Molal Freezing Point Depression Constant

Process in which adding a solute to a solvent decreases the freezing signal of the solvent

This commodity is about the phenomenon acquired by solutes. For the phenomenon in pure fluids, see supercooling.

Workers spreading salt from a salt truck for deicing the road.

Freezing point depression is responsible for keeping water ice cream soft beneath 0°C.^[1]

Freezing-point low is a drop in the temperature at which a substance freezes, caused when a smaller corporeality of some other, not-volatile substance is added. Examples include adding salt into water (used in water ice cream makers and for de-icing roads), alcohol in h2o, ethylene or propylene glycol in water (used in antifreeze in cars), adding copper to molten silver (used to make solder that flows at a lower temperature than the silver pieces existence joined), or the mixing of two solids such as impurities into a finely powdered drug.

In all cases, the substance added/nowadays 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 freezing betoken than the pure solvent or solid because the chemic potential of the solvent in the mixture is lower than that of the pure solvent, the departure betwixt the 2 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-indicate elevation. Freezing-point depression is what causes ocean water (a mixture of table salt and other compounds in water) to remain liquid at temperatures below 0 °C (32 °F), the freezing point of pure water.

Explanation [edit]

Using vapour pressure [edit]

The freezing point is the temperature at which the liquid solvent and solid solvent are at equilibrium, and so that their vapour pressures are equal. When a not-volatile solute is added to a volatile liquid solvent, the solution vapour pressure will be lower than that of the pure solvent. As a upshot, the solid will reach equilibrium with the solution at a lower temperature than with the pure solvent.^[two] This explanation in terms of vapor pressure level is equivalent to the argument based on chemical potential, since the chemic potential of a vapor is logarithmically related to force per unit area. All of the colligative properties event from a lowering of the chemical potential of the solvent in the presence of a solute. This lowering is an entropy result. The greater randomness of the solution (as compared to the pure solvent) acts in opposition to freezing, and then that a lower temperature must be reached, over a broader range, earlier equilibrium betwixt the liquid solution and solid solution phases is accomplished. Melting signal determinations are commonly exploited in organic chemistry to assist in identifying substances and to ascertain their purity.

Due to crystal defect [edit]

Salt prevents the water molecules from solidifying into water ice crystals at 0 °C (32 °F), instead staying slushy at that temperature, before eventually freezing around −9 °C (sixteen °F).^[iii]

Consider the problem in which the solvent freezes to a very nearly pure crystal, regardless of the presence of the nonvolatile solute. This typically occurs only because the solute molecules do non fit well in the crystal, i.e. substituting a solute for a solvent molecule in the crystal has high enthalpy. In this example, for low solute concentrations, the freezing point depression depends solely on the concentration of solute particles, non on their individual properties. The freezing indicate depression thus is called a colligative holding.^[iv]

The explanation for the freezing point depression is so simply that as solvent molecules exit the liquid and join the solid, they leave behind a smaller book of liquid in which the solute particles can roam. The resulting reduced entropy of the solute particles thus is contained of their properties. This approximation ceases to hold when the concentration becomes large enough for solute-solute interactions to get important. In that example, the freezing point depression depends on item properties of the solute other than its concentration.^{[ commendation needed ]}

Uses [edit]

The phenomenon of freezing-point depression has many practical uses. The radiator fluid in an automobile is a mixture of water and ethylene glycol. The freezing-indicate depression prevents radiators from freezing in wintertime. Route salting takes advantage of this effect to lower the freezing signal 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, glace ice. Normally used sodium chloride can depress the freezing indicate of water to about −21 °C (−half-dozen °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, then in airports safer media such as sodium formate, potassium formate, sodium acetate, and potassium acetate are used instead.

Pre-treating roads with salt relies on the warmer road surface to initially melt the snowfall and brand a solution; Pre-treatment of bridges (which are colder than roads) does not typically piece of work.^[5]

Freezing-bespeak depression is used by some organisms that alive in extreme cold. Such creatures have evolved means through which they tin produce a high concentration of various compounds such as sorbitol and glycerol. This elevated concentration of solute decreases the freezing point of the water within them, preventing the organism from freezing solid fifty-fifty as the h2o 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.^[6] 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 claret.^[7]

Conifers have concentrated cell sap that also acts similar antifreeze in winters.^[8]

With the formula beneath, freezing-betoken depression can be used to measure the degree of dissociation or the tooth mass of the solute. This kind of measurement is called cryoscopy (Greek cryo = cold, scopos = observe; "observe the cold"^[ix]) and relies on exact measurement of the freezing indicate. The degree of dissociation is measured by determining the van 't Hoff factor i by first determining m _B and so comparison information technology to g _solute. In this case, the tooth mass of the solute must exist known. The molar mass of a solute is determined by comparing yard _B 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 equally common a measurement method as information technology once was, but it was included in textbooks at the turn of the 20th century. As an example, information technology was however taught as a useful analytic process in Cohen's Practical Organic Chemistry of 1910,^[10] in which the molar mass of naphthalene is adamant using a Beckmann freezing apparatus.

Laboratory uses [edit]

Freezing-point low can also be used as a purity assay tool when analyzed past differential scanning calorimetry. The results obtained are in mol%, just the method has its place, where other methods of analysis neglect.

In the laboratory, lauric acid may exist used to investigate the molar mass of an unknown substance via the freezing-point depression. The choice of lauric acid is user-friendly because the melting signal of the pure compound is relatively high (43.8 °C). Its cryoscopic constant is three.9 °C·kg/mol. Past melting lauric acrid with the unknown substance, allowing it to absurd, and recording the temperature at which the mixture freezes, the tooth mass of the unknown compound may be determined.^{[11] [ citation needed ]}

This is besides the same principle acting in the melting-point depression observed when the melting bespeak 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 (admitting in unlike directions).

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

This phenomenon is applicable in preparing a freezing mixture to make ice foam. For this purpose, NaCl or some other salt is used to lower the melting point of ice.

FPD measurements are as well used in the dairy industry to ensure that milk has not had extra water added. Milk with a FPD of over 0.509 °C is considered to be unadulterated.^[12]

Formula [edit]

For dilute solution [edit]

Freezing temperature of seawater at dissimilar pressures and some substances as a function of salinity. See image description for source.

If the solution is treated every bit an ideal solution, the extent of freezing-point depression depends only on the solute concentration that can be estimated past a simple linear relationship with the cryoscopic abiding ("Blagden'due south Law").

${\displaystyle \Delta t\propto {\frac {\text{Moles of dissolved species}}{\text{Weight of solvent}}}}$

${\displaystyle \Delta t=K_{f}bi}$

where:

Some values of the cryoscopic constant K _f for selected solvents:^[13]

Chemical compound	Freezing point (°C)	K f in K⋅kg/mol
Acetic acid	16.6	3.90
Benzene	5.5	5.12
Camphor	179.eight	39.vii
Carbon disulfide	−112	3.8
Carbon tetrachloride	−23	30
Chloroform	−63.five	4.68
Cyclohexane	6.four	20.ii
Ethanol	−114.6	one.99
Ethyl ether	−116.2	i.79
Naphthalene	80.2	six.9
Phenol	41	vii.27
Water	0	1.86[14]

For concentrated solution [edit]

The simple relation above doesn't consider the nature of the solute, and then it is only effective in a diluted solution. For a more accurate calculation at a higher concentration, for ionic solutes, Ge and Wang (2010)^{[xv] [16]} proposed a new equation:

${\displaystyle \Delta T_{\text{F}}={\frac {\Delta H_{T_{\text{F}}}^{\text{fus}}-2RT_{\text{F}}\cdot \ln a_{\text{liq}}-{\sqrt {ii\Delta C_{p}^{\text{fus}}T_{\text{F}}^{ii}R\cdot \ln a_{\text{liq}}+(\Delta H_{T_{\text{F}}}^{\text{fus}})^{2}}}}{2\left({\frac {\Delta H_{T_{\text{F}}}^{\text{fus}}}{T_{\text{F}}}}+{\frac {\Delta C_{p}^{\text{fus}}}{2}}-R\cdot \ln a_{\text{liq}}\right)}}.}$

In the in a higher place equation, T _F is the normal freezing betoken of the pure solvent (273 K for h2o, for example); a _liq is the action of the solvent in the solution (h2o activeness for aqueous solution); ΔH ^fus _TF is the enthalpy alter of fusion of the pure solvent at T _F, which is 333.6 J/yard for h2o at 273 K; ΔC ^fus _p is the difference between the estrus capacities of the liquid and solid phases at T _F, which is 2.11 J/(thousand·Grand) for water.

The solvent activeness tin can be calculated from the Pitzer model or modified TCPC model, which typically requires 3 adjustable parameters. For the TCPC model, these parameters are bachelor^{[17] [xviii] [xix] [20]} for many single salts.

See also [edit]

• Melting-bespeak depression
• Humid-point elevation
• Colligative backdrop
• Deicing
• Eutectic point
• Frigorific mixture
• List of boiling and freezing information of solvents
• Snow removal

References [edit]

1. ^ "Controlling the hardness of water ice cream, gelato and similar frozen desserts". Nutrient Science and Technology. 2021-03-xviii. doi:10.1002/fsat.3510_3.x. ISSN 1475-3324.
2. ^ Petrucci, Ralph H.; Harwood, William S.; Herring, F. Geoffrey (2002). General Chemistry (8th ed.). Prentice-Hall. pp. 557–558. ISBN0-13-014329-4.
3. ^ Pollock, Julie. "Common salt Doesn't Cook Ice—Hither's How It Makes Winter Streets Safer". Scientific American.
4. ^ Atkins, Peter (2006). Atkins' Physical Chemistry. Oxford University Press. pp. 150–153. ISBN0198700725.
5. ^ Pollock, Julie. "Salt Doesn't Melt Ice—Hither'south How It Makes Winter Streets Safer". Scientific American.
6. ^ Treberg, J. R.; Wilson, C. E.; Richards, R. C.; Ewart, Thou. V.; Driedzic, W. R. (2002). "The freeze-avoidance response of smelt Osmerus mordax: initiation and subsequent suppression 6353". The Journal of Experimental Biology. 205 (Pt 10): 1419–1427. doi:10.1242/jeb.205.10.1419.
7. ^ L. Sherwood et al., Animal Physiology: From Genes to Organisms, 2005, Thomson Brooks/Cole, Belmont, CA, ISBN 0-534-55404-0, p. 691–692.
8. ^ Ray, C. Claiborne (2002-02-05). "Q & A". The New York Times. ISSN 0362-4331. Retrieved 2022-02-x .
9. ^ BIOETYMOLOGY – Biomedical Terms of Greek Origin. cryoscopy. bioetymology.blogspot.com.
10. ^ Cohen, Julius B. (1910). Practical Organic Chemistry. London: MacMillan and Co.
11. ^ "Archived copy" (PDF). Archived from the original (PDF) on 2020-08-03. Retrieved 2019-07-08 . {{cite spider web}}: CS1 maint: archived re-create every bit title (link)
12. ^ "Freezing Bespeak Low of Milk". Dairy UK. 2014. Archived from the original on 2014-02-23.
13. ^ P. W. Atkins, Physical Chemistry, quaternary Ed., p. C17 (Tabular array 7.2)
14. ^ Aylward, Gordon; Findlay, Tristan (2002), SI Chemical Data 5th ed. (5 ed.), Sweden: John Wiley & Sons, p. 202, ISBN0-470-80044-five
15. ^ Ge, Xinlei; Wang, Xidong (2009). "Estimation of Freezing Point Depression, Humid Point Elevation, and Vaporization Enthalpies of Electrolyte Solutions". Industrial & Engineering science Chemical science Inquiry. 48 (10): 5123. doi:10.1021/ie900434h. ISSN 0888-5885.
16. ^ Ge, Xinlei; Wang, Xidong (2009). "Calculations of Freezing Point Low, Boiling Indicate Elevation, Vapor Pressure level and Enthalpies of Vaporization of Electrolyte Solutions by a Modified Three-Characteristic Parameter Correlation Model". Journal of Solution Chemistry. 38 (9): 1097–1117. doi:10.1007/s10953-009-9433-0. ISSN 0095-9782. S2CID 96186176.
17. ^ Ge, Xinlei; Wang, Xidong; Zhang, Mei; Seetharaman, Seshadri (2007). "Correlation and Prediction of Activity and Osmotic Coefficients of Aqueous Electrolytes at 298.15 K by the Modified TCPC Model". Journal of Chemic & Engineering Information. 52 (2): 538–547. doi:x.1021/je060451k. ISSN 0021-9568.
18. ^ Ge, Xinlei; Zhang, Mei; Guo, Min; Wang, Xidong (2008). "Correlation and Prediction of Thermodynamic Backdrop of Some Complex Aqueous Electrolytes by the Modified 3-Characteristic-Parameter Correlation Model". Journal of Chemical & Engineering Information. 53 (four): 950–958. doi:10.1021/je7006499. ISSN 0021-9568.
19. ^ Ge, Xinlei; Zhang, Mei; Guo, Min; Wang, Xidong (2008). "Correlation and Prediction of Thermodynamic Properties of Nonaqueous Electrolytes by the Modified TCPC Model". Journal of Chemical & Engineering Data. 53 (one): 149–159. doi:10.1021/je700446q. ISSN 0021-9568.
20. ^ Ge, Xinlei; Wang, Xidong (2009). "A Elementary Ii-Parameter Correlation Model for Aqueous Electrolyte Solutions across a Wide Range of Temperatures†". Journal of Chemic & Engineering Data. 54 (ii): 179–186. doi:ten.1021/je800483q. ISSN 0021-9568.

Molal Freezing Point Depression Constant,

Source: https://en.wikipedia.org/wiki/Freezing-point_depression

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