Derive an expression relating the depression of freezing point with the amount of solute present in the solution. from Chemistry Solutions Class 12 Nagaland Board
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Class 10 Class 12
Derive an expression relating the depression of freezing point with the amount of solute present in the solution.


the freezing point of a substance may be defined as the temperature at which the vapour pressure of the substance in its liquid phase is equal to its vapour pressure in the solid phase.
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.

Let Tf0 be the freezing point of pure solvent and Tf be its freezing point when non-volatile solute is dissolved in it. The decrease in freezing point.
Tf = Tf0 - Tf

Similar to elevation of boiling point, depression of freezing point (ΔTf) for dilute solution (ideal solution) is directly proportional to molality,
m of the solution. Thus,
ΔTf ∝ m

ΔTf= Kfm

The proportionality constant, Kf, which depends on the nature of the solvent is known as Freezing Point Depression Constant or Molal Depression Constant or Cryoscopic Constant. The unit of Kf is K kg mol-1

If w2 gram of the solute having molar mass as M2, present in wgram of solvent, produces the depression in freezing point ΔTf of the
solvent then molality of the solute is given by the equation:
m= w2M2w11000 substituting this value in Tf = KfmTf = Kf × w2 ×1000M2×w1M2 = Kf × w2 ×1000Tf×w1

Thus for determining the molar mass of the solute we should know the quantities w1, w2, ΔTf, along with the molal freezing point depression constant.



Calculate the mass percentage of benzene (C6H6) and carbon tetrachloride (CCl4) if 22 g of benzene is dissolved in 122 g of carbon tetrachloride.

Mass % of benzene
                      = mass of benzenemass of solution ×100= 2222+122×100= 22144×100 = 15.28%
Mass% of carbon tetrachloride = 100 - 15.28
                          = 84.72%

Calculate the molarity of each of the following solution (a) 30 g of Co(NO3)2.6H2O in 4.3 L solution (b) 30 mL of 0.5 MH2SO4 diluted to 500 mL.


Molarity (M) is defined as number of moles of solute dissolved in one litre (or one cubic decimetre) of solution.

(a) Mol. mass of Co(NO3). 6H2O

               =58.9+(14+3×16)2+6(18)=58.9+(14+48)×2+108=58.9+124+108 = 290.9

Moles of Co(NO)3.6H2O
                                       =30290.9=0.103 mol.
Volume of solution = 4.3 L
          M=Moles of soluteVolume of solution in litre    = 1034.3 = 0.024 M

(b) Number of moles present in 1000 ml of 0.5M H2SO4= 0.5 mol
therefore number of moles present in 30ml of 0.5M H2SO4=0.5×301000mol =0.015mol
therefore molarity =0.015/0.5L 

thus molarity is 0.03M



Calculate the mole fraction of benzene in solution containing 30% by mass in carbon tetrachloride.

Let the total mass of the solution be 100g and mass of benzene be 30 g
therefore mass of tetrachloride= (100-30)g = 70g
Molar mass of benzene,


Calculate the mass of urea (NH2CONH2) required in making 2.5 kg 0.25 of molal aqueous solution.


Molality (m) is defined as the number of moles of the solute per kilogram (kg) of the solvent and is expressed as:

= Moles of soluteMass of solvent in kg
Mol. mass of urea NH2CONH2
                 = 14 + 2 + 12 + 16 + 14 + 2
                 = 60 g mol-1

Molality (m) = Moles of soluteMass of solvent in kg

25 = Moles of solute2.5

or Moles of solute
                = 0.25 x 0.25 =  0.625

  Mass of urea
                   = Moles of solute x Molar mass

                   = 0.625 x 60 = 37.5 g


Calculate (a) molality (b) molarity and (c) mole fraction of KI if the density of 20% (mass/mass) aqueous KI is 1.202 g mL-1.

(a) 20% (mass/mass) means that 20 g of KI is present in 80 g of water.

Therefore, Moles of KI in solution

moles of KI = 20/166 =0.12mol
moles of water =80/18 =4.44mol
therefore, mole fraction of KI
=moles of  KImoles of KI + moles of water

=0.120.12+4.44= 0.0263