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Elevation of boiling point

A liquid boils at a temperature when its vapor pressure becomes equal to the atmospheric pressure.
 
Since the addition of a non-volatile solute decreases the vapor pressure of the solvent, the boiling point of the solution becomes greater than that of the pure solvent.
 
Description: 45229.png
 
If Tb is the boiling point of a pure solvent and Description: 45237.png is the boiling point of the solution, then the elevation in boiling point is represented as ΔTb. Thus,
 
Description: 45245.png
 
Since, elevation in boiling point is proportional to the decrease in vapor pressure which in turn is proportional to the concentration of solute. Thus,
 
ΔTb m
 
where m is the molality of the solution.
 
or ΔTb = Kbm
 
where Kb is the molal boiling point elevation constant or ebullioscopic constant.
 
Molal boiling point elevation constant (Kb): It is the elevation in boiling point achieved when a solution of a non-volatile solute of concentration 1 molal is boiled. Its unit is (K kg)/mol. Kb is related to molar enthalpy of vaporization as
 
Description: 45257.png
 
where M is the molar mass of solvent, R is the universal gas constant, Tb is the boiling point of pure solvent, and ΔHvap is the enthalpy of vaporization of solvent.

Depression in freezing point

Freezing point is defined as the temperature when the vapor pressures of the liquid and the solid are equal.
 
If Tf is the freezing point of pure solvent, and Description: 45266.png is the freezing point of the solution, then the depression in freezing point is represented as ΔTf. Thus,
 
Description: 45275.png
 
Since depression in freezing point is proportional to the decrease in vapor pressure which in turn is proportional to the concentration of solute. Thus,
 
ΔTf m
 
where m is the molality of the solution.
 
Description: 47798.png
 
or ΔTf = Kf m
 
where Kf is the molal freezing point depression constant or cryoscopic constant.
 
Molal freezing point depression constant (Kf ): It is the depression in freezing point achieved when a solution of a non-volatile solute of concentration 1 molal is frozen. Its unit is (K kg)/mol.
 
Kf is related to molar enthalpy of fusion as
 
Description: 45293.png
 
where M is the molar mass of solvent, R is the universal gas constant, Tf is the freezing point of pure solvent, and ΔHfusion is the enthalpy of fusion of solid solvent.

Osmotic pressure

It is the excess pressure that must be applied to a solution to prevent the passage of solvent when the two liquids are separated by a perfectly semipermeable membrane.
 
πV = nRT
 
Description: 45301.png
 
where π is the osmotic pressure in atmospheres, n is the number of moles of solute (w/M) in V liters of solution at temperature T (kelvin), R is equal to 0.0821 L-atm/(K mol), and C is the molarity of the solution. The measurement of osmotic pressure provides a method of determining molecular weights of proteins, polymer, and other macromolecules.




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