Freezing-point depression

1
Freezing-point depression
This article talks about the melting and freezing point depression due to mixtures of compounds. For
depression due to small particle size, see melting point depression.
Freezing-point depression describes the process in which adding a solute to a solvent decreases the freezing point
of the solvent.
Examples include salt in water, alcohol in water, or the mixing of two solids such as impurities in a finely powdered
drug. In such cases, the added compound is the solute, and the original solid can be thought of as the solvent. The
resulting solution or solid-solid mixture has a lower freezing point than the pure solvent or solid did. This
phenomenon is what causes sea water, (a mixture of salt (and other things) in water) to remain liquid at temperatures
below 0C (32F), the freezing point of pure water.
Uses
Ice on a road.
The phenomenon of freezing point
depression has many practical uses.
The radiator fluid in an automobile is a
mixture of water and ethylene glycol
(antifreeze). As a result of freezing
point depression, radiators do not
freeze in winter (unless it is extremely
cold, e.g. 30 to 40C (22 to
40F)). 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.
The maximum depression of the
freezing point is about 18C (0F),
so if the ambient temperature is lower,
salt (sodium chloride) will be ineffective.
Freezing-point depression is used by some organisms that live in extreme cold. Such creatures have evolved means
through which they can produce 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 the air around them is very cold. Examples include some
species of arctic-living fish, such as rainbow smelt, which can survive in freezing temperatures for long periods. 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.
[1]
With the formula below, freezing-point depression can be used to measure the degree of dissociation or the molar
mass of the solute. This kind of measurement is called cryoscopy (Greek cryo = cold, scopos = observe "observe the
cold"
[2]
) 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
B
and then comparing it to m
solute
. In this case, the molar
mass of the solute must be known. The molar mass of a solute is determined by comparing m
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 as common a measurement method as it once was, but it was included in
Freezing-point depression
2
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,
[3]
in which the molar mass of naphthalene is determined using a Beckmann
freezing apparatus.
Freezing-point depression can also be used as a purity analysis tool when analysed by differential scanning
calorimetry. The results obtained are in mol%, but the method has its place, where other methods of analysis fail.
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 used in the dairy industry to ensure that milk has not had extra water added. Milk with FPD
of over 0.509 m *C is considering to be unadulterated.
Freezing-point depression of a solvent and a solute
Consider the problem in which the solvent freezes to a very nearly pure crystal, regardless of the presence of the
solute. This typically occurs simply because the solute molecules do not fit well in the crystal, i.e. substituting a
solute for a solvent molecule in the crystal has high enthalpy. In this case, for low solute concentrations, the freezing
point depression depends solely on the concentration of solute particles, not on their individual properties. The
freezing point depression thus is called a colligative property.
[citation needed]
The explanation for the freezing point depression is then simply that as solvent molecules leave the liquid and join
the solid, they leave behind a smaller volume of liquid in which the solute particles can roam. The resulting reduced
entropy of the solute particles thus is independent of their properties. This approximation ceases to hold when the
concentration becomes large enough for solute-solute interactions to become important. In that case, the freezing
point depression depends on particular properties of the solute other than its concentration.
[citation needed]
Calculation
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 ("Blagden's Law"):
T
F
= K
F
b i
T
F
, the freezing point depression, is defined as T
F (pure solvent)
- T
F (solution)
.
K
F
, the cryoscopic constant, which is dependent on the properties of the solvent, not the solute. Note: When
conducting experiments, a higher K
F
value makes it easier to observe larger drops in the freezing point. For water,
K
F
= 1.853 Ckg/mol.
b is the molality (mol solute per kg of solvent)
i is the van 't Hoff factor (number of ion particles per individual molecule of solute, e.g. i = 2 for NaCl, 3 for
BaCl
2
).
This simple relation doesn't include the nature of the solute, so this is only effective in a diluted solution. For a more
accurate calculation at a higher concentration, Ge and Wang (2010)
[4][5]
proposed a new equation:
In the above equation, T
F
is the normal freezing point of the pure solvent (0
o
C for water for example); a
liq
is the
activity of the solution (water activity for aqueous solution); H
fus
T
F is the enthalpy change of fusion of the pure
Freezing-point depression
3
solvent at T
F
, which is 333.6 J/g for water at 0
o
C; C
fus
p
is the differences of heat capacity between the liquid and
solid phases at T
F
, which is 2.11 J/g/K for water.
The solvent activity can be calculated from Pitzer model or modified TCPC model, which typically requires 3
adjustable parameters. For the TCPC model, these parameters are available at reference
[6][7][8][9]
for many single
salts.
References
[1] L. Sherwood et al., Animal Physiology: From Genes to Organisms, 2005, Thomson Brooks/Cole, Belmont, CA, ISBN 0-534-55404-0, p.
691-692
[2] BIOETYMOLOGY- Biomedical Terms of Greek Origin bioetymology.blogspot.com (http:/ / bioetymology. blogspot. com/ 2011/ 06/
cryoscopy.html)
[3] Julius B. Cohen Practical Organic Chemistry 1910 Link to online text (http:/ / archive. org/ details/ PracticalOrganicChemistry)
[4] X. Ge, X. Wang. Estimation of Freezing Point Depression, Boiling Point Elevation and Vaporization enthalpies of electrolyte solutions. Ind.
Eng. Chem. Res. 48(2009)2229-2235. http:/ / pubs.acs.org/ doi/ abs/ 10. 1021/ ie801348c (Correction: 2009, 48, 5123)http:/ / pubs. acs. org/
doi/ abs/ 10. 1021/ ie900434h
[5] X. Ge, X. Wang. 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. J. Sol. Chem. 38(2009)1097-1117.http:/ / www.
springerlink. com/ content/ 21670685448p5145/
[6] X. Ge, X. Wang, M. Zhang, S. Seetharaman. Correlation and Prediction of Activity and Osmotic Coefficients of Aqueous Electrolytes at
298.15 K by the Modified TCPC Model. J. Chem. Eng. data. 52 (2007) 538-547.http:/ / pubs. acs. org/ doi/ abs/ 10. 1021/ je060451k
[7] X. Ge, M. Zhang, M. Guo, X. Wang. Correlation and Prediction of thermodynamic properties of Some Complex Aqueous Electrolytes by the
Modified Three-Characteristic-Parameter Correlation Model. J. Chem. Eng. Data. 53(2008)950-958. http:/ / pubs. acs. org/ doi/ abs/ 10. 1021/
je7006499
[8] X. Ge, M. Zhang, M. Guo, X. Wang, Correlation and Prediction of Thermodynamic Properties of Non-aqueous Electrolytes by the Modified
TCPC Model. J. Chem. Eng. data. 53 (2008)149-159.http:/ / pubs. acs. org/ doi/ abs/ 10. 1021/ je700446q
[9] X. Ge, X. Wang. A Simple Two-Parameter Correlation Model for Aqueous Electrolyte across a wide range of temperature. J. Chem. Eng.
Data. 54(2009)179-186.http:/ / pubs.acs. org/ doi/ abs/ 10. 1021/ je800483q
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