# Properties of salt solutions

### Activity coefficient

The figure to the right shows the mean ionic activity coefficient of calcium nitrate at 0°C, calculated with the Extended UNIQUAC model. Experimental data from Calahorro C.V., Alvaro J.H., and Gonzalez D.L. “Coefficientes de actividad media de los iones H^{+}, Mg^{2+}, Ca^{2+}, Sr^{2+}, Ba^{2+} en disoluciones acuosas de sus correspondientos nitratos”, Anales de Quimica 75(1979)833-838 are plotted along with the calculated data. The experimental measurements were done in the dilute region, while the calculated data extend to the solubility limit og calcium nitrate at 0°C. The mean ionic activity coefficients is one of the important properties of salt solutions.

The mean activity coefficient γ_{± }of Ca(NO_{3})_{2} is defined by the equation:

Due to the nature of the thermodynamic model, activity coefficients are calculated for each single ion. The calculated single ion activity coefficients can be used for calculating mean ionic activity coefficients. These single ion activity coefficients do not represent the thermodynamic value of the single ion activity coefficient measured experimentally. According to many researchers, single ion activity coefficients can not be measured experimentally at all (F. Malatesta “The Impossibility of Measuring Individual Ion Activity Coefficients Using Ion Selective Electrodes”, Journal of Solution Chemistry, Vol. 29, No. 9, 2000, https://doi.org/10.1023/A:1005137929282).

### Osmotic coefficient

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_{4}calculated at 50°C with the Extended UNIQUAC model. Experimental data from Bhatnagar and Campbell, Osmotic Coefficients of Sodium Sulphate in water from 50 to 150°C, Canadian journal of chemistry 59(1981)123-126, https://doi.org/10.1139/v81-019 are plotted along with the calculated data. If the water activity was plotted as a function of the molality of salt, the result would be an almost straight line. In order to reflect the behavior of salts at high dilutiuon, the water activity is usually expressed as osmotic coefficient. The osmotic coefficient is given the symbol Φ and is defined:

a_{w }is the activity of water M_{w} is the molar mass of water in kg/mol, *ν* is the number of ions formed when one mol of salt is dissolved in water, *m*_{s} is the molality (mol/kg H_{2}O) of salt, n_{w} is the amount of water and n_{s} is the amount of salt, both in mol. At high dilution, the water activity is close to 1 and the logarithm to the water activity is close to 0. By dividing the logarithm of the water activity by the number of moles of ions present at these conditions, the osmotic coefficient reflects the concentration dependence of the water activity in much more detail than the water activity itself does.

### Heat of dilution

The enthalpy change per mole of salt associated with the dilution of a salt solution from molality m1 to molality m2 at constant temperature is the integral heat of dilution, ΔH(m1→m2). The differential heat of dilution is the enthalpy change by adding a differential amount of solvent to a solution.

The integral heat of dilution to infinite dilution is the enthalpy change by diluting a salt solution from a certain molality to infinite dilution. The integral heat of dilution to infinite dilution is the negative of he relative enthalpy. The relative enthalpy is the excess enthalpy relative to the unsymmetric standard state. In this standard state, activity coefficients tend to 1 as the concentration is decreased towards infinite dilution.

On the graph to below, experimental values of the integral heat of dilution of ammonia solutions to infinite dilution are plotted together with values calculated with the Extended UNIQUAC model.

### Heat of solution

The integral heat of solution is the enthalpy change by dissolving crystalline salt to form a solution of molality m. The differential heat of solution is the enthalpy change when a differential amount of salt is dissolved in a solution. When the solute is a gas, the corresponding concepts integral heat of absorption and differential heat of absorption are used.

### Apparent molal heat capacity

The apparent molal heat capacity of a salt is the heat capacity of an aqueous solution of one mol of the salt minus the heat capacity of the corresponding amount of pure water. The apparent molal heat capacity therefore indicates the apparent effect of adding salt to water.

In some cases the heat capacity decreases below that of pure water in other cases it increases. The defining equation for the apparent molal heat capacity C_{pφ} is:

### Further reading on properties of salt solutions

The programming guide for the Extended UNIQUAC model gives details about deriving these properties of salt solutions from the Gibbs excess function. General definitions and derivations of the properties can be found in “Electrolyte Solutions: Thermodynamics, Crystallization, Separation methods”, https://doi.org/10.11581/dtu:00000073