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. 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 (solid or liquids) is normally taken as unity (the number 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 composition arises because molecules in non-ideal gases or solutions interact with each other, either to attract or to repel each other. The activity of an ion is particularly influenced by its surroundings. Activities should be used to define equilibrium constants but, in practice, concentrations are often used 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 ( i, is defined as: : where μi is the chemical potential of the species under the conditions of interest, μoi is the chemical potential of that species in the chosen standard state, R is the gas constant, T is the thermodynamic temperature and e is Euler’s number. This definition can also be written in terms of the chemical potential: : Hence the activity will depend on any factor that alters the chemical potential. These include temperature, pressure, chemical environment, etc. In specialised cases, other factors may have to be considered, such as the presence of an electric or magnetic field or the position in a gravitational field. However, the most common use of activity is to describe the variation in chemical potential with the composition of a mixture. The activity also depends on the choice of standard state, as it describes the difference between an actual chemical potential and a standard chemical potential. In principle, the choice of standard state is arbitrary, although there are certain conventional standard states which are usually used in different situations. Absolute activity does not require a standard state. Activity coefficient The activity coefficient γ, which is also a dimensionless quantity, relates the activity to a measured amount fraction xi (or yi in the gas phase), molality bi, mass fraction wi, amount concentration ci or mass concentration ρi: : The division by the standard molality bo or the standard amount concentration co is necessary to ensure that both the activity and the activity coefficient are dimensionless, as is conventional. The activity is the same regardless of the ways to express composition and the standard state chosen so the above expressions are equal. When the activity coefficient is close to one, the substance shows almost ideal behaviour according to Henry’s law. In these cases, the activity can be substituted with the appropriate dimensionless measure of composition xi, bi/bo or ci/co. It is also possible to define an activity coefficient in terms of Raoult’s law: the International Union of Pure and Applied Chemistry (IUPAC) recommends the symbol ƒ for this activity coefficient, although this should not be confused with fugacity. .

Richard Goodwin

Richard Goodwin has been working as a tech journalist for over 10 years. He has written for Den of Geek, Fortean Times, IT PRO, PC Pro, ALPHR, and many other technology sites. He is the editor and owner of KnowYourMobile.

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