Colligative Properties of Solution

COLLIGATIVE PROPERTIES OF SOLUTIONS

Solutions, especially liquid solutions, generally have markedly different properties than either the pure solvent or the solute. For example, a solution of sugar in water is neither crystalline like sugar nor tasteless like water.

Concentrated - A solution of high concentration.

Concentration - The amount of solute dissolved in a given amount of solvent.

Dilute - A solution of low concentration or the process of lowering the concentration of a solution by the addition of solvent.

Dilution - The decrease of the concentration of a solution by the addition of more solvent.

Dissolve - To become a part of a solution.

Nonvolatile - A substance that does not have an appreciable vapor pressure.

Raoult's Law - The vapor pressure of a solution is the product of the mole fraction of the solvent and the vapor pressure of the pure solvent.

Solubility - The amount of a particular solute that can dissolve in a given amount of a particular solvent. Solubilities are generally listed in g / L.

Solute - A minor component of a solution.

Solution - A homogeneous mixture.

Solvent - The major component of a solution.

colligative propertiese - are properties of solutions that depend on the ratio of the number of solute particles to the number of solvent molecules in a solution, and not on the type of chemical species present.The number ratio can be related to the various units for concentration of solutions. The assumption that solution properties are independent of the nature of solute particles is only exact for ideal solutions, and is approximate for dilute real solutions. In other words, colligative properties are a set of solution properties that can be reasonably approximated by assuming that the solution is ideal.

Colligative properties include:

• Relative lowering of vapor pressure

• Elevation of boiling point

• Depression of freezing point

• Osmotic pressure studied for dilute solutions, whose behavior may often be approximated as that of an ideal solution 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 ionization taking place.
  Colligative properties are mostly ideal solution,
  Relative lowering of vapor pressure
  The vapor pressure of a liquid is the pressure of the vapor which is in equilibrium with that liquid. 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

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 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

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 atmosphere.

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

Here i is the van 't Hoff factor as above, K_b 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 K_b can be evaluated from the thermodynamic condition for liquid-vapor equilibrium. At the boiling point the chemical potential μ_Aof 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 ΔH_vap is the solvent molar enthalpy of vaporization

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.

These are analogous to Boyle's law and Charles's Law for gases. Similarly, the combined ideal gas law, , has as analog 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 + π.