Colligative properties

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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. [1] The number ratio can be related to the various units for concentration of a solution such as molarity, molality, normality (chemistry), etc. The assumption that solution properties are independent of nature of solute particles is exact only for ideal solutions, which are solutions that exhibit thermodynamic properties analogous to those of an ideal gas, and is approximate for dilute real solutions. In other words, colligative properties are a set of solution properties that can be reasonably approximated by the assumption that the solution is ideal.

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Only properties which result from the dissolution of a nonvolatile solute in a volatile liquid solvent are considered. [2] They are essentially solvent properties which are changed by the presence of the solute. The solute particles displace some solvent molecules in the liquid phase and thereby reduce the concentration of solvent and increase its entropy, so that the colligative properties are independent of the nature of the solute. The word colligative is derived from the Latin colligatus meaning bound together. [3] This indicates that all colligative properties have a common feature, namely that they are related only to the number of solute molecules relative to the number of solvent molecules and not to the nature of the solute. [4]

Colligative properties include:

For a given solute-solvent mass ratio, all colligative properties are inversely proportional to solute molar mass.

Measurement of colligative properties for a dilute solution of a non-ionized solute such as urea or glucose in water or another solvent can lead to determinations of relative molar masses, both for small molecules and for polymers which cannot be studied by other means. Alternatively, measurements for ionized solutes can lead to an estimation of the percentage of dissociation taking place.

Colligative properties are studied mostly for dilute solutions, whose behavior may be approximated as that of an ideal solution. In fact, all of the properties listed above are colligative only in the dilute limit: at higher concentrations, the freezing point depression, boiling point elevation, vapor pressure elevation or depression, and osmotic pressure are all dependent on the chemical nature of the solvent and the solute.

Relative lowering of vapor pressure

A vapor is a substance in a gaseous state at a temperature lower than its critical point. Vapor Pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its solid or liquid state. The vapor pressure of a solvent is lowered when a non-volatile solute is dissolved in it to form a solution.

For an ideal solution, the equilibrium vapor pressure is given by Raoult's law as

where is the vapor pressure of the pure component (i= A, B, ...) and is the mole fraction of the component in the solution

For a solution with a solvent (A) and one non-volatile solute (B), and

The vapor pressure lowering relative to pure solvent is , which is proportional to the mole fraction of solute.

If the solute dissociates in solution, then the number of moles of solute is increased by the van 't Hoff factor , which represents the true number of solute particles for each formula unit. For example, the strong electrolyte MgCl2 dissociates into one Mg2+ ion and two Cl ions, so that if ionization is complete, i = 3 and , where is calculated with moles of solute i times initial moles and moles of solvent same as initial moles of solvent before dissociation. The measured colligative properties show that i is somewhat less than 3 due to ion association.

Boiling point and freezing point

Addition of solute to form a solution stabilizes the solvent in the liquid phase, and lowers the solvent's chemical potential so that solvent molecules have less tendency to move to the gas or solid phases. As a result, liquid solutions slightly above the solvent boiling point at a given pressure become stable, which means that the boiling point increases. Similarly, liquid solutions slightly below the solvent freezing point become stable meaning that the freezing point decreases. Both the boiling point elevation and the freezing point depression are proportional to the lowering of vapor pressure in a dilute solution.

These properties are colligative in systems where the solute is essentially confined to the liquid phase. Boiling point elevation (like vapor pressure lowering) is colligative for non-volatile solutes where the solute presence in the gas phase is negligible. Freezing point depression is colligative for most solutes since very few solutes dissolve appreciably in solid solvents.

Boiling point elevation (ebullioscopy)

The boiling point of a liquid at a given external pressure is the temperature () at which the vapor pressure of the liquid equals the external pressure. The normal boiling point is the boiling point at a pressure equal to 1 atm.

The boiling point of a pure solvent is increased by the addition of a non-volatile solute, and the elevation can be measured by ebullioscopy. It is found that

[5]

Here i is the van 't Hoff factor as above, Kb is the ebullioscopic constant of the solvent (equal to 0.512 °C kg/mol for water), and m is the molality of the solution.

The boiling point is the temperature at which there is equilibrium between liquid and gas phases. At the boiling point, the number of gas molecules condensing to liquid equals the number of liquid molecules evaporating to gas. Adding a solute dilutes the concentration of the liquid molecules and reduces the rate of evaporation. To compensate for this and re-attain equilibrium, the boiling point occurs at a higher temperature.

If the solution is assumed to be an ideal solution, Kb can be evaluated from the thermodynamic condition for liquid-vapor equilibrium. At the boiling point the chemical potential μA of the solvent in the solution phase equals the chemical potential in the pure vapor phase above the solution.

where the asterisks indicate pure phases. This leads to the result , where R is the molar gas constant, M is the solvent molar mass and ΔHvap is the solvent molar enthalpy of vaporization. [6]

Freezing point depression (cryoscopy)

The freezing point () of a pure solvent is lowered by the addition of a solute which is insoluble in the solid solvent, and the measurement of this difference is called cryoscopy. It is found that

[5] (which can also be written as )

Here Kf is the cryoscopic constant (equal to 1.86 °C kg/mol for the freezing point of water), i is the van 't Hoff factor, and m the molality (in mol/kg). This predicts the melting of ice by road salt.

In the liquid solution, the solvent is diluted by the addition of a solute, so that fewer molecules are available to freeze. Re-establishment of equilibrium is achieved at a lower temperature at which the rate of freezing becomes equal to the rate of liquefying. 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. The equality of chemical potentials permits the evaluation of the cryoscopic constant as , where ΔfusH is the solvent molar enthalpy of fusion. [6]

Osmotic pressure

The osmotic pressure of a solution is the difference in pressure between the solution and the pure liquid solvent when the two are in equilibrium across a semipermeable membrane, which allows the passage of solvent molecules but not of solute particles. If the two phases are at the same initial pressure, there is a net transfer of solvent across the membrane into the solution known as osmosis. The process stops and equilibrium is attained when the pressure difference equals the osmotic pressure.

Two laws governing the osmotic pressure of a dilute solution were discovered by the German botanist W. F. P. Pfeffer and the Dutch chemist J. H. van’t Hoff:

  1. The osmotic pressure of a dilute solution at constant temperature is directly proportional to its concentration.
  2. The osmotic pressure of a solution is directly proportional to its absolute temperature. [7]

These are analogous to Boyle's law and Charles's law for gases. Similarly, the combined ideal gas law, , has as an analogue for ideal solutions , where is osmotic pressure; V is the volume; n is the number of moles of solute; R is the molar gas constant 8.314 J K−1 mol−1; T is absolute temperature; and i is the Van 't Hoff factor.

The osmotic pressure is then proportional to the molar concentration , since

The osmotic pressure is proportional to the concentration of solute particles ci and is therefore a colligative property.

As with the other colligative properties, this equation is a consequence of the equality of solvent chemical potentials of the two phases in equilibrium. In this case the phases are the pure solvent at pressure P and the solution at total pressure (P + ). [8]

History

The word colligative (Latin: co, ligare) was introduced in 1891 by Wilhelm Ostwald. Ostwald classified solute properties in three categories: [9] [10]

  1. colligative properties, which depend only on solute concentration and temperature and are independent of the nature of the solute particles
  2. additive properties such as mass, which are the sums of properties of the constituent particles and therefore depend also on the composition (or molecular formula) of the solute, and
  3. constitutional properties, which depend further on the molecular structure of the given solute.

Related Research Articles

<span class="mw-page-title-main">Solution (chemistry)</span> Homogeneous mixture of a solute and a solvent

In chemistry, a solution is a special type of homogeneous mixture composed of two or more substances. In such a mixture, a solute is a substance dissolved in another substance, known as a solvent. If the attractive forces between the solvent and solute particles are greater than the attractive forces holding the solute particles together, the solvent particles pull the solute particles apart and surround them. These surrounded solute particles then move away from the solid solute and out into the solution. The mixing process of a solution happens at a scale where the effects of chemical polarity are involved, resulting in interactions that are specific to solvation. The solution usually has the state of the solvent when the solvent is the larger fraction of the mixture, as is commonly the case. One important parameter of a solution is the concentration, which is a measure of the amount of solute in a given amount of solution or solvent. The term "aqueous solution" is used when one of the solvents is water.

<span class="mw-page-title-main">Osmotic pressure</span> Measure of the tendency of a solution to take in pure solvent by osmosis

Osmotic pressure is the minimum pressure which needs to be applied to a solution to prevent the inward flow of its pure solvent across a semipermeable membrane. It is also defined as the measure of the tendency of a solution to take in its pure solvent by osmosis. Potential osmotic pressure is the maximum osmotic pressure that could develop in a solution if it were separated from its pure solvent by a semipermeable membrane

Raoult's law ( law) is a relation of physical chemistry, with implications in thermodynamics. Proposed by French chemist François-Marie Raoult in 1887, it states that the partial pressure of each component of an ideal mixture of liquids is equal to the vapor pressure of the pure component multiplied by its mole fraction in the mixture. In consequence, the relative lowering of vapor pressure of a dilute solution of nonvolatile solute is equal to the mole fraction of solute in the solution.

<span class="mw-page-title-main">Vapor pressure</span> Pressure exerted by a vapor in thermodynamic equilibrium

Vapor pressure or equilibrium vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases at a given temperature in a closed system. The equilibrium vapor pressure is an indication of a liquid's thermodynamic tendency to evaporate. It relates to the balance of particles escaping from the liquid in equilibrium with those in a coexisting vapor phase. A substance with a high vapor pressure at normal temperatures is often referred to as volatile. The pressure exhibited by vapor present above a liquid surface is known as vapor pressure. As the temperature of a liquid increases, the attractive interactions between liquid molecules become less significant in comparison to the entropy of those molecules in the gas phase, increasing the vapor pressure. Thus, liquids with strong intermolecular interactions are likely to have smaller vapor pressures, with the reverse true for weaker interactions.

<span class="mw-page-title-main">Partial pressure</span> Pressure of a component gas in a mixture

In a mixture of gases, each constituent gas has a partial pressure which is the notional pressure of that constituent gas as if it alone occupied the entire volume of the original mixture at the same temperature. The total pressure of an ideal gas mixture is the sum of the partial pressures of the gases in the mixture.

In chemistry, the molar mass of a chemical compound is defined as the ratio between the mass and the amount of substance of any sample of said compound. The molar mass is a bulk, not molecular, property of a substance. The molar mass is an average of many instances of the compound, which often vary in mass due to the presence of isotopes. Most commonly, the molar mass is computed from the standard atomic weights and is thus a terrestrial average and a function of the relative abundance of the isotopes of the constituent atoms on Earth. The molar mass is appropriate for converting between the mass of a substance and the amount of a substance for bulk quantities.

In chemical thermodynamics, activity is a measure of the "effective concentration" of a species in a mixture, in the sense that the species' chemical potential depends on the activity of a real solution in the same way that it would depend on concentration for an ideal solution. The term "activity" in this sense was coined by the American chemist Gilbert N. Lewis in 1907.

In physical chemistry, Henry's law is a gas law that states that the amount of dissolved gas in a liquid is directly proportional to its partial pressure above the liquid. The proportionality factor is called Henry's law constant. It was formulated by the English chemist William Henry, who studied the topic in the early 19th century.

The self-ionization of water (also autoionization of water, and autodissociation of water, or simply dissociation of water) is an ionization reaction in pure water or in an aqueous solution, in which a water molecule, H2O, deprotonates (loses the nucleus of one of its hydrogen atoms) to become a hydroxide ion, OH. The hydrogen nucleus, H+, immediately protonates another water molecule to form a hydronium cation, H3O+. It is an example of autoprotolysis, and exemplifies the amphoteric nature of water.

<span class="mw-page-title-main">Freezing-point depression</span> Process in which adding a solute to a solvent decreases the freezing point of the solvent

Freezing-point depression is a drop in the maximum temperature at which a substance freezes, caused when a smaller amount of another, non-volatile substance is added. Examples include adding salt into water, alcohol in water, ethylene or propylene glycol in water, adding copper to molten silver, or the mixing of two solids such as impurities into a finely powdered drug.

While typical formulas for the calculation of different colligative properties are used in general for non-electrolytic solutions, Electrolytes don't follow these rules because they dissociate in their solutions. The Van't Hoff factor (i) is used for calculation of colligative properties of electrolytes. The van 't Hoff factor i 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 freezing-point depression. The van 't Hoff factor is the ratio between the actual concentration of particles produced when the substance is dissolved and the concentration of a substance as calculated from its mass. For most non-electrolytes dissolved in water, the van 't Hoff factor is essentially 1.

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 zero the enthalpy of mixing is, the more "ideal" the behavior of the solution becomes. The vapor pressures of the solvent and solute obey Raoult's law and Henry's law, respectively, and the activity coefficient is equal to one for each component.

In chemical thermodynamics, the fugacity of a real gas is an effective partial pressure which replaces the mechanical partial pressure in an accurate computation of chemical equilibrium. It is equal to the pressure of an ideal gas which has the same temperature and molar Gibbs free energy as the real gas.

In thermodynamics, the cryoscopic constant, Kf, relates molality to freezing point depression. It is the ratio of the latter to the former:

Boiling-point elevation is the phenomenon whereby the boiling point of a liquid 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-volatile solute, such as a salt, is added to a pure solvent, such as water. The boiling point can be measured accurately using an ebullioscope.

François-Marie Raoult was a French chemist who conducted research into the behavior of solutions, especially their physical properties.

<span class="mw-page-title-main">Osmotic concentration</span> Molarity of osmotically active particles

Osmotic concentration, formerly known as osmolarity, is the measure of solute concentration, defined as the number of osmoles (Osm) of solute per litre (L) of solution. The osmolarity of a solution is usually expressed as Osm/L, in the same way that the molarity of a solution is expressed as "M". Whereas molarity measures the number of moles of solute per unit volume of solution, osmolarity measures the number of osmoles of solute particles per unit volume of solution. This value allows the measurement of the osmotic pressure of a solution and the determination of how the solvent will diffuse across a semipermeable membrane (osmosis) separating two solutions of different osmotic concentration.

<span class="mw-page-title-main">Flory–Huggins solution theory</span> Lattice model of polymer solutions

Flory–Huggins solution theory is a lattice model of the thermodynamics of polymer solutions which takes account of the great dissimilarity in molecular sizes in adapting the usual expression for the entropy of mixing. The result is an equation for the Gibbs free energy change for mixing a polymer with a solvent. Although it makes simplifying assumptions, it generates useful results for interpreting experiments.

In thermodynamics, the ebullioscopic constantKb relates molality b to boiling point elevation. It is the ratio of the latter to the former:

An osmotic coefficient is a quantity which characterises the deviation of a solvent from ideal behaviour, referenced to Raoult's law. It can be also applied to solutes. Its definition depends on the ways of expressing chemical composition of mixtures.

References

  1. McQuarrie, Donald, et al. Colligative properties of Solutions" General Chemistry Mill Valley: Library of Congress, 2011. ISBN   978-1-89138-960-3.
  2. KL Kapoor Applications of Thermodynamics Volume 3
  3. K.J. Laidler and J.L. Meiser, Physical Chemistry (Benjamin/Cummings 1982), p.196
  4. Castellan, Gilbert W. (1983). Physical Chemistry (3rd ed.). Addison-Wesley. p. 281. ISBN   978-0201103861 . Retrieved 20 July 2019.
  5. 1 2 Tro, Nivaldo J. (2018). Chemistry; Structure and Properties (Textbook.) (2nd ed.). Pearson Education. pp. 563–566. ISBN   978-0-134-52822-9.
  6. 1 2 T. Engel and P. Reid, Physical Chemistry (Pearson Benjamin Cummings 2006) p.204-5
  7. "Van't Hoff's Laws of Osmotic Pressure - QS Study". qsstudy.com. Retrieved 2022-03-08.
  8. Engel and Reid p.207
  9. W.B. Jensen, J. Chem. Educ. 75, 679 (1998) Logic, History, and the Chemistry Textbook I. Does Chemistry Have a Logical Structure?
  10. H.W. Smith, Circulation 21, 808 (1960) Theory of Solutions: A Knowledge of the Laws of Solutions ...