Osmotic coefficient explained
An osmotic coefficient
is a quantity which characterises the deviation of a
solvent from
ideal behaviour, referenced to
Raoult's law. It can be also applied to solutes. Its definition depends on the ways of expressing
chemical composition of mixtures.
The osmotic coefficient based on molality m is defined by:
and on a mole fraction basis by:
where
is the
chemical potential of the pure solvent and
is the
chemical potential of the solvent in a solution,
MA is its
molar mass,
xA its
mole fraction,
R the
gas constant and
T the
temperature in
Kelvin. The latter osmoticcoefficient is sometimes called the
rational osmotic coefficient. The values for the two definitions are different, but since
the two definitions are similar, and in fact both approach 1 as the concentration goes to zero.
Applications
For liquid solutions, the osmotic coefficient is often used to calculate the salt activity coefficient from the solvent activity, or vice versa. For example, freezing point depression measurements, or measurements of deviations from ideality for other colligative properties, allows calculation of the salt activity coefficient through the osmotic coefficient.
Relation to other quantities
In a single solute solution, the (molality based) osmotic coefficient and the solute activity coefficient
are related to the
excess Gibbs free energy
by the relations:
and there is thus a differential relationship between them (temperature and pressure held constant):
d((\phi-1)m)=md(ln\gamma)
Liquid electrolyte solutions
For a single salt solute with molal activity (
), the osmotic coefficient can be written as
where
is the stochiometric number of salt and
the activity of the solvent.
can be calculated from the salt activity coefficient via:
[1] \phi=1+
md\left(ln(\gamma\pm)\right)
Moreover, the activity coefficient of the salt
can be calculated from:
[2]
According to Debye–Hückel theory, which is accurate only at low concentrations, is asymptotic to , where I is ionic strength and A is the Debye–Hückel constant (equal to about 1.17 for water at 25 °C).
This means that, at least at low concentrations, the vapor pressure of the solvent will be greater than that predicted by Raoult's law. For instance, for solutions of magnesium chloride, the vapor pressure is slightly greater than that predicted by Raoult's law up to a concentration of 0.7 mol/kg, after which the vapor pressure is lower than Raoult's law predicts. For aqueous solutions, the osmotic coefficients can be calculated theoretically by Pitzer equations[3] or TCPC model.[4] [5] [6] [7]
See also
Notes and References
- Book: Pitzer, Kenneth S. . Activity Coefficients in Electrolyte Solutions . CRC Press . 2018.
- Book: Pitzer, Kenneth. Activity Coefficients in Electrolyte Solutions. CRC Press. 1991. 978-1-315-89037-1. 13.
- I. Grenthe and H. Wanner, Guidelines for the extrapolation to zero ionic strength, http://www.nea.fr/html/dbtdb/guidelines/tdb2.pdf
- Ge. Xinlei. Wang. Xidong. Zhang. Mei. Seetharaman. Seshadri. Correlation and Prediction of Activity and Osmotic Coefficients of Aqueous Electrolytes at 298.15 K by the Modified TCPC Model. Journal of Chemical & Engineering Data. 52. 2. 2007. 538–547. 0021-9568. 10.1021/je060451k.
- Ge. Xinlei. Zhang. Mei. Guo. Min. Wang. Xidong. Correlation and Prediction of Thermodynamic Properties of Nonaqueous Electrolytes by the Modified TCPC Model. Journal of Chemical & Engineering Data. 53. 1. 2008. 149–159. 0021-9568. 10.1021/je700446q.
- Ge. Xinlei. Zhang. Mei. Guo. Min. Wang. Xidong. Correlation and Prediction of Thermodynamic Properties of Some Complex Aqueous Electrolytes by the Modified Three-Characteristic-Parameter Correlation Model. Journal of Chemical & Engineering Data. 53. 4. 2008. 950–958. 0021-9568. 10.1021/je7006499.
- Ge. Xinlei. Wang. Xidong. A Simple Two-Parameter Correlation Model for Aqueous Electrolyte Solutions across a Wide Range of Temperatures†. Journal of Chemical & Engineering Data. 54. 2. 2009. 179–186. 0021-9568. 10.1021/je800483q.