Derive and expression Depression of freezing point.
Answers
According to Raoult's law, when a non-volatile solid is added to the solvent its vapour pressure decreases and now it would become equal to that of solid solvent at lower temperature. Thus, the freezing point of the solvent decreases.
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Answer:
Freezing point of a substance is the temperature at which the vapour pressure
of the substance in its liquid phase is equal to the vapour pressure in the solid phase.
If the vapour pressure of the solution is equal to the vapour pressure of the pure solid solvent then the solution freezes.
According to Raoult’s law, addition of non-volatile solute decreases the vapour pressure of the solvent and would be equal to that of solid solvent at lower This decreases the freezing point of thesolvent.
The decrease in the freezing point = ΔTf = Tf – Tf0. This is known as depression in freezing point.
Tf0 = freezing point of pure solvent
Tf0 = freezing point when non-volatile solute is dissolved
In a dilute solution the depression of freezing point Tf is directly proportional to molality of the solution. Mathematically,
ΔTf ∝m
ΔTf = Kf m
Kf = Proportionality constant depending upon the nature of the solvent. This is known as Freezing Point Depression Constant or Molal Depression Constant or Cryoscopic Constant. The unit of Kf is K kg mol-1.
Let w2 and M2 = Masses and molar masses of solute
w1= Mass of solvent
Putting this value of molality in the equation ΔTf = Kf m
M2 can be determined by the equation
The values of Kf and Kb can be determined from the following relations.
R= gas constant
M1 = molar mass of the solvent
Δfus H= enthalpies for the fusion of the solvent.
Δvap H= enthalpies for the vaporization of the solvent.