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Freezing-point depression is a drop in the minimum temperature at which a substance freezes, caused when a smaller amount of another, non- volatile substance is added. Examples include adding salt into water (used in
ice cream maker domestic ice cream maker is a machine used to make small quantities of ice cream for personal consumption. Ice cream makers may prepare the mixture by employing the hand-cranking method or by employing an electric motor. The resulting prepara ...
s and for de-icing roads), alcohol in water, 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 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 A solvent (s) (from the Latin '' solvō'', "loosen, untie, solve") is a substance that dissolves a solute, resulting in a solution. A solvent is usually a liquid but can also be a solid, a gas, or a supercritical fluid. Water is a solvent for ...
. The resulting liquid solution or solid-solid mixture has a lower freezing point than the pure solvent or solid because the
chemical potential In thermodynamics, the chemical potential of a species is the energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potential of a speci ...
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 Boiling-point elevation describes the phenomenon that the boiling point of a liquid (a solvent) will be higher when another compound is added, meaning that a solution has a higher boiling point than a pure solvent. This happens whenever a non-vol ...
. Freezing-point depression is what causes
sea water Seawater, or salt water, is water from a sea or ocean. On average, seawater in the world's oceans has a salinity of about 3.5% (35 g/L, 35 ppt, 600 mM). This means that every kilogram (roughly one liter by volume) of seawater has approx ...
(a mixture of salt and other compounds in water) to remain liquid at temperatures below , 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
vapour pressure Vapor pressure (or vapour pressure in English-speaking countries other than the US; see spelling differences) or equilibrium vapor pressure is defined as the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phase ...
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. 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 In chemistry, colligative properties are those properties of solutions that depend on the ratio of the number of solute particles to the number of solvent particles in a solution, and not on the nature of the chemical species present. The number ...
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 Organic chemistry is a subdiscipline within chemistry involving the scientific study of the structure, properties, and reactions of organic compounds and organic materials, i.e., matter in its various forms that contain carbon atoms.Clayden, J ...
to aid in identifying substances and to ascertain their purity.


Due to crystal defect

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 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 Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant ...
. 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. 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 Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodyna ...
of the solute particles thus is independent of their properties. This approximation ceases to hold when the
concentration In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: '' mass concentration'', '' molar concentration'', ''number 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.


Uses

The phenomenon of freezing-point depression has many practical uses. The radiator fluid in an automobile is a mixture of water and
ethylene glycol Ethylene glycol ( IUPAC name: ethane-1,2-diol) is an organic compound (a vicinal diol) with the formula . It is mainly used for two purposes, as a raw material in the manufacture of polyester fibers and for antifreeze formulations. It is an o ...
. 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 Sodium chloride , commonly known as salt (although sea salt also contains other chemical salts), is an ionic compound with the chemical formula NaCl, representing a 1:1 ratio of sodium and chloride ions. With molar masses of 22.99 and 35. ...
can depress the freezing point of water to about . If the road surface temperature is lower, NaCl becomes ineffective and other salts are used, such as
calcium chloride Calcium chloride is an inorganic compound, a salt with the chemical formula . It is a white crystalline solid at room temperature, and it is highly soluble in water. It can be created by neutralising hydrochloric acid with calcium hydroxide. Ca ...
, 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. Freezing-point depression is used by some organisms that live in extreme cold. Such creatures have
evolved Evolution is change in the heritable characteristics of biological populations over successive generations. These characteristics are the expressions of genes, which are passed on from parent to offspring during reproduction. Variati ...
means through which they can produce a high concentration of various compounds such as
sorbitol Sorbitol (), less commonly known as glucitol (), is a sugar alcohol with a sweet taste which the human body metabolizes slowly. It can be obtained by reduction of glucose, which changes the converted aldehyde group (−CHO) to a primary alcoho ...
and
glycerol Glycerol (), also called glycerine in British English and glycerin in American English, is a simple triol compound. It is a colorless, odorless, viscous liquid that is sweet-tasting and non-toxic. The glycerol backbone is found in lipids known ...
. 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 The Arctic ( or ) is a polar regions of Earth, polar region located at the northernmost part of Earth. The Arctic consists of the Arctic Ocean, adjacent seas, and parts of Canada (Yukon, Northwest Territories, Nunavut), Danish Realm (Greenla ...
-living
fish Fish are Aquatic animal, aquatic, craniate, gill-bearing animals that lack Limb (anatomy), limbs with Digit (anatomy), digits. Included in this definition are the living hagfish, lampreys, and Chondrichthyes, cartilaginous and bony fish as we ...
such as the rainbow smelt, which produces glycerol and other molecules to survive in frozen-over estuaries during the winter months. 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 Glycogen is a multibranched polysaccharide of glucose that serves as a form of energy storage in animals, fungi, and bacteria. The polysaccharide structure represents the main storage form of glucose in the body. Glycogen functions as one of ...
in the frog's liver and subsequent release of massive amounts of
glucose Glucose is a simple sugar with the molecular formula . Glucose is overall the most abundant monosaccharide, a subcategory of carbohydrates. Glucose is mainly made by plants and most algae during photosynthesis from water and carbon dioxide, u ...
into the blood. 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") and relies on exact measurement of the freezing point. The degree of dissociation is measured by determining the
van 't Hoff factor The van 't Hoff factor (named after Dutch chemist Jacobus Henricus van 't Hoff) is a measure of the effect of a solute on colligative properties such as osmotic pressure, relative lowering in vapor pressure, boiling-point elevation and free ...
''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 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, in which the molar mass of
naphthalene Naphthalene is an organic compound with formula . It is the simplest polycyclic aromatic hydrocarbon, and is a white crystalline solid with a characteristic odor that is detectable at concentrations as low as 0.08  ppm by mass. As an aromat ...
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 Differential scanning calorimetry (DSC) is a thermoanalytical technique in which the difference in the amount of heat required to increase the temperature of a sample and reference is measured as a function of temperature. Both the sample and ref ...
. 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 °C). Its cryoscopic constant is 3.9 °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. 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 A melting-point apparatus is a scientific instrument used to determine the melting point of a substance. Some types of melting-point apparatuses include the Thiele tube, Fisher-Johns apparatus, Gallenkamp (Electronic) melting-point apparatus and ...
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. This phenomenon is applicable in preparing a freezing mixture to make
ice cream Ice cream is a sweetened frozen food typically eaten as a snack or dessert. It may be made from milk or cream and is flavoured with a sweetener, either sugar or an alternative, and a spice, such as cocoa or vanilla, or with fruit such as ...
. For this purpose, NaCl or another salt is used to lower the melting point of ice. 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 °C is considered to be unadulterated.


Formula


For dilute solution

If the solution is treated as an
ideal solution In chemistry, an ideal solution or ideal mixture is a solution that exhibits thermodynamic properties analogous to those of a mixture of ideal gases. The enthalpy of mixing is zero as is the volume change on mixing by definition; the closer to ze ...
, 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"). : \Delta T_f \propto \frac : \Delta T_f = K_fbi where: * \Delta T_f is the decrease in freezing point, defined as the freezing point T_f^0 of the pure solvent minus the freezing point T_f of the solution, as the formula above results in a positive value given that all factors are positive. From the \Delta T_f calculated using the formula above, the freezing point of the solution can then be calculated as T_f = T_f^0 - \Delta T_f. * K_f, 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.) * b is the
molality Molality is a measure of the number of moles of solute in a solution corresponding to 1 kg or 1000 g of solvent. This contrasts with the definition of molarity which is based on a specified volume of solution. A commonly used unit for molali ...
(moles of solute per kilogram of solvent) * i is the
van 't Hoff factor The van 't Hoff factor (named after Dutch chemist Jacobus Henricus van 't Hoff) is a measure of the effect of a solute on colligative properties such as osmotic pressure, relative lowering in vapor pressure, boiling-point elevation and free ...
(number of ion particles per formula unit of solute, e.g. i = 2 for NaCl, 3 for BaCl2). Some values of the cryoscopic constant ''K''f for selected solvents:


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) proposed a new equation: : \Delta T_\text = \frac. In the above equation, ''T''F is the normal freezing point of the pure solvent (273 K for water, for example); ''a''liq is the activity of the solvent in the solution (water activity for aqueous solution); Δ''H''fusTF is the enthalpy change of fusion of the pure solvent at ''T''F, which is 333.6 J/g for water at 273 K; Δ''C''fusp is the difference between the heat capacities of the liquid and solid phases at ''T''F, which is 2.11 J/(g·K) for water. The solvent activity can be calculated from the Pitzer model or modified
TCPC model Pitzer equations are important for the understanding of the behaviour of ions dissolved in natural waters such as rivers, lakes and sea-water. They were first described by physical chemist Kenneth Pitzer. The parameters of the Pitzer equations are ...
, which typically requires 3 adjustable parameters. For the TCPC model, these parameters are available for many single salts.


See also

* Melting-point depression *
Boiling-point elevation Boiling-point elevation describes the phenomenon that the boiling point of a liquid (a solvent) will be higher when another compound is added, meaning that a solution has a higher boiling point than a pure solvent. This happens whenever a non-vol ...
*
Colligative properties In chemistry, colligative properties are those properties of solutions that depend on the ratio of the number of solute particles to the number of solvent particles in a solution, and not on the nature of the chemical species present. The number ...
* Deicing *
Eutectic point A eutectic system or eutectic mixture ( ) is a homogeneous mixture that has a melting point lower than those of the constituents. The lowest possible melting point over all of the mixing ratios of the constituents is called the ''eutectic temp ...
*
Frigorific mixture A frigorific mixture is a mixture of two or more phases in a chemical system that, so long as none of the phases are completely consumed during equilibration, reaches an equilibrium temperature that is independent of the starting temperature of ...
*
List of boiling and freezing information of solvents See also *Freezing-point depression *Boiling-point elevation Boiling-point elevation describes the phenomenon that the boiling point of a liquid (a solvent) will be higher when another compound is added, meaning that a solution has a higher boi ...
*
Snow removal Snow removal or snow clearing is the job of removing snow after a snowfall to make travel easier and safer. This is done by both individual households and by governments and institutions. De-icing and anti-icing De-icing is defined as removal ...


References

{{Authority control Amount of substance Chemical properties Phase transitions