Thermodynamic activity

[1] By convention, activity is treated as a dimensionless quantity, although its value depends on customary choices of standard state for the species.

Alternatively, this equation can be written as: In general, the activity depends on any factor that alters the chemical potential.

Such factors may include: concentration, temperature, pressure, interactions between chemical species, electric fields, etc.

In principle, the choice of standard state is arbitrary; however, it is often chosen out of mathematical or experimental convenience.

Alternatively, it is also possible to define an "absolute activity" (i.e., the fugacity in statistical mechanics), λ, which is written as: Note that this definition corresponds to setting as standard state the solution of

The most convenient way of expressing the composition of a generic mixture is by using the mole fractions xi (written yi in the gas phase) of the different components (or chemical species: atoms or molecules) present in the system, where The standard state of each component in the mixture is taken to be the pure substance, i.e. the pure substance has an activity of one.

Therefore, one introduces the notions of where ν = ν+ + ν– represent the stoichiometric coefficients involved in the ionic dissociation process Even though γ+ and γ– cannot be determined separately, γ± is a measurable quantity that can also be predicted for sufficiently dilute systems using Debye–Hückel theory.

For non-volatile components, such as sucrose or sodium chloride, this approach will not work since they do not have measurable vapor pressures at most temperatures.

This involves the use of partial molar volumes, which measure the change in chemical potential with respect to pressure.

Another way to determine the activity of a species is through the manipulation of colligative properties, specifically freezing point depression.

Using freezing point depression techniques, it is possible to calculate the activity of a weak acid from the relation, where b′ is the total equilibrium molality of solute determined by any colligative property measurement (in this case ΔTfus), b is the nominal molality obtained from titration and a is the activity of the species.

The prevailing view that single ion activities are unmeasurable, or perhaps even physically meaningless, has its roots in the work of Edward A. Guggenheim in the late 1920s.

By implication, if the prevailing view on the physical meaning and measurability of single ion activities is correct it relegates pH to the category of thermodynamically unmeasurable quantities.

For this reason the International Union of Pure and Applied Chemistry (IUPAC) states that the activity-based definition of pH is a notional definition only and further states that the establishment of primary pH standards requires the application of the concept of 'primary method of measurement' tied to the Harned cell.

The same author also proposes a method of measuring single ion activity coefficients based on purely thermodynamic processes.

Solid and liquid activities do not depend very strongly on pressure because their molar volumes are typically small.