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Class 10 Class 12
What is meant by abnormal mass of solute? Discuss the factors which bring abnormality in the experimentally determined molecular masses of solutes using colligative properties.


A molar mass that is either lower or higher than the expected or normal value is called as abnormal molar mass.

In order to account for all such abnormalities, introduced a factor
(i) known as van 't Hoff's factor, which represents the extent of association (or) dissociation of a solute.

Van't Hoff's factor is defined as the ratio of the observed colligative property to the calculated colligative property.

i = Observed colligative property / Calculated colligative property

Observed colligative property ∝ 1/Molar Mass

i = Mc/Mo

Van't Hoff's factor
(i) represents the extent of association (or) dissociation of a solute

i = Total number of moles of particles after association or dissociation / Number of moles of particles before association or disscussion

Experimentally determined molar mass is always lower than actual value for dissociation.

Molar Mass ∝ 1/Colligative Property

If the solute undergoes association in a solution, then the value of van 't Hoff's factor is less than one. If the solute undergoes dissociation then 'i' is greater than one.


                       KCl → K+ + Cl-

     1 molecule of KCl furnishes 2 ions in solution

i = Total number of moles of particles after dissociation / Number of moles of particles before dissociation

 i = 2/1 = 2

           2CH3COOH ⇔(CH3COOH)2
          Ethanoic acid     Dimer of Ethanoic acid

i = Total number of moles of particles after association / Number of moles of particles before association

i = 1/2 =  0.5



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            

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 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 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