In 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.
Definition The relative activity of a species i, denoted ai, is defined as:
a i = e μ i − μ i ⊖ R T {\displaystyle a_{i}=e^{\frac {\mu _{i}-\mu _{i}^{\ominus }}{RT}}}
where μi is the (molar) chemical potential of the species i under the conditions of interest, μoi is the (molar) chemical potential of that species under some defined set of standard conditions, R is the gas constant, T is the thermodynamic temperature and e is the exponential constant. Alternatively, this equation can be written as:
μ i = μ i ⊖ + R T ln a i {\displaystyle \mu _{i}=\mu _{i}^{\ominus }+RT\ln {a_{i}}}
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. Depending on the circumstances, some of these factors, in particular concentration and interactions, may be more important than others. The activity depends on the choice of standard state such that changing the standard state will also change the activity. This means that activity is a relative term that describes how "active" a compound is compared to when it is under the standard state conditions. 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", λ, which is written as:
λ i = e μ i R T {\displaystyle \lambda _{i}=e^{\frac {\mu _{i}}{RT}}\,}
Note that this definition corresponds to setting as standard state the solution of μ i = 0 {\displaystyle \mu _{i}=0} , if the latter exists.
Activity coefficient
The activity coefficient γ, which is also a dimensionless quantity, relates the activity to a measured mole fraction xi (or yi in the gas phase), molality bi, mass fraction wi, molar concentration (molarity) ci or mass concentration ρi:
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