Colligative Properties of Solution

束一的性質（そくいつてきせいしつ）とは不揮発性溶質の希薄溶液における相平衡の性質で、溶質を溶媒で希釈する際に化学ポテンシャルが減少することを原因として、蒸気圧降下、沸点上昇、凝固点降下、浸透圧といった現象を引き起こす。

化学ポテンシャルの強度は溶質のモル分率に依存する為、束一的性質を原因とする現象は溶質の種類によらずモル濃度（より正確には活量）の大小でその強度が決定付けられる。それ故、高分子化合物などの（平均）分子量は、束一的性質に基づいて沸点上昇、凝固点降下、浸透圧の変化量をもとに決定することが可能である。

         Colligative properties are those properties of solutions that depend on the number of dissolved particles in solution, but not on the identities of the solutes. For example, the freezing point of salt water is lower than that of pure water, due to the presence of the salt dissolved in the water. To a good approximation, it does not matter whether the salt dissolved in water is sodium chloride or potassium nitrate; if the molar amounts of solute are the same and the number of ion are the same, the freezing points will be the same. For example, AlCl ₃ and K ₃ PO ₄ would exhibit essentially the same colligative properties, since each compound dissolves to produce four ions per formula unit. The four commonly studied colligative properties are freezing point depression, boiling point elevation, vapor pressure lowering, and osmotic pressure. Since these properties yield information on the number of solute particles in solution, one can use them to obtain the molecular weight of the solute.

Vapor Pressure Lowering

• The escaping tendency of a solvent is measured by its vapor pressure
• Vapor pressure measures the concentration of solvent molecules in the gas phase.
• Adding a nonvolatile solute lowers the vapor pressure of the solvent since a smaller proportion of the molecules at the surface of the solution are solvent molecules, fewer solvent molecules can escape from the solution compared to the pure solvent.
• The quantitative relationship between vapor pressure lowering and concentration in an ideal solution is stated in Raoult's Law.  

          In predicting the expected freezing point of a solution, one must consider not only the number of formula units present, but also the number of ions that result from each formula unit, in the case of ionic compounds. One can calculate the change in freezing point (Δ T _f ) relative to the pure solvent using the equation:

Δ T _f = i K _f m

where K _f is the freezing point depression constant for the solvent (1.86°C·kg/mol for water), m is the number of moles of solute in solution per kilogram of solvent, and i is the number of ions present per formula unit (e.g., i = 2 for NaCl). This formula is approximate, but it works well for low solute concentrations.

Boiling-Point Elevation

• A liquid boils at the temperature at which its vapor pressure equals atmospheric pressure.
• The presence of a nonvolatile solute lowers the vapor pressure of a solution so it is necessary to heat the solution to a higher temperature in order for it to boil.
• The amount by which the boiling point is raised is known as the boiling point elevation.
• The boiling-point elevation is proportional to the concentration of solute particles expressed as moles of solute per kilogram of solvent.

         The formula used to calculate the change in boiling point (Δ T _b ) relative to the pure solvent is similar to that used for freezing point depression:

Δ T _b = i K _b m ,

where K _b is the boiling point elevation constant for the solvent (0.52°C·kg/mol for water), and m and i have the same meanings as in the freezing point depression formula. Note that Δ T _b represents an increase in the boiling point, whereas Δ T _f represents a decrease in the freezing point.

Freezing-Point Depression

• The presence of a nonvolatile solute lowers the freezing point of a solvent.
• In order to freeze the solvent, it must be cooled to a lower temperature in order to compensate for its lower escaping tendency.
• The amount by which the freezing point is lowered is known as the freezing point depression.
• The freezing-point depression is proportional to the concentration of solute particles expressed as moles of solute per kilogram of solvent.

          Raoult's law states that the vapor pressure of the solvent over the solution is proportional to the fraction of solvent molecules in the solution; that is, if twothirds of the molecules are solvent molecules, the vapor pressure due to the solvent is approximately two-thirds of what it would be for pure solvent at that temperature. If the solute has a vapor pressure of its own, then the total vapor pressure over the solution would be:

P _vap = ⅔ (pure solvent vapor pressure) + ⅓ (pure solute vapor pressure)

Osmotic Pressure

• When two liquids, such as a solvent and a solution, are separated by a semipermeable membrane that allows only solvent molecules to pass through, then there is a net transfer of solvent molecules from the solvent to the solution. This process is called osmosis.
• Osmosis can be stopped by applying pressure to compensate for the difference in escaping tendencies. The pressure required to stop osmosis is called osmotic pressure.
• In dilute solutions, osmotic pressure is directly proportional to the molarity of the solution and its temperature in Kelvin.

         The following figure describes vapor pressure over a benzene-toluene solution, plotted as a function of the fraction of benzene molecules in the solution. The solid curve is the total vapor pressure, while the short-dashed and long-dashed curves are the vapor pressures from the benzene and toluene, respectively. Note that the two dashed curves add up to the solid curve.

 References: http://www.chemistryexplained.com/Ce-Co/Colligative-Properties.html
                   http://www.ausetute.com.au/colligative.html