# 4.3: Activity and Activity Coefficients

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Up to this point in the course we have assumed that the solutions with which we are dealing are what are called ideal solutions. However, real solutions will deviate from this kind of behavior. In the case of gases, fugacity is a parameter that can be used to accommodate for deviations from ideal models. Likewise, in solutions, the parameter called activity is used to allow for the deviation of real solutes from limiting ideal behavior. The activity of a solute A is related to its concentration by

$a_A=\gamma \dfrac{m_A}{m^o}$

where $$\gamma$$ is the activity coefficient, $$m_A$$ is the molality of the solute A, and $$m^o$$ is unit molality. The activity coefficient is unitless in this definition, and so the activity itself is also unitless. Furthermore, the activity coefficient approaches unity as the molality of the solute approaches zero, meanng that dilute solutions behave ideally. The use of activity to describe the solute allows us to use the simple model for chemical potential by inserting the activity of a solute in place of its mole fraction:

$\mu_A =\mu_A^o + RT \ln a_A$

In Water Chemistry, Mark Benjamin defines activity coefficient, via a rearrangement of the first equation above, as the ratio of two activities: the activity per mole or per molecule in the actual state of interest, divided by the activity per mole or per molecule in the reference state (standard state). Because the activities are expressed per mole or per molecule, they could be expressed as 'per concentration.' Likewise, the activity of a solute in the standard state is defined as 1. So, the activity coefficient expression simplifies to:

$\gamma_A=\dfrac{activity_A}{C_{A-real}/C_{A-std state}}$

The problem that then remains is the measurement of the activity coefficients themselves, which may depend on temperature, pressure, and even concentration. Fortunately, some theoretical and empirical relationships have been developed to estimate activity coefficients based on the charge of an ion, the abundance of other ions in the solution (termed ionic strength), and the properties of the solvent (often water). Some of these methods are presented in the next section.