Editing Freezing-point depression (section)

===For concentrated solution===
The simple relation above doesn't consider the nature of the solute, so it is only effective in a diluted solution. For a more accurate calculation at a higher concentration, for ionic solutes, Ge and Wang (2010)<ref name="GeWang2009-1">{{cite journal|last1=Ge|first1=Xinlei|last2=Wang|first2=Xidong|title=Estimation of Freezing Point Depression, Boiling Point Elevation, and Vaporization Enthalpies of Electrolyte Solutions|journal=[[Industrial & Engineering Chemistry Research]]|volume=48|issue=10|year=2009|pages=5123|issn=0888-5885|doi=10.1021/ie900434h|doi-access=free}}</ref><ref>{{cite journal|last1=Ge|first1=Xinlei|last2=Wang|first2=Xidong|title=Calculations of Freezing Point Depression, Boiling Point Elevation, Vapor Pressure and Enthalpies of Vaporization of Electrolyte Solutions by a Modified Three-Characteristic Parameter Correlation Model|journal=Journal of Solution Chemistry|volume=38|issue=9|year=2009|pages=1097–1117|issn=0095-9782|doi=10.1007/s10953-009-9433-0|s2cid=96186176}}</ref> proposed a new equation:

:<math>
\Delta T_\text{F} = \frac{\Delta H^\text{fus}_{T_\text{F}} - 2RT_\text{F} \cdot \ln a_\text{liq} - \sqrt{2\Delta C^\text{fus}_p T^2_\text{F}R \cdot \ln a_\text{liq} + (\Delta H^\text{fus}_{T_\text{F}})^2}}{2\left(\frac{\Delta H^\text{fus}_{T_\text{F}}}{T_\text{F}} + \frac{\Delta C^\text{fus}_p}{2} - R \cdot \ln a_\text{liq}\right)}.
</math>

In the above equation, ''T''<sub>F</sub> is the normal freezing point of the pure solvent (273&nbsp;K for water, for example); ''a''<sub>liq</sub> is the activity of the solvent in the solution (water activity for aqueous solution); Δ''H''<sup>fus</sup><sub>T<sub>F</sub></sub> is the enthalpy change of fusion of the pure solvent at ''T''<sub>F</sub>, which is 333.6 J/g for water at 273&nbsp;K; Δ''C''<sup>fus</sup><sub>p</sub> is the difference between the heat capacities of the liquid and solid phases at ''T''<sub>F</sub>, which is 2.11 J/(g·K) for water.

The solvent activity can be calculated from the [[Pitzer equations|Pitzer model]] or modified [[TCPC model]], which typically requires 3 adjustable parameters. For the TCPC model, these parameters are available<ref name="GeWang2007">{{cite journal|last1=Ge|first1=Xinlei|last2=Wang|first2=Xidong|last3=Zhang|first3=Mei|last4=Seetharaman|first4=Seshadri|title=Correlation and Prediction of Activity and Osmotic Coefficients of Aqueous Electrolytes at 298.15 K by the Modified TCPC Model|journal=Journal of Chemical & Engineering Data|volume=52|issue=2|year=2007|pages=538–547|issn=0021-9568|doi=10.1021/je060451k}}</ref><ref name="GeZhang2008-1">{{cite journal|last1=Ge|first1=Xinlei|last2=Zhang|first2=Mei|last3=Guo|first3=Min|last4=Wang|first4=Xidong|title=Correlation and Prediction of Thermodynamic Properties of Some Complex Aqueous Electrolytes by the Modified Three-Characteristic-Parameter Correlation Model|journal=Journal of Chemical & Engineering Data|volume=53|issue=4|year=2008|pages=950–958|issn=0021-9568|doi=10.1021/je7006499}}</ref><ref name="GeZhang2008-2">{{cite journal|last1=Ge|first1=Xinlei|last2=Zhang|first2=Mei|last3=Guo|first3=Min|last4=Wang|first4=Xidong|title=Correlation and Prediction of Thermodynamic Properties of Nonaqueous Electrolytes by the Modified TCPC Model|journal=Journal of Chemical & Engineering Data|volume=53|issue=1|year=2008|pages=149–159|issn=0021-9568|doi=10.1021/je700446q}}</ref><ref name="GeWang2009-2">{{cite journal|last1=Ge|first1=Xinlei|last2=Wang|first2=Xidong|title=A Simple Two-Parameter Correlation Model for Aqueous Electrolyte Solutions across a Wide Range of Temperatures†|journal=Journal of Chemical & Engineering Data|volume=54|issue=2|year=2009|pages=179–186|issn=0021-9568|doi=10.1021/je800483q}}</ref> for many single salts.