**Glossary**

### Activity Coefficient

A knowledge of the variation with temperature and composition of the activity of component k, a_{k}, or the activity coefficient of k, γ_{k}, is of primary importance in solution thermodynamics. This is required for the determination of the partial molar Gibbs energy of mixing of the component; which again is required for the determination of equilibrium state of any chemical reaction involving component k in the solid solution. Generally, the variation of a_{k} or γ_{k} with temperature and composition must be determined experimentally.

The activity coefficient is a unitless thermodynamic function. If γ_{k} = 1 (an ideal solution), the activity of component k is equal to its mole fraction and the behavior of k, from the point of view of its chemical potential, is completely determined by its composition. If γ_{k} > 1 (a nonideal solution where the component k is said to exhibit a positive deviation from Raoult's law), then a_{k} > x_{k} and in the evaluation of its chemical potential, component k "acts as if" the solution contains more of k than the mole fraction suggests. Similarly, if γ_{k} < 1 (a nonideal solution where the component k exhibits a negative deviation from Raoult's law) so that a_{k} < x_{k}, the component "acts as if" there is less of it present than the composition suggests.

In general, the higher the temperature of a nonideal solution, the smaller the deviation of its components from ideal behavior. In other words, if γ_{k} > 1 then an increase in temperature causes γ_{k} to decrease toward 1, and if γ_{k} < 1 an increase in temperature causes γ_{k} to increase toward 1.

The relationship between the activity coefficient of k, temperature, and the partial molar heat of solution of k, ΔH_{k}^{M}, is given as

∂(R·ln γ_{k}) / ∂(1/T) = ΔH_{k}^{M}

Thus, if γ_{k} > 1 then ΔH_{k}^{M} is a positive quantity, indicating that the mixing process is **endothermic**. Conversely, if γ_{k} < 1 then ΔH_{k}^{M} is a negative quantity, indicating that the mixing process is **exothermic**.

In an A-B binary system, endothermic mixing indicates a tendency toward **phase separation** or **clustering** in the solution. The A-A and B-B attractions are greater than A-B attractions, i.e., the A atoms attempt to be coordinated only by A atoms, and the B atoms attempt to be coordinated only by B atoms. Conversely, exothermic mixing indicates a tendency toward **compound formation** or **ordering** between the two components. The A-B attractions are greater than either A-A or B-B attractions, i.e., the A atoms attempt to have only B atoms as nearest neighbors, and the B atoms attempt to have only A atoms as nearest neighbors.

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