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Inchemistry,colligative properties are those properties ofsolutions that depend on the ratio of the number of solute particles to the number ofsolventparticles in a solution, and not on the nature of the chemical species present.[1] The number ratio can be related to the various units forconcentration of a solution such asmolarity,molality,normality, etc.
The assumption that solution properties are independent of nature of solute particles is exact only forideal solutions, which are solutions that exhibitthermodynamic properties analogous to those of anideal 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.
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 Latincolligatus meaningbound 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 asurea orglucose in water or another solvent can lead to determinations of relativemolar masses, both for small molecules and forpolymers which cannot be studied by other means. Alternatively, measurements for ionized solutes can lead to an estimation of the percentage ofdissociation 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.
Avapor is a substance in a gaseous state at a temperature lower than itscritical 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 anideal solution, the equilibrium vapor pressure is given byRaoult's law aswhere is the vapor pressure of thepure component (i= A, B, ...) and is themole fraction of the component in the solution.
For a solution with a solvent (A) and one non-volatile solute (B), and.
The vapor pressurelowering relative to pure solvent is, which is proportional to the mole fraction of solute.
If the solutedissociates in solution, then the number of moles of solute is increased by thevan 't Hoff factor, which represents the true number of solute particles for each formula unit. For example, thestrong electrolyteMgCl2 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 thati is somewhat less than 3 due toion association.
Addition of solute to form a solution stabilizes the solvent in the liquid phase, and lowers the solvent'schemical 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 theboiling point elevation and thefreezing 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.
Theboiling point of a liquid at a given external pressure is the temperature () at which the vapor pressure of the liquid equals the external pressure. Thenormal boiling point is the boiling point at a pressure equal to 1atm.
The boiling point of a pure solvent is increased by the addition of a non-volatile solute, and the elevation can be measured byebullioscopy. It is found that
Herei is thevan 't Hoff factor as above,Kb is theebullioscopic constant of the solvent (equal to 0.512 °C kg/mol for water), andm is themolality 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 anideal solution,Kb can be evaluated from thethermodynamic condition for liquid-vapor equilibrium. At the boiling point, thechemical potential μA of the solvent in the solution phase equals the chemical potential in the pure vapor phase above the solution.
The asterisks indicate pure phases. This leads to the result, where R is themolar gas constant, M is the solventmolar mass and ΔHvap is the solvent molarenthalpy of vaporization.[6]
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 calledcryoscopy. It is found that
HereKf is thecryoscopic constant (equal to 1.86 °C kg/mol for the freezing point of water),i is the van 't Hoff factor, andm the molality (in mol/kg). This predicts the melting of ice byroad 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 molarenthalpy of fusion.[6]
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 asemipermeable 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 asosmosis. 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 botanistW. F. P. Pfeffer and the Dutch chemistJ. H. van't Hoff:
These are analogous toBoyle's law andCharles's law for gases. Similarly, the combinedideal 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 molargas constant 8.314 J K−1 mol−1;T is absolute temperature; andi is theVan 't Hoff factor.
The osmotic pressure is then proportional to themolar concentration, since
The osmotic pressure is proportional to the concentration of solute particlesci and is therefore a colligative property.
As with the other colligative properties, this equation is a consequence of the equality of solventchemical potentials of the two phases in equilibrium. In this case the phases are the pure solvent at pressureP and the solution at total pressure (P +).[8]
The word colligative (Latin: co, ligare) was introduced in 1891 byWilhelm Ostwald. Ostwald classified solute properties in three categories:[9][10]