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Measure of the effective concentration of a species in a mixture
In chemical thermodynamics, activity (symbol a) 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. By convention, activity is treated as a dimensionless quantity, although its value depends on customary choices of standard state for the species. The activity of pure substances in condensed phases (solids and liquids) is taken as a = 1. Activity depends on temperature, pressure and composition of the mixture, among other things. For gases, the activity is the effective partial pressure, and is usually referred to as fugacity. The difference between activity and other measures of concentration arises because the interactions between different types of molecules in non ideal gases or solutions are different from interactions between the same types of molecules. The activity of an ion is particularly influenced by its surroundings. Equilibrium constants should be defined by activities but, in practice, are often defined by concentrations instead. The same is often true of equations for reaction rates. However, there are circumstances where the activity and the concentration are significantly different and, as such, it is not valid to approximate with concentrations where activities are required. Two examples serve to illustrate this point:
In a solution of potassium hydrogen iodate KH(IO3)2 at 0.02 M the activity is 40% lower than the calculated hydrogen ion concentration, resulting in a much higher pH than expected. When a 0.1 M hydrochloric acid solution containing methyl green indicator is added to a 5 M solution of magnesium chloride, the color of the indicator changes from green to yellow—indicating increasing acidity—when in fact the acid has been diluted. Although at low ionic strength (< 0.1 M) the activity coefficient approaches unity, this coefficient can actually increase with ionic strength in a high ionic strength regime. For hydrochloric acid solutions, the minimum is around 0.4 M.

The most direct way of measuring the activity of a volatile species is to measure its equilibrium partial vapor pressure. For water as solvent, the water activity aw is the equilibrated relative humidity. 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. However, in such cases it is possible to measure the vapor pressure of the solvent instead. Using the Gibbs–Duhem relation it is possible to translate the change in solvent vapor pressures with concentration into activities for the solute. The simplest way of determining how the activity of a component depends on pressure is by measurement of densities of solution, knowing that real solutions have deviations from the additivity of (molar) volumes of pure components compared to the (molar) volume of the solution. 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. There are also electrochemical methods that allow the determination of activity and its coefficient. The value of the mean ionic activity coefficient γ± of ions in solution can also be estimated with the Debye–Hückel equation, the Davies equation or the Pitzer equations.

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. However, chemists have not given up the idea of single ion activities. For example, pH is defined as the negative logarithm of the hydrogen ion activity. 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. Nevertheless, the concept of single ion activities continues to be discussed in the literature, and at least one author purports to define single ion activities in terms of purely thermodynamic quantities. The same author also proposes a method of measuring single ion activity coefficients based on purely thermodynamic processes.

Example values of activity coefficients of sodium chloride in aqueous solution are given in the table. In an ideal solution, these values would all be unity. The deviations tend to become larger with increasing molality and temperature, but with some exceptions. +Activity coefficients of sodium chloride in aqueous solutionMolality (mol/kg) 25 °C 50 °C 100 °C 200 °C 300 °C 350 °C 0.05 0.820 0.814 0.794 0.725 0.592 0.473 0.50 0.680 0.675 0.644 0.619 0.322 0.182 2.00 0.669 0.675 0.641 0.450 0.212 0.074 5.00 0.873 0.886 0.803 0.466 0.167 0.044