# Standard state

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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 superscript circle ° (degree symbol) or a Plimsoll (⦵) character is used to designate a thermodynamic quantity in the standard state, such as change in enthalpyH°), change in entropyS°), or change in Gibbs free energyG°). [1] [2] The degree symbol has become widespread, although the Plimsoll is recommended in standards, see discussion about typesetting below.

## Contents

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 ΔHf = 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]

### 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. [10] [11] 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). [12] 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.

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). [13] 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. [13]

## Typesetting

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. [14] 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. [15] A range of similar symbols are used in the literature: a stroked lowercase letter O (o), [16] a superscript zero (0) [17] or a circle with a horizontal bar either where the bar extends beyond the boundaries of the circle ( U+29B5CIRCLE WITH HORIZONTAL BAR) or is enclosed by the circle, dividing the circle in half (U+2296CIRCLED MINUS). [18] [19] When compared to the plimsoll symbol used on vessels, the horizontal bar should extend beyond the boundaries of the circle; care should be taken not to confuse the symbol with the Greek letter theta (uppercase Θ or ϴ, lowercase θ ).

Ian M. Mills, who was involved in producing a revision of Quantities, Units and Symbols in Physical Chemistry , suggested that a superscript zero (${\displaystyle ^{0}}$) is an equal alternative to indicate "standard state", though a degree symbol (°) is used in the same article. [19] The degree symbol has come into widespread use in general, inorganic, and physical chemistry textbooks in recent years. [20] [21] [22]

## Related Research Articles

Enthalpy, a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant pressure, which is conveniently provided by the large ambient atmosphere. The pressure–volume term expresses the work required to establish the system's physical dimensions, i.e. to make room for it by displacing its surroundings. The pressure-volume term is very small for solids and liquids at common conditions, and fairly small for gases. Therefore, enthalpy is a stand-in for energy in chemical systems; bond, lattice, solvation and other "energies" in chemistry are actually enthalpy differences. As a state function, enthalpy depends only on the final configuration of internal energy, pressure, and volume, not on the path taken to achieve it.

In chemistry, a solution is a special type of homogeneous mixture composed of two or more substances. In such a mixture, a solute is a substance dissolved in another substance, known as a solvent. The mixing process of a solution happens at a scale where the effects of chemical polarity are involved, resulting in interactions that are specific to solvation. The solution usually has the state of the solvent when the solvent is the larger fraction of the mixture, as is commonly the case. One important parameter of a solution is the concentration, which is a measure of the amount of solute in a given amount of solution or solvent. The term "aqueous solution" is used when one of the solvents is water.

The enthalpy of vaporization, also known as the (latent) heat of vaporization or heat of evaporation, is the amount of energy (enthalpy) that must be added to a liquid substance to transform a quantity of that substance into a gas. The enthalpy of vaporization is a function of the pressure at which that transformation takes place.

The thermodynamic free energy is a concept useful in the thermodynamics of chemical or thermal processes in engineering and science. The change in the free energy is the maximum amount of work that a thermodynamic system can perform in a process at constant temperature, and its sign indicates whether the process is thermodynamically favorable or forbidden. Since free energy usually contains potential energy, it is not absolute but depends on the choice of a zero point. Therefore, only relative free energy values, or changes in free energy, are physically meaningful.

Solvation describes the interaction of solvent with dissolved molecules. Both ionized and uncharged molecules interact strongly with solvent, and the strength and nature of this interaction influence many properties of the solute, including solubility, reactivity, and color, as well as influencing the properties of the solvent such as the viscosity and density. In the process of solvation, ions are surrounded by a concentric shell of solvent. Solvation is the process of reorganizing solvent and solute molecules into solvation complexes. Solvation involves bond formation, hydrogen bonding, and van der Waals forces. Solvation of a solute by water is called hydration.

In chemistry and thermodynamics, the standard enthalpy of formation or standard heat of formation of a compound is the change of enthalpy during the formation of 1 mole of the substance from its constituent elements, with all substances in their standard states. The standard pressure value p = 105 Pa(= 100 kPa = 1 bar) is recommended by IUPAC, although prior to 1982 the value 1.00 atm (101.325 kPa) was used. There is no standard temperature. Its symbol is ΔfH. The superscript Plimsoll on this symbol indicates that the process has occurred under standard conditions at the specified temperature (usually 25 °C or 298.15 K). Standard states are as follows:

1. For a gas: the hypothetical state it would have assuming it obeyed the ideal gas equation at a pressure of 1 bar
2. For a gaseous or solid solute present in a diluted ideal solution: the hypothetical state of concentration of the solute of exactly one mole per liter (1 M) at a pressure of 1 bar extrapolated from infinite dilution
3. For a pure substance or a solvent in a condensed state (a liquid or a solid): the standard state is the pure liquid or solid under a pressure of 1 bar
4. For an element: the form in which the element is most stable under 1 bar of pressure. One exception is phosphorus, for which the most stable form at 1 bar is black phosphorus, but white phosphorus is chosen as the standard reference state for zero enthalpy of formation.

In chemistry, solubility is the ability of a substance, the solute, to form a solution with another substance, the solvent. Insolubility is the opposite property, the inability of the solute to form such a solution.

In chemistry, the standard molar entropy is the entropy content of one mole of pure substance at a standard state of pressure and any temperature of interest. These are often chosen to be the standard temperature and pressure.

In chemical thermodynamics, activity is a measure of the "effective concentration" of a species in a mixture, in the sense that the species' chemical potential depends on the activity of a real solution in the same way that it would depend on concentration for an ideal solution. The term "activity" in this sense was coined by the American chemist Gilbert N. Lewis in 1907.

Physical properties of materials and systems can often be categorized as being either intensive or extensive, according to how the property changes when the size of the system changes. According to IUPAC, an intensive quantity is one whose magnitude is independent of the size of the system, whereas an extensive quantity is one whose magnitude is additive for subsystems.

In thermodynamics, the Gibbs free energy is a thermodynamic potential that can be used to calculate the maximum amount of work that may be performed by a thermodynamically closed system at constant temperature and pressure. It also provides a necessary condition for processes such as chemical reactions that may occur under these conditions.

In chemistry, a mixture is a material made up of two or more different chemical substances which are not chemically bonded. A mixture is the physical combination of two or more substances in which the identities are retained and are mixed in the form of solutions, suspensions and colloids.

In chemistry, an ideal solution or ideal mixture is a solution that exhibits thermodynamic properties analogous to those of a mixture of ideal gases. The enthalpy of mixing is zero as is the volume change on mixing by definition; the closer to zero the enthalpy of mixing is, the more "ideal" the behavior of the solution becomes. The vapor pressures of the solvent and solute obey Raoult's law and Henry's law, respectively, and the activity coefficient is equal to one for each component.

In chemistry, the amount of substance n in a given sample of matter is defined as the quantity or number of discrete atomic-scale particles in it divided by the Avogadro constant NA. The particles or entities may be molecules, atoms, ions, electrons, or other, depending on the context, and should be specified (e.g. amount of sodium chloride nNaCl). The value of the Avogadro constant NA has been defined as 6.02214076×1023 mol−1. The mole (symbol: mol) is a unit of amount of substance in the International System of Units, defined (since 2019) by fixing the Avogadro constant at the given value. Sometimes, the amount of substance is referred to as the chemical amount.

In chemical thermodynamics, the fugacity of a real gas is an effective partial pressure which replaces the mechanical partial pressure in an accurate computation of the chemical equilibrium constant. It is equal to the pressure of an ideal gas which has the same temperature and molar Gibbs free energy as the real gas.

An activity coefficient is a factor used in thermodynamics to account for deviations from ideal behaviour in a mixture of chemical substances. In an ideal mixture, the microscopic interactions between each pair of chemical species are the same and, as a result, properties of the mixtures can be expressed directly in terms of simple concentrations or partial pressures of the substances present e.g. Raoult's law. Deviations from ideality are accommodated by modifying the concentration by an activity coefficient. Analogously, expressions involving gases can be adjusted for non-ideality by scaling partial pressures by a fugacity coefficient.

In thermodynamics, the entropy of mixing is the increase in the total entropy when several initially separate systems of different composition, each in a thermodynamic state of internal equilibrium, are mixed without chemical reaction by the thermodynamic operation of removal of impermeable partition(s) between them, followed by a time for establishment of a new thermodynamic state of internal equilibrium in the new unpartitioned closed system.

ISO 31-8 is the part of international standard ISO 31 that defines names and symbols for quantities and units related to physical chemistry and molecular physics.

Thermodynamic databases contain information about thermodynamic properties for substances, the most important being enthalpy, entropy, and Gibbs free energy. Numerical values of these thermodynamic properties are collected as tables or are calculated from thermodynamic datafiles. Data is expressed as temperature-dependent values for one mole of substance at the standard pressure of 101.325 kPa, or 100 kPa. Unfortunately, both of these definitions for the standard condition for pressure are in use.

This glossary of chemistry terms is a list of terms and definitions relevant to chemistry, including chemical laws, diagrams and formulae, laboratory tools, glassware, and equipment. Chemistry is a physical science concerned with the composition, structure, and properties of matter, as well as the changes it undergoes during chemical reactions; it features an extensive vocabulary and a significant amount of jargon.

## References

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• 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:.
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20. 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. "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.
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