CHEMISTRY TEXTBOOK

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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
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