Phenol associates in benzene to a …

We know,

K_f = Molal depression constant ( 5.12 K Kg/mol)

w_B = weight of the solute 

w_A = weight of the solvent 

M_B = Observed molar mass of the solute.

Substituting the values we get,

Calculated molecular weight of phenol = 12 x 6 + 1 x 5 + 16 + 1

  = 94 g

The association of phenol can be represented as:

Here, x is the degree of association.

The total number of particles after association

Now,

Hence, the fraction of phenol dimerized = 73%

Question: 

Phenol associates in benzene to certain extent to form a dimer. A solution that is containing 20 x 10-3kg of phenol dissolved in 1 kg of benzene has its freezing point decreased by 0.61 K. Calculate the fraction of phenol that has dimerised.

Solution:

∆ Tf = Kf wB 1000/ wA MB

0.69 = 5.12 x 20 x 10^-3 x 10^3 / 1 x MB

MB = 5.12 x 20 / 1 x 0.69

Molecular weight of phenol = 94g

Calculated M . W / observed M . W = No. of particles after association/ No. of particles before association

94 / 148.4 = 1 - x/2  /  1

x = 0.73 per mole

Fraction of C6H5OH = 0.73 x 100 = 73%