# Physics:Standard state

Short description: Reference point (°) used to calculate the properties of a material under different conditions

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°). 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. 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. 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).

### 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. 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.

### 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). 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. 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). 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.

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. The degree symbol has come into widespread use in general, inorganic, and physical chemistry textbooks in recent years.