Standard state

In chemistry, the standard state of a material (pure substance, mixture or solution) is a reference point used to calculate its properties under different conditions. A degree sign (°) or a superscript Plimsoll symbol (^⦵) is used to designate a thermodynamic quantity in the standard state, such as change in enthalpy (ΔH°), change in entropy (ΔS°), or change in Gibbs free energy (ΔG°).^[1]^[2] The degree symbol has become widespread, although the Plimsoll is recommended in standards, see discussion about 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.^[3] The standard state should not be confused with standard temperature and pressure (STP) for gases,^[4] nor with the standard solutions used in analytical chemistry.^[5] STP is commonly used for calculations involving gases that approximate an ideal gas, whereas standard state conditions are used for thermodynamic calculations.^[6]

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 K and 10⁵ 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 298.15 K (25.00 °C; 77.00 °F) or, somewhat less commonly, 273.15 K (0.00 °C; 32.00 °F).^[6]

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^⦵ or P° equal to 10⁵ Pa, or 1 bar.^[7]^[8] 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 10⁵ Pa (or 1 bar). For most elements, the reference point of Δ_fH^⦵ = 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 metastable.^[9] This is because the thermodynamically stable black allotrope is difficult to prepare pure.^[10]

Solutes

For a substance in solution (solute), the standard state 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).^[8] 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 1 mol/kg, while the standard state molarity is 1 mol/dm³.

Other choices are possible. For example, the use of a standard state concentration of 10⁻⁷ mol/L for the hydrogen ion in a real, aqueous solution is common in the field of biochemistry.^[11]^[12] 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 1 mol/dm³).^[13] 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 isotherm) the most common standard state is a relative coverage of θ° = 0.5, as this choice results in a cancellation of the configurational entropy term and is also consistent with neglecting to include the standard state (which is a common error).^[14] The advantage of using 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.^[14]

Typesetting

This section contains uncommon Unicode characters. Without proper rendering support, you may see question marks, boxes, or other symbols instead of the intended characters.

At the time of development in the nineteenth century, the superscript Plimsoll symbol (^⦵) was adopted to indicate the non-zero nature of the standard state.^[15] 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.^[16] A range of similar symbols are used in the literature: a stroked lowercase letter O (^o),^[17] a superscript zero (⁰)^[18] or a circle with a horizontal bar either where the bar extends beyond the boundaries of the circle (U+29B5 ⦵ CIRCLE WITH HORIZONTAL BAR) or is enclosed by the circle, dividing the circle in half (U+2296 ⊖ CIRCLED MINUS).^[19]^[20] 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 ϴ, lowercase θ ). As of 2024, the character U+1CEF0 𜻰 <RESERVED-1CEF0> has been proposed for Unicode. It is a regular-sized Unicode symbol meant to be used in superscripted form when denoting standard state, replacing U+29B5 for this purpose.^[21]^[22]

Ian M. Mills, who was involved in producing a revision of Quantities, Units and Symbols in Physical Chemistry, suggested that a superscript zero ( $^{0}$ ) is an equal alternative to indicate "standard state", though a degree symbol (°) is used in the same article.^[20] The degree symbol has come into widespread use in general, inorganic, and physical chemistry textbooks in recent years.^[23]^[24]^[25] When read out loud, the symbol is pronounced "naught".

References

International Union of Pure and Applied Chemistry (1982). "Notation for states and processes, significance of the word standard in chemical thermodynamics, and remarks on commonly tabulated forms of thermodynamic functions" (PDF). Pure Appl. Chem. 54 (6): 1239–50. doi:10.1351/pac198254061239. S2CID 53868401.
IUPAC–IUB–IUPAB Interunion Commission of Biothermodynamics (1976). "Recommendations for measurement and presentation of biochemical equilibrium data". J. Biol. Chem. 251 (22): 6879–85. doi:10.1016/S0021-9258(17)32917-4.

^ Toolbox, Engineering (2017). "Standard state and enthalpy of formation, Gibbs free energy of formation, entropy and heat capacity". Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!. www.EngineeringToolBox.com. Retrieved 2019-12-27.
^ Helmenstine, PhD, Ann Marie (March 8, 2019). "What Are Standard State Conditions? - Standard Temperature and Pressure". Science, Tech, Math > Science. thoughtco.com. Retrieved 2019-12-27.
^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "standard state". doi:10.1351/goldbook.S05925
^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "standard conditions for gases". doi:10.1351/goldbook.S05910
^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "standard solution". doi:10.1351/goldbook.S05924
^ ^a ^b Helmenstine, PhD, Ann Marie (July 6, 2019). "Standard Conditions Versus Standard State". Science, Tech, Math > Science. thoughtco.com. Retrieved 2020-09-06.
^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "standard pressure". doi:10.1351/goldbook.S05921
^ ^a ^b "Activities and their Effects on Equilibria". Chemistry LibreTexts. 29 January 2016.
^ Housecroft C.E. and Sharpe A.G., Inorganic Chemistry (2nd ed., Pearson Prentice-Hall 2005) p.392
^ Rard, Joseph A.; Wolery, Thomas J. (2007). "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". Journal of Solution Chemistry. 36: 1585–1599. doi:10.1007/s10953-007-9205-7. Retrieved 24 December 2023. 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.
^ Chang, Raymond; Thoman, John W. Jr. (2014). Physical Chemistry for the Chemical Sciences. New York: University Science Books. pp. 346–347.
^ Sherwood, Dennis; Dalby, Paul (2018). Modern Thermodynamics for Chemists and Biochemists. Oxford Scholarship Online. doi:10.1093/oso/9780198782957.003.0023. ISBN 978-0-19-878295-7. Retrieved 18 May 2021.
^ Chang, Raymond; Thoman, John W. Jr. (2014). Physical Chemistry for the Chemical Sciences. New York: University Science Books. pp. 228–231.
^ ^a ^b Savara, Aditya (2013). "Standard States for Adsorption on Solid Surfaces: 2D Gases, Surface Liquids, and Langmuir Adsorbates". J. Phys. Chem. C. 117 (30): 15710–15715. doi:10.1021/jp404398z.
^ Prigogine, I. & Defay, R. (1954) Chemical thermodynamics, p. xxiv
^ 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
^ IUPAC (1993) Quantities, units and symbols in physical chemistry (also known as The Green Book) (2nd ed.), p. 51
^ Narayanan, K. V. (2001) A Textbook of Chemical Engineering Thermodynamics (8th printing, 2006), p. 63
^ "Miscellaneous Mathematical Symbols-B" (PDF). Unicode. 2013. Retrieved 2013-12-19.
^ ^a ^b 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.]
^ Soiffer, Neil; Sargent, Murray; Freytag, Asmus (20 October 2023). "Proposal for Ten Chemical Symbols" (PDF). Retrieved 25 December 2023.
^ "Recommendations to UTC #177 November 2023 on Script Proposals" (PDF). 1 November 2023. Retrieved 25 December 2023.
^ Flowers, Paul; Theopold, Klaus; Langley, Richard; Robinson, William R.; Frantz, Don; Hooker, Paul; Kaminski, George; Look, Jennifer; Martinez, Carol; Eklund, Andrew; Blaser, Mark; Sorensen, Tom; Soult, Allison; Milliken, Troy; Moravec, Vicki; Powell, Jason; El-Giar, Emad; Bott, Simon; Carpenetti, Don (14 February 2019). "5.3 Enthalpy". Chemistry 2e. Open Stax. Retrieved 9 April 2022. We will include a superscripted "o" in the enthalpy change symbol to designate standard state.
^ Miessler, Gary L.; Fischer, Paul J.; Tarr, Donald A. (2014). Inorganic Chemistry (5th ed.). New Jersey: Pearson Education. p. 438.
^ Chang, Raymond; Thoman, John W. Jr. (2014). Physical Chemistry for the Chemical Sciences. New York: University Science Books. p. 101. The symbol for a standard state is a 'circle' superscript

[Toolbox-1] Toolbox, Engineering (2017). "Standard state and enthalpy of formation, Gibbs free energy of formation, entropy and heat capacity". Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!. www.EngineeringToolBox.com. Retrieved 2019-12-27.

[Thought-2] Helmenstine, PhD, Ann Marie (March 8, 2019). "What Are Standard State Conditions? - Standard Temperature and Pressure". Science, Tech, Math > Science. thoughtco.com. Retrieved 2019-12-27.

[GB1-3] IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "standard state". doi:10.1351/goldbook.S05925

[4] IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "standard conditions for gases". doi:10.1351/goldbook.S05910

[5] IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "standard solution". doi:10.1351/goldbook.S05924

[Thought2-6] Helmenstine, PhD, Ann Marie (July 6, 2019). "Standard Conditions Versus Standard State". Science, Tech, Math > Science. thoughtco.com. Retrieved 2020-09-06.

[7] IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "standard pressure". doi:10.1351/goldbook.S05921

[libretext-8] "Activities and their Effects on Equilibria". Chemistry LibreTexts. 29 January 2016.

[9] Housecroft C.E. and Sharpe A.G., Inorganic Chemistry (2nd ed., Pearson Prentice-Hall 2005) p.392

[10] Rard, Joseph A.; Wolery, Thomas J. (2007). "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". Journal of Solution Chemistry. 36: 1585–1599. doi:10.1007/s10953-007-9205-7. Retrieved 24 December 2023. 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.

[11] Chang, Raymond; Thoman, John W. Jr. (2014). Physical Chemistry for the Chemical Sciences. New York: University Science Books. pp. 346–347.

[12] Sherwood, Dennis; Dalby, Paul (2018). Modern Thermodynamics for Chemists and Biochemists. Oxford Scholarship Online. doi:10.1093/oso/9780198782957.003.0023. ISBN 978-0-19-878295-7. Retrieved 18 May 2021.

[13] Chang, Raymond; Thoman, John W. Jr. (2014). Physical Chemistry for the Chemical Sciences. New York: University Science Books. pp. 228–231.

[Savara-14] Savara, Aditya (2013). "Standard States for Adsorption on Solid Surfaces: 2D Gases, Surface Liquids, and Langmuir Adsorbates". J. Phys. Chem. C. 117 (30): 15710–15715. doi:10.1021/jp404398z.

[15] Prigogine, I. & Defay, R. (1954) Chemical thermodynamics, p. xxiv

[16] 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

[17] IUPAC (1993) Quantities, units and symbols in physical chemistry (also known as The Green Book) (2nd ed.), p. 51

[18] Narayanan, K. V. (2001) A Textbook of Chemical Engineering Thermodynamics (8th printing, 2006), p. 63

[19] "Miscellaneous Mathematical Symbols-B" (PDF). Unicode. 2013. Retrieved 2013-12-19.

[Mills-20] 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.]

[21] Soiffer, Neil; Sargent, Murray; Freytag, Asmus (20 October 2023). "Proposal for Ten Chemical Symbols" (PDF). Retrieved 25 December 2023.

[22] "Recommendations to UTC #177 November 2023 on Script Proposals" (PDF). 1 November 2023. Retrieved 25 December 2023.

[23] Flowers, Paul; Theopold, Klaus; Langley, Richard; Robinson, William R.; Frantz, Don; Hooker, Paul; Kaminski, George; Look, Jennifer; Martinez, Carol; Eklund, Andrew; Blaser, Mark; Sorensen, Tom; Soult, Allison; Milliken, Troy; Moravec, Vicki; Powell, Jason; El-Giar, Emad; Bott, Simon; Carpenetti, Don (14 February 2019). "5.3 Enthalpy". Chemistry 2e. Open Stax. Retrieved 9 April 2022. We will include a superscripted "o" in the enthalpy change symbol to designate standard state.

[24] Miessler, Gary L.; Fischer, Paul J.; Tarr, Donald A. (2014). Inorganic Chemistry (5th ed.). New Jersey: Pearson Education. p. 438.

[25] Chang, Raymond; Thoman, John W. Jr. (2014). Physical Chemistry for the Chemical Sciences. New York: University Science Books. p. 101. The symbol for a standard state is a 'circle' superscript

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Standard state

Conventional standard states

Gases

Liquids and solids

Solutes

Adsorbates

Typesetting

See also

References

Ahmad Al-Habsyi

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Diadem

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