Editing Freezing-point depression

{{Short description|Drop in freezing temperature of a solvent due to the addition of solute}}
{{About|the phenomenon caused by solutes|the phenomenon in pure fluids|supercooling}}

[[File:Salt truck Milwaukee.jpg|thumb|Workers spreading salt from a salt truck for deicing the road]]

[[File:Gelato ice cream.jpg|thumb|Freezing point depression is responsible for keeping ice cream soft below 0&nbsp;°C.<ref>{{Cite journal |date=2021-03-18 |title=Controlling the hardness of ice cream, gelato and similar frozen desserts |journal=Food Science and Technology |doi=10.1002/fsat.3510_3.x |s2cid=243583017 |issn=1475-3324|doi-access=free }}</ref>]]
'''Freezing-point depression''' is a drop in the maximum temperature at which a substance [[freezing|freezes]], caused when a smaller amount of another, non-[[Volatility (chemistry)|volatile]] substance is added. Examples include adding salt into water (used in [[ice cream maker]]s and for [[De-icing#Chemical de-icers|de-icing roads]]), [[Alcohol (chemistry)|alcohol]] in water, [[Ethylene glycol|ethylene]] or [[propylene glycol]] in water (used in [[antifreeze]] in cars), adding [[copper]] to molten [[silver]] (used to make [[Solder#Hard_solder|solder]] that flows at a lower temperature than the silver pieces being joined), or the mixing of two solids such as impurities into a finely powdered drug.

In all cases, the substance added/present in smaller amounts is considered the [[solute]], while the original substance present in larger quantity is thought of as the [[solvent]]. The resulting liquid solution or solid-solid mixture has a lower [[Melting point|freezing point]] than the pure solvent or solid because the [[chemical potential]] of the solvent in the mixture is lower than that of the pure solvent, the difference between the two being proportional to the [[natural logarithm]] of the [[mole fraction]]. In a similar manner, the chemical potential of the vapor above the solution is lower than that above a pure solvent, which results in [[boiling-point elevation]]. Freezing-point depression is what causes [[sea water]] (a mixture of salt and other compounds in water) to remain liquid at temperatures below {{convert|0|C|F}}, the freezing point of pure water.

==Explanation==
===Using vapour pressure===
The freezing point is the temperature at which the liquid solvent and solid solvent are at equilibrium, so that their [[vapor pressure]]s are equal. When a non-volatile solute is added to a volatile liquid solvent, the solution vapour pressure will be lower than that of the pure solvent. As a result, the solid will reach equilibrium with the solution at a lower temperature than with the pure solvent.<ref>{{cite book |last1=Petrucci |first1=Ralph H. |last2=Harwood |first2=William S. |last3=Herring |first3=F. Geoffrey |date=2002 |title=General Chemistry |edition=8th |publisher=Prentice-Hall |pages=557–558 |isbn=0-13-014329-4 }}</ref> This explanation in terms of vapor pressure is equivalent to the argument based on chemical potential, since the chemical potential of a vapor is logarithmically related to pressure. All of the [[colligative properties]] result from a lowering of the chemical potential of the solvent in the presence of a solute. This lowering is an [[entropy]] effect. The greater randomness of the solution (as compared to the pure solvent) acts in opposition to freezing, so that a lower temperature must be reached, over a broader range, before equilibrium between the liquid solution and [[solid solution]] phases is achieved. Melting point determinations are commonly exploited in [[organic chemistry]] to aid in identifying substances and to ascertain their purity.

=== Due to concentration and entropy ===

In the liquid solution, the solvent is diluted by the addition of a solute, so that fewer molecules are available to freeze (a lower concentration of solvent exists in a solution versus pure solvent). Re-establishment of equilibrium is achieved at a lower temperature at which the rate of freezing becomes equal to the rate of liquefying. The solute is not occluding or preventing the solvent from solidifying, it is simply diluting it so there is a reduced probability of a solvent making an attempt at freezing in any given moment.  

At the lower freezing point, the vapor pressure of the liquid is equal to the vapor pressure of the corresponding solid, and the chemical potentials of the two phases are equal as well.

==Uses==
The phenomenon of freezing-point depression has many practical uses. The radiator fluid in an automobile is a mixture of water and [[antifreeze|ethylene glycol]]. The freezing-point depression prevents radiators from freezing in winter. Road salting takes advantage of this effect to lower the freezing point of the ice it is placed on. Lowering the freezing point allows the street ice to melt at lower temperatures, preventing the accumulation of dangerous, slippery ice. Commonly used [[sodium chloride]] can depress the freezing point of water to about {{convert|-21|C|F}}. If the road surface temperature is lower, NaCl becomes ineffective and other salts are used, such as [[calcium chloride]], [[magnesium chloride]] or a mixture of many. These salts are somewhat aggressive to metals, especially iron, so in airports safer media such as [[sodium formate]], [[potassium formate]], [[sodium acetate]], and [[potassium acetate]] are used instead.

[[File:2018-07-26 08 09 30 View north along New Jersey State Route 23 at Scenic Lake Road in Hardyston Township, Sussex County, New Jersey.jpg|thumb|Pre-treating roads with salt relies on the warmer road surface to initially melt the snow and make a solution; Pre-treatment of bridges (which are colder than roads) does not typically work.<ref name=":0">{{Cite web |last=Pollock |first=Julie |title=Salt Doesn't Melt Ice&mdash;Here's How It Makes Winter Streets Safer |url=https://www.scientificamerican.com/article/salt-doesnt-melt-ice-heres-how-it-makes-winter-streets-safer/ |access-date= |website=Scientific American |language=en}}</ref>]]
[[File:Les feuilles toutes givrées du petit pommier.jpg|thumb|Dissolved solutes prevent sap and other fluids in trees from freezing in winter.<ref>{{Cite news|last=Ray|first=C. Claiborne|date=2002-02-05|title=Q & A|language=en-US|work=The New York Times|url=https://www.nytimes.com/2002/02/05/science/q-a-461229.html|access-date=2022-02-10|issn=0362-4331}}</ref>]]
Freezing-point depression is used by some organisms that live in extreme cold. Such creatures have [[evolution|evolved]] means through which they can produce a high concentration of various compounds such as [[sorbitol]] and [[glycerol]]. This elevated concentration of solute decreases the freezing point of the water inside them, preventing the organism from freezing solid even as the water around them freezes, or as the air around them becomes very cold. Examples of organisms that produce antifreeze compounds include some species of [[arctic]]-living [[fish]] such as the [[rainbow smelt]], which produces glycerol and other molecules to survive in frozen-over estuaries during the winter months.<ref>{{cite journal|last1=Treberg|first1= J. R. |last2=Wilson |first2=C. E.|last3= Richards|first3= R. C. |last4=Ewart|first4= K. V. |last5=Driedzic|first5= W. R. |year=2002 |journal= The Journal of Experimental Biology |volume=205 |pages=1419–1427 |title=The freeze-avoidance response of smelt ''Osmerus mordax'': initiation and subsequent suppression 6353 |issue=Pt 10 |doi= 10.1242/jeb.205.10.1419 |pmid= 11976353 |url=http://jeb.biologists.org/content/205/10/1419.long|url-access=subscription }}</ref> In other animals, such as the [[spring peeper]] frog (''Pseudacris crucifer''), the molality is increased temporarily as a reaction to cold temperatures. In the case of the peeper frog, freezing temperatures trigger a large-scale breakdown of [[glycogen]] in the frog's liver and subsequent release of massive amounts of [[glucose]] into the blood.<ref>L. Sherwood et al., ''Animal Physiology: From Genes to Organisms'', 2005, Thomson Brooks/Cole, Belmont, CA, {{ISBN|0-534-55404-0}}, p.&nbsp;691–692.</ref>
With the formula below, freezing-point depression can be used to measure the degree of [[dissociation (chemistry)|dissociation]] or the [[molar mass]] of the solute. This kind of measurement is called '''cryoscopy''' ([[Ancient Greek|Greek]] ''cryo'' = cold, ''scopos'' = observe; "observe the cold"<ref>Bioetymology – Biomedical Terms of Greek Origin. [http://bioetymology.blogspot.com/2011/06/cryoscopy.html cryoscopy]. bioetymology.blogspot.com.</ref>) and relies on exact measurement of the freezing point. The degree of dissociation is measured by determining the [[van 't Hoff factor]] ''i'' by first determining ''m''<sub>B</sub> and then comparing it to ''m''<sub>solute</sub>. In this case, the molar mass of the solute must be known. The molar mass of a solute is determined by comparing ''m''<sub>B</sub> with the amount of solute dissolved. In this case, ''i'' must be known, and the procedure is primarily useful for organic compounds using a nonpolar solvent. Cryoscopy is no longer as common a measurement method as it once was, but it was included in textbooks at the turn of the 20th century. As an example, it was still taught as a useful analytic procedure in Cohen's ''Practical Organic Chemistry '' of 1910,<ref>{{cite book|first =Julius B. |last =Cohen|url =https://archive.org/details/PracticalOrganicChemistry |title =Practical Organic Chemistry|date = 1910|publisher = MacMillan and Co.|location = London}}</ref> in which the [[molar mass]] of [[naphthalene]] is determined using a ''Beckmann freezing apparatus''.

===Laboratory uses===
Freezing-point depression can also be used as a purity analysis tool when analyzed by [[differential scanning calorimetry]]. The results obtained are in mol%, but the method has its place, where other methods of analysis fail.

In the laboratory, [[lauric acid]] may be used to investigate the [[molar mass]] of an unknown substance via the freezing-point depression. The choice of lauric acid is convenient because the melting point of the pure compound is relatively high (43.8&nbsp;°C). Its [[cryoscopic constant]] is 3.9&nbsp;°C·kg/mol. By melting lauric acid with the unknown substance, allowing it to cool, and recording the temperature at which the mixture freezes, the molar mass of the unknown compound may be determined.<ref>{{Cite web |url=http://faculty.sites.uci.edu/chem1l/files/2015/04/Freezing-Point-Depression.pdf |title=Archived copy |access-date=2019-07-08 |archive-date=2020-08-03 |archive-url=https://web.archive.org/web/20200803132047/http://faculty.sites.uci.edu/chem1l/files/2015/04/Freezing-Point-Depression.pdf |url-status=dead }}</ref>{{Citation needed|reason=This source is from a college-level general chemistry lab and does not provide evidence that actual chemists use lauric acid for this use.|date=February 2020}}

This is also the same principle acting in the melting-point depression observed when the melting point of an impure solid mixture is measured with a [[melting-point apparatus]] since melting and freezing points both refer to the liquid-solid [[phase transition]] (albeit in different directions).

In principle, the boiling-point elevation and the freezing-point depression could be used interchangeably for this purpose. However, the [[cryoscopic constant]] is larger than the [[ebullioscopic constant]], and the freezing point is often easier to measure with precision, which means measurements using the freezing-point depression are more precise.

FPD measurements are also used in the dairy industry to ensure that milk has not had extra water added. Milk with a FPD of over 0.509&nbsp;°C is considered to be unadulterated.<ref>{{cite web
 |title       = Freezing Point Depression of Milk
 |publisher   = Dairy UK
 |year        = 2014
 |url         = http://www.dairyuk.org/component/docman/doc_download/3940-freezing-point-depression-of-milk
 |archive-date = 2014-02-23
 |archive-url  = https://web.archive.org/web/20140223151245/http://www.dairyuk.org/component/docman/doc_download/3940-freezing-point-depression-of-milk
 |url-status     = dead
}}</ref>

==Formula==
===For dilute solution===
[[File:Tfreeze vs SA.png|thumb|237x237px|Freezing temperature of seawater at different pressures and some substances as a function of salinity. See image description for source.]]
If the solution is treated as an [[ideal solution]], the extent of freezing-point depression depends only on the solute concentration that can be estimated by a simple linear relationship with the cryoscopic constant ("[[Charles Blagden|Blagden]]'s Law").

:<math> \Delta T_f \propto \frac{\text{Moles of dissolved species}}{\text{Mass of solvent}}</math>

:<math> \Delta T_f = K_fbi</math>

where:
* <math>\Delta T_f</math> is the decrease in freezing point, defined as the freezing point <math> T_f^0</math> of the pure solvent minus the freezing point <math> T_f</math> of the solution, as the formula above results in a positive value given that all factors are positive. From the <math> \Delta T_f</math> calculated using the formula above, the freezing point of the solution can then be calculated as <math> T_f = T_f^0 - \Delta T_f</math>.
* <math>K_f</math>, the [[cryoscopic constant]], which is dependent on the properties of the solvent, not the solute. (Note: When conducting experiments, a higher ''k'' value makes it easier to observe larger drops in the freezing point.)
* <math>b</math> is the [[molality]] (moles of solute per kilogram of solvent)
* <math>i</math> is the [[van 't Hoff factor]] (number of ion particles per formula unit of solute, e.g. i = 2 for NaCl, 3 for BaCl<sub>2</sub>).

Some values of the cryoscopic constant ''K''<sub>f</sub> for selected solvents:<ref>{{cite book|first = P. W.|last = Atkins|title = Physical Chemistry|edition = 4th |page = C17 (Table 7.2)|isbn = 978-0716720737|publisher = Freeman|date = 1990}}</ref>

{| class="wikitable sortable"  
! Compound !! Freezing point (°C) !! ''K''<sub>f</sub> in [[kelvin|K]]⋅kg/[[mole (unit)|mol]]
|- 
| [[Acetic acid]] || 16.6 || 3.90
|- 
| [[Benzene]] || 5.5 || 5.12
|-
| [[Camphor]] || 179.8|| 39.7
|-
| [[Carbon disulfide]] || −112 || 3.8
|-
| [[Carbon tetrachloride]] || −23 || 30
|- 
| [[Chloroform]] || −63.5 || 4.68
|-  
| [[Cyclohexane]] ||  6.4  || 20.2
|-
| [[Ethanol]] || −114.6 || 1.99
|-
| [[Ethyl ether]] || −116.2 || 1.79
|-
| [[Naphthalene]] || 80.2 || 6.9
|-
| [[Phenol]] || 41 || 7.27
|-
| [[Water]] || 0 || 1.86<ref>{{Citation
  | last1 = Aylward
  | first1 = Gordon
  | author-link = Gordon Aylward
  | last2 = Findlay
  | first2 = Tristan
  | author2-link = Tristan Findlay
  | title = SI Chemical Data 5th ed.
  | place = Sweden
  | publisher = John Wiley & Sons
  | year = 2002
  | edition = 5
  | pages = 202
  | isbn = 0-470-80044-5}}</ref>
|}

===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.

==Ethanol example==

The freezing point of ethanol water mixture is shown in the following graph.

[[File:Phase diagram ethanol water s l en.svg|frameless]]

==See also==
*[[Melting-point depression]]
*[[Boiling-point elevation]]
*[[Colligative properties]]
*[[Deicing]]
*[[Eutectic point]]
*[[Frigorific mixture]]
*[[List of boiling and freezing information of solvents]]
*[[Snow removal]]

==References==
{{Reflist|30em}}
{{Chemical solutions}}
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[[Category:Amount of substance]]
[[Category:Chemical properties]]
[[Category:Phase transitions]]