Editing Thermodynamic activity (section)

==Definition==
The relative activity of a species {{mvar|i}}, denoted {{mvar|a<sub>i</sub>}}, is defined<ref name="GoldBook">{{GoldBookRef|title=activity (relative activity), ''a''|file=A00115}}</ref><ref name="GreenBook">{{GreenBookRef2nd|pages=49–50}}</ref> as:
:<math>a_i = e^{\frac{\mu_i - \mu^{\ominus}_i}{RT}}</math>
where {{mvar|μ<sub>i</sub>}} is the (molar) [[chemical potential]] of the species {{mvar|i}} under the conditions of interest, {{math|''μ''{{su|p=<s>o</s>|b=''i''}}}} is the (molar) chemical potential of that species under some defined set of standard conditions, {{mvar|R}} is the [[gas constant]], {{mvar|T}} is the [[thermodynamic temperature]] and {{mvar|e}} is [[e (mathematical constant)|the exponential constant]].

Alternatively, this equation can be written as:
:<math>\mu_i = \mu_i^{\ominus} + RT\ln{a_i}</math>

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", {{mvar|λ}}, which is written as:

:<math>\lambda_i = e^{\frac{\mu_i}{RT}}\,</math>

Note that this definition corresponds to setting as standard state the solution of <math>\mu_i = 0</math>, if the latter exists.

===Activity coefficient===
{{Main|Activity coefficient}}
The activity coefficient {{mvar|γ}}, which is also a dimensionless quantity, relates the activity to a measured [[mole fraction]] {{mvar|x<sub>i</sub>}} (or {{mvar|y<sub>i</sub>}} in the gas phase), [[molality]] {{mvar|b<sub>i</sub>}}, [[mass fraction (chemistry)|mass fraction]] {{mvar|w<sub>i</sub>}},  [[molar concentration]] (molarity) {{mvar|c<sub>i</sub>}} or [[mass concentration (chemistry)|mass concentration]] {{mvar|ρ<sub>i</sub>}}:<ref name="McQuarrie&Simon"> McQuarrie, D. A.; Simon, J. D. ''Physical Chemistry – A Molecular Approach'', p. 990 & p. 1015 (Table 25.1), University Science Books, 1997. </ref> 
:<math>a_{ix} = \gamma_{x,i} x_i,\ a_{ib} = \gamma_{b,i}\frac {b_i} {b^{\ominus}},\, a_{iw}=\gamma_{w,i} w_i,\ a_{ic} = \gamma_{c,i} \frac{c_i}{c^{\ominus}},\, a_{ir} = \gamma_{\rho,i} \frac{\rho_i}{\rho^{\ominus}}\, </math>

The division by the standard molality {{math|''b''<sup><s>o</s></sup>}} (usually 1 mol/kg) or the standard molar concentration {{math|''c''<sup><s>o</s></sup>}} (usually 1 mol/L) is necessary to ensure that both the activity and the activity coefficient are dimensionless, as is conventional.<ref name="GreenBook"/>

The activity depends on the chosen standard state and composition scale;<ref name="McQuarrie&Simon"/> for instance, in the dilute limit it approaches the mole fraction, mass fraction, or numerical value of molarity, all of which are different. However, the activity coefficients are similar.{{citation needed|date=February 2022}}

When the activity coefficient is close to 1, the substance shows almost ideal behaviour according to [[Henry's law]] (but not necessarily in the sense of an [[ideal solution]]). In these cases, the activity can be substituted with the appropriate dimensionless measure of composition {{mvar|x<sub>i</sub>}}, {{math|{{sfrac|''b<sub>i</sub>''|''b''<sup><s>o</s></sup>}}}} or {{math|{{sfrac|''c<sub>i</sub>''|''c''<sup><s>o</s></sup>}}}}. 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 {{mvar|f}} for this activity coefficient,<ref name="GreenBook"/> although this should not be confused with [[fugacity]].
:<math>a_i = f_i x_i\,</math>