# 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 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°).   (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.  IUPAC recommends using a standard pressure p = 105  Pa.  Strictly speaking, temperature is not part of the definition of a standard state. For example, as discussed below, the standard state of a gas is conventionally chosen to be unit pressure (usually in bar) ideal gas, regardless of the temperature. 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). 

The standard state should not be confused with standard temperature and pressure (STP) for gases,  nor with the standard solutions used in analytical chemistry.  STP is commonly used for calculations involving gases that approximate an ideal gas, whereas standard state conditions are used for thermodynamic calculations. 

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.

### 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 (105 Pa, or 1 bar). 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. 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. 

### Solutes

For a substance in solution (solute), the standard state is the hypothetical state it would have at the standard state molality or amount concentration but exhibiting infinite-dilution behavior. 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. Standard state molality is 1 molkg1, while standard state amount concentration is 1 moldm3.

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) 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).  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 a relative coverage based standard state and in additional column an 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. 

## 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.  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.  A range of similar symbols are used in the literature: a stroked lowercase letter O (o),  a superscript zero (0)  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).   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 ).

## Related Research Articles In statistical mechanics, entropy is an extensive property of a thermodynamic system. It quantifies the number Ω of microscopic configurations that are consistent with the macroscopic quantities that characterize the system. Under the assumption that each microstate is equally probable, the entropy is the natural logarithm of the number of microstates, multiplied by the Boltzmann constant kB. Formally, Enthalpy is a property of a thermodynamic system, that is a convenient state function preferred in many measurements in chemical, biological, and physical systems at a constant pressure. It is defined as the sum of the system's internal energy and the product of its pressure and volume. 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 environment. As a state function, enthalpy depends only on the final configuration of internal energy, pressure, and volume, and not on the path taken to achieve it.

Standard temperature and pressure are standard sets of conditions for experimental measurements to be established to allow comparisons to be made between different sets of data. The most used standards are those of the International Union of Pure and Applied Chemistry (IUPAC) and the National Institute of Standards and Technology (NIST), although these are not universally accepted standards. Other organizations have established a variety of alternative definitions for their standard reference conditions. 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 a 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. Thermodynamic temperature is the absolute measure of temperature and is one of the principal parameters of 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 solute present in an ideal solution: a concentration of exactly one mole per liter (1 M) at a pressure of 1 bar
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. An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics.

In chemistry, the standard molar entropy is the entropy content of one mole of substance under a standard state.

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. This reflects the corresponding mathematical ideas of mean and measure, respectively. In thermodynamics, the Gibbs free energy is a thermodynamic potential that can be used to calculate the maximum of reversible work that may be performed by a thermodynamic system at a constant temperature and pressure. The Gibbs free energy (, measured in joules in SI) is the maximum amount of non-expansion work that can be extracted from a thermodynamically closed system. This maximum can be attained only in a completely reversible process. When a system transforms reversibly from an initial state to a final state, the decrease in Gibbs free energy equals the work done by the system to its surroundings, minus the work of the pressure forces.

In chemistry, an ideal solution or ideal mixture is a solution in which the gas phase 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 behaviour of the solution becomes. The vapor pressure of the solution obeys either Raoult's law or Henry's law, and the activity coefficient of each component is equal to one.

In chemistry, the amount of substance in a given sample of matter is defined as the number of discrete atomic-scale particles in it divided by the Avogadro constant NA. In a truly atomistic view, the amount of substance is simply the number of particles that constitute the substance. The particles or entities may be molecules, atoms, ions, electrons, or other, depending on the context. The value of the Avogadro constant NA has been defined as 6.02214076×1023 mol−1. In the truly atomistic view, 1 mol = 6.02214076×1023 particles (the Avogadro number) and therefore the conversion constant is simply NA = 1. The amount of substance is sometimes 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.

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.

The enthalpy of mixing is the enthalpy liberated or absorbed from a substance upon mixing. When a substance or compound is combined with any other substance or compound the enthalpy of mixing is the consequence of the new interactions between the two substances or compounds. This enthalpy if released exothermically can in an extreme case cause an explosion.

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• IUPAC–IUB–IUPAB Interunion Commission of Biothermodynamics (1976). "Recommendations for measurement and presentation of biochemical equilibrium data" (PDF). J. Biol. Chem. 251 (22): 6879–85.
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