_and_Mixtures/Nonideal_Solutions/Activities_and_their_Effects_on_Equilibria |website=Chemistry LibreTexts |language=en |date=29 January 2016}}</ref> No real gas has perfectly ideal behavior, but this definition of the standard state allows corrections for non-ideality to be made consistently for all the different gases.

=== Liquids and solids ===
The standard state for liquids and solids is simply the state of the pure substance subjected to a total pressure of {{val|e=5|u=Pa}} (or 1 [[bar (unit)|bar]]). For most elements, the reference point of Δ<sub>f</sub>''H''<sup>⦵</sup>&nbsp;= 0 is defined for the most stable [[allotrope]] of the element, such as [[graphite]] in the case of [[carbon]], and the β-phase ([[white tin]]) in the case of [[tin]]. An exception is white [[phosphorus]], the most common allotrope of phosphorus, which is defined as the standard state despite the fact that it is only [[metastability|metastable]].<ref>Housecroft C.E. and Sharpe A.G., ''Inorganic Chemistry'' (2nd ed., Pearson Prentice-Hall 2005) p.392</ref> This is because the thermodynamically stable black allotrope is difficult to prepare pure.<ref>{{cite journal |last1=Rard |first1=Joseph A. |last2=Wolery |first2=Thomas J. |date=2007 |title=The Standard Chemical-Thermodynamic Properties of Phosphorus and Some of its Key Compounds and Aqueous Species: An Evaluation of Differences between the Previous Recommendations of NBS/NIST and CODATA |url=https://link.springer.com/article/10.1007/s10953-007-9205-7 |journal=Journal of Solution Chemistry |volume=36 |issue= |pages=1585–1599 |doi=10.1007/s10953-007-9205-7 |access-date=24 December 2023 |quote=Although white phosphorus is not the thermodynamically stable allotrope, the red and black forms are difficult to prepare in pure form, which makes them less suitable for quantitative thermodynamic measurements.}}</ref>

=== Solutes ===
For a substance in solution (solute), the standard state {{not a typo|C°}} is usually chosen as the hypothetical state it would have at the standard state [[molality]] or [[amount concentration]] but exhibiting infinite-dilution behavior (where there are no solute-solute interactions, but solute-solvent interactions are present).<ref name="libretext"/> The reason for this unusual definition is that the behavior of a solute at the limit of infinite dilution is described by equations which are very similar to the equations for ideal gases. Hence taking infinite-dilution behavior to be the standard state allows corrections for non-ideality to be made consistently for all the different solutes. The standard state molality is {{val|1|u=mol/kg}}, while the standard state molarity is {{val|1|u=mol/dm3}}.

Other choices are possible. For example, the use of a standard state concentration of 10<sup>−7</sup>&nbsp;mol/L for the hydrogen ion in a real, aqueous solution is common in the field of [[biochemistry]].<ref>{{cite book |last1=Chang |first1=Raymond | last2=Thoman | first2=John W. Jr. |title=Physical Chemistry for the Chemical Sciences |date=2014|publisher=University Science Books |location=New York |pages=346–347}}</ref><ref>{{cite book |last1=Sherwood |first1=Dennis |last2=Dalby |first2=Paul |title=Modern Thermodynamics for Chemists and Biochemists |date=2018 |publisher=Oxford Scholarship Online |doi=10.1093/oso/9780198782957.003.0023 |isbn=978-0-19-878295-7 |url=https://oxford.universitypressscholarship.com/view/10.1093/oso/9780198782957.001.0001/oso-9780198782957-chapter-23 |access-date=18 May 2021}}</ref> In other application areas such as [[electrochemistry]], the standard state is sometimes chosen as the actual state of the real solution at a standard concentration (often {{val|1|u=mol/dm3}}).<ref>{{cite book |last1=Chang |first1=Raymond | last2=Thoman | first2=John W. Jr. |title=Physical Chemistry for the Chemical Sciences |date=2014 |publisher=University Science Books |location=New York |pages=228–231}}</ref> The [[activity coefficients]] will not transfer from convention to convention and so it is very important to know and understand what conventions were used in the construction of tables of standard thermodynamic properties before using them to describe solutions.

=== Adsorbates ===
For molecules adsorbed on surfaces there have been various conventions proposed based on hypothetical standard states. For adsorption that occurs on specific sites ([[Langmuir adsorption model|Langmuir adsorption isotherm]]) the most common standard state is a relative coverage of {{nowrap|''θ''° {{=}} 0.5}}, as this choice results in a cancellation of the [[configuration entropy|configurational entropy]] term and is also consistent with neglecting to include the standard state (which is a common error).<ref name="Savara">{{cite journal |doi=10.1021/jp404398z |title=Standard States for Adsorption on Solid Surfaces: 2D Gases, Surface Liquids, and Langmuir Adsorbates |journal=J. Phys. Chem. C |volume=117 |pages=15710–15715  |year=2013 |last1=Savara |first1=Aditya |issue=30 |doi-access= }}</ref>  The advantage of using {{nowrap|''θ''° {{=}} 0.5}} is that the configurational term cancels and the [[entropy]] extracted from thermodynamic analyses is thus reflective of intra-molecular changes between the bulk phase (such as gas or liquid) and the adsorbed state. There may be benefit to tabulating values based on both the relative coverage based standard state and in an additional column the absolute coverage based standard state. For 2D gas states, the complication of discrete states does not arise and an absolute density base standard state has been proposed, similar for the 3D gas phase.<ref name="Savara" />

== Typesetting ==
{{Contains special characters|Uncommon Unicode|section}}
At the time of development in the nineteenth century, the superscript [[Plimsoll symbol]] (<sup>⦵</sup>) was adopted to indicate the non-zero nature of the standard state.<ref>Prigogine, I. & Defay, R. (1954) ''Chemical thermodynamics'', p. xxiv</ref> [[IUPAC]] recommends in the 3rd edition of ''[[Quantities, Units and Symbols in Physical Chemistry]]'' a symbol which seems to be a degree sign (°) as a substitute for the plimsoll mark. In the very same publication the plimsoll mark appears to be constructed by combining a horizontal stroke with a degree sign.<ref>E.R. Cohen, T. Cvitas, J.G. Frey, B. Holmström, K. Kuchitsu, R. Marquardt, I. Mills, F. Pavese, M. Quack, J. Stohner, H.L. Strauss, M. Takami, and A.J. Thor, "Quantities, Units and Symbols in Physical Chemistry", IUPAC Green Book, 3rd Edition, 2nd Printing, IUPAC & RSC Publishing, Cambridge (2008), p. 60</ref> A range of similar symbols are used in the literature: a stroked lowercase letter O (<sup><s>o</s></sup>),<ref>IUPAC (1993) ''Quantities, units and symbols in physical chemistry'' (also known as ''The Green Book'') (2nd ed.), p. 51</ref> a superscript zero (<sup>0</sup>)<ref>Narayanan, K. V. (2001) ''A Textbook of Chemical Engineering Thermodynamics'' (8th printing, 2006), p. 63</ref> or a circle with a horizontal bar either where the bar extends beyond the boundaries of the circle ({{Unichar|29B5|Circle with horizontal bar|ulink=}}) or is enclosed by the circle, dividing the circle in half ({{Unichar|2296|Circled minus}}).<ref>{{cite web|url=https://www.unicode.org/charts/PDF/U2980.pdf| publisher=Unicode| title=Miscellaneous Mathematical Symbols-B|date=2013|access-date=2013-12-19}}</ref><ref name=Mills>Mills, I. M. (1989) "The choice of names and symbols for quantities in chemistry". ''Journal of Chemical Education'' (vol. 66, number 11, November 1989 p. 887–889) [Note that Mills refers to the symbol ⊖ (Unicode 2296 "Circled minus" as displayed in https://www.unicode.org/charts/PDF/U2980.pdf) as a plimsoll symbol although it lacks an extending bar in the printed article.]</ref> Compared to the plimsoll symbol used in 1800s text, the U+29B5 glyph is too large and its horizontal line does not sufficiently extend beyond the boundaries of the circle. It is easily confused with the Greek letter [[theta]] (uppercase Θ or {{not a typo|ϴ}}, lowercase θ). As of 2024, the character {{Unichar|1CEF0|Medium small white circle with horizontal bar}} has been proposed for Unicode.<ref>{{cite web |title=Proposed New Characters: The Pipeline |url=https://www.unicode.org/alloc/Pipeline.html |website=www.unicode.org |access-date=15 June 2024}}</ref> It is a regular-sized Unicode symbol meant to be used in superscripted form when denoting standard state, replacing U+29B5 for this purpose.<ref>{{cite web |last1=Soiffer |first1=Neil |last2=Sargent |first2=Murray |last3=Freytag |first3=Asmus |title=Proposal for Ten Chemical Symbols |url=https://www.unicode.org/L2/L2023/23193r2-ten-chemical-symbols.pdf |access-date=25 December 2023 |date=20 October 2023}}</ref><ref>{{cite web |title=Recommendations to UTC #177 November 2023 on Script Proposals |url=https://www.unicode.org/L2/L2023/23238r-script-adhoc-rept.pdf |access-date=25 December 2023 |date=1 November 2023}}</ref>

Ian M. Mills, who was involved in producing a revision of ''[[Quantities, Units and Symbols in Physical Chemistry]]'', suggested that a superscript zero (<math>^0</math>) is an equal alternative to indicate "standard state", though a degree symbol (°) is used in the same article.<ref name=Mills/> The degree symbol has come into widespread use in general, inorganic, and physical chemistry textbooks in recent years.<ref>{{cite book|last1=Flowers |first1=Paul |last2=Theopold |first2=Klaus |last3=Langley |first3=Richard |last4=Robinson |first4=William R. |last5=Frantz |first5=Don |last6=Hooker |first6=Paul |last7=Kaminski |first7=George |last8=Look |first8=Jennifer |last9=Martinez |first9=Carol |last10=Eklund |first10=Andrew |last11=Blaser |first11=Mark |last12=Sorensen |first12=Tom |last13=Soult |first13=Allison |last14=Milliken |first14=Troy |last15=Moravec |first15=Vicki |last16=Powell |first16=Jason |last17=El-Giar |first17=Emad |last18=Bott |first18=Simon |last19=Carpenetti |first19=Don |title=Chemistry 2e |chapter-url= https://openstax.org/books/chemistry-2e/pages/5-3-enthalpy#term235|chapter=5.3 Enthalpy |date=14 February 2019 |publisher=Open Stax |access-date=9 April 2022|quote=We will include a superscripted "o" in the enthalpy change symbol to designate standard state.}}</ref><ref>{{cite book |last1=Miessler |first1=Gary L. |last2=Fischer |first2=Paul J. |last3=Tarr |first3=Donald A. |title=Inorganic Chemistry |date=2014 |publisher=Pearson Education |location=New Jersey |edition=5th|page=438}}</ref><ref>{{cite book |last1=Chang |first1=Raymond | last2=Thoman | first2=John W. Jr. |title=Physical Chemistry for the Chemical Sciences |date=2014 |publisher=University Science Books |location=New York|page=101|quote=The symbol for a standard state is a 'circle' superscript}}</ref> When read out loud, the symbol is pronounced "naught".

== See also ==
* [[Standard conditions for temperature and pressure]]
* [[Standard molar entropy]]

== References ==
* {{cite journal | author = International Union of Pure and Applied Chemistry | author-link = International Union of Pure and Applied Chemistry | year = 1982 | title = Notation for states and processes, significance of the word ''standard'' in chemical thermodynamics, and remarks on commonly tabulated forms of thermodynamic functions | url = http://media.iupac.org/publications/pac/1982/pdf/5406x1239.pdf | journal = [[Pure and Applied Chemistry|Pure Appl. Chem.]] | volume = 54 | issue = 6 | pages = 1239–50 | doi = 10.1351/pac198254061239| s2cid = 53868401 }}
* {{cite journal | author = IUPAC–IUB–IUPAB Interunion Commission of Biothermodynamics | year = 1976 | title = Recommendations for measurement and presentation of biochemical equilibrium data | url = https://www.jbc.org/article/S0021-9258(17)32917-4/pdf | journal = [[Journal of Biological Chemistry|J. Biol. Chem.]] | volume = 251 | issue = 22 | pages = 6879–85| doi = 10.1016/S0021-9258(17)32917-4 | doi-access = free }}
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[[Category:Thermodynamics]]

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