Standard State

A standard state is a reference state chosen by convention for describing the properties of substances in thermodynamics. It specifies how a substance’s reference properties are defined, including its physical phase, pressure, and, where relevant, composition and idealized behavior. A standard state may be hypothetical rather than experimentally realizable. Its purpose is to provide a consistent basis for comparing thermodynamic data and calculating changes associated with chemical reactions. Different definitions apply to gases, pure condensed substances, and dissolved solutes. (old.goldbook.iupac.org)

Pressure, temperature, and notation

The recommended standard pressure is

Here, pressure is expressed using the pascal, the pressure unit of the International System of Units. IUPAC recommended this value in 1982; previously, $101\,325\ \mathrm{Pa}$, equivalent to one standard atmosphere, was commonly used. Older thermodynamic tables may therefore employ a different reference pressure. (goldbook.iupac.org)

A standard state does not imply a fixed temperature. Standard thermodynamic quantities are defined at a specified temperature and can be evaluated at different temperatures. Many tables use $298.15\ \mathrm{K}$, or $25\,^\circ\mathrm{C}$, but that temperature is not inherent in the definition. Numerical data should identify both the temperature and the standard-state convention. A superscript circle or the standard-state symbol $⦵$ distinguishes standard quantities, such as standard enthalpy, $H^\circ$, and standard entropy, $S^\circ$. (publications.iupac.org)

Definitions for different substances

Gases. The standard state is the hypothetical pure gas at standard pressure, behaving as an ideal gas. It is not necessarily the actual state of the real gas at one bar. Ideal behavior defines the reference even when intermolecular interactions cause measurable departures from that behavior. (old.goldbook.iupac.org)

Pure liquids and solids. The standard state is the pure substance in the specified liquid or solid phase at standard pressure. The phase must be identified: liquid and solid forms have different reference properties. For a component treated using a pure-substance convention, the same reference can be used when that component occurs in a mixture. (old.goldbook.iupac.org)

Solutes. The usual standard state is hypothetical: the solute has a specified standard concentration or molality while retaining the behavior characteristic of infinite dilution. Common choices are a standard molar concentration of $1\ \mathrm{mol\,dm^{-3}}$ or a standard molality of $1\ \mathrm{mol\,kg^{-1}}$. The latter measures amount of solute per mass of solvent. This reference does not assert that a real solution at either concentration is ideal. The solvent and concentration scale are part of the specification. (old.goldbook.iupac.org)

Chemical potential and activity

Standard states enter calculations through the chemical potential, $\mu_i$, and thermodynamic activity, $a_i$, of component $i$:

Here, $\mu_i^\circ$ is the standard chemical potential, $R$ is the molar gas constant, and $T$ is absolute temperature. Activity is dimensionless; the equation gives $a_i=1$ when the chemical potential equals its standard value. Both the activity and standard chemical potential depend on the chosen convention. (goldbook.iupac.org)

For a gas using the ideal-gas standard state,

where $f_i$ is its fugacity. In an ideal gas mixture, fugacity equals partial pressure, so $a_i=p_i/p^\circ$. For a solute on the molality scale,

where $\gamma_i$ is the activity coefficient. Under the infinite-dilution convention, this coefficient approaches unity as the solution becomes infinitely dilute. (mail.goldbook.iupac.org)

Changing the standard state changes the numerical division between $\mu_i^\circ$ and $RT\ln a_i$, not the physical chemical potential. Consequently, activities and tabulated standard quantities must use compatible conventions. (goldbook.iupac.org)

Reaction quantities and equilibrium

For a reaction with stoichiometric coefficients $\nu_i$, positive for products and negative for reactants, the standard reaction Gibbs energy is

The reaction Gibbs energy at the actual composition is

where $Q$ is the reaction quotient. The standard quantity refers to the participants’ reference states, rather than their actual concentrations or pressures in a reacting mixture. (media.iupac.org)

At chemical equilibrium, $\Delta_{\mathrm r}G=0$, giving

The thermodynamic equilibrium constant, $K^\circ$, is dimensionless because it is constructed from activities. A negative standard reaction Gibbs energy corresponds to $K^\circ>1$; the direction of change in a particular mixture nevertheless depends on its reaction quotient. (goldbook.iupac.org)

Related reference conventions

Standard state should be distinguished from standard temperature and pressure (STP). STP specifies a particular temperature–pressure pair for gases: IUPAC’s standard conditions are $273.15\ \mathrm{K}$ and $10^5\ \mathrm{Pa}$. Standard-state thermodynamics instead permits different specified temperatures and includes composition conventions for solutions. (goldbook.iupac.org)

An elemental reference state is another related concept: it identifies the form of a chemical element used as the thermochemical reference at a given temperature and standard pressure. NIST’s reference-state table lists gaseous molecular hydrogen and oxygen, and crystalline graphite for carbon. Identifying an elemental reference form is distinct from defining standard-state properties for every possible phase of that element. (goldbook.iupac.org)