CHEMISTRY TEXTBOOK

Substitution of this value of m in Eq. (2.13)
gives

∆Tb = Kb

1000 W 2
M 2 W 1
Hence,

M 2 =

1000 KbW 2

∆TbW 1

(2.15) 2.9 Depression in freezing point

Recall that freezing point of a liquid

is the temperature at which liquid and solid

are in equilibrium and the two phases have

the same vapour pressure.

The general experimental observation

is that the freezing point of a solvent is

lowered by dissolving a nonvolatile solute into

it. Thus, freezing point of solution containing

a nonvolatile solute is lower than that of pure

solvent.

If Tf is the freezing point of pure

solvent and Tf that of a solution in which

nonovolatile solute is dissolved, Tf > Tf. The

difference between the freezing point of pure

solvent and that of the solution is depression

in freezing point.

Thus ∆Tf = Tf - Tf (2.16)

2.9.1 Freezing point depression as a

consequence of vapour pressure lowering

The effect of dissolution of a

nonvolatile solute into a solvent on freezing

point of solvent can be understood in terms

of the vapour pressure lowering.

Problem 2.6 : The normal boiling point of

ethyl acetate is 77.06^0 C. A solution of 50

g of a nonvolatile solute in 150 g of ethyl

acetate boils at 84.27^0 C. Evaluate the

molar mass of solute if Kb for ethyl acetate

is 2.77^0 C kg mol-1.

Solution :

M 2 =

1000 KbW 2

∆TbW 1

W 2 = 50 g, W 1 = 150 g,

∆Tb = Tb-T^0 b = 84.27^0 C - 77.06^0 C

= 7.21^0 C = 7.21 K

Kb = 2.77^0 C kg mol-1 = 2.77 K kg mol-1

Substitution of these in above equation

M 2 =

1000 g Kg-1 × 2.77 K kg mol-1 × 50 g

7.21 K × 150 g^

= 128 g mol-1

Problem 2.7 : 3.795 g of sulphur is dissolved

in 100 g of carbon disulfide. This solution

boils at 319.81 K. What is the molecular

formula of sulphur in solution? The boiling

point of the solvent is 319.45 K.

(Given that Kb for CS 2 = 2.42 K kg mol-1 and

atomic mass of S = 32 u

M 2 =

1000 KbW 2

∆TbW 1

W 1 = 100 g, W 2 = 3.795 g

∆Tb = (319.81 - 319.45)K = 0.36 K

M 2 =

1000 g kg-1 × 2.42 K kg mol-1 × 3.795 g

0.36 K × 100 g

= 255.10 g mol-1

Atomic mass of S = 32 u

Therefore number of atoms in a molecule of

sulphur

=

molar mass of S

atomic mass of S =

255.1

32

= 7.92 ≈ 8

The molecular formula would be S 8 in CS 2

Fig. 2.7 : Variation of vapour pressure with

temperature of pure solvent, solid solvent and

solution

B

D

C

A

E

F

T T 0

Solid solvent

Solution

Liquid solvent

Vapour Pressure

Temperature

0

0

0