PHYSICAL CHEMISTRY IN BRIEF

CHAP. 7: PHASE EQUILIBRIA [CONTENTS] 203

• The increase in the boiling temperature at constant pressureis given by the
  relation
  ∆T=T−Tb, 1 =. KEm 2 =KE

m 2

M 2 m 1

, (7.35)

whereTis the boiling temperature of the dilute solution andTb, 1 is the boiling temper-

ature of the pure solvent,m 2 is the molality of the solute^1 KEdenotes the ebullioscopic

constant which may be determined from the properties of the pure solvent

KE=

RTb^2 , 1 M 1

∆vapH 1

, (7.36)

where ∆vapH 1 is the enthalpy of vaporization of the pure solvent at the boiling temper-

atureTb, 1.

Example

After the dissolution of 1 g of a certain substance in 100 g water(1), an increase in the normal

boiling temperature by 0.05◦C was measured. What was the molar mass of this substance?

Data: The enthalpy of vaporization of water∆vapH 1 = 40. 650 kJ mol−^1.

Solution

We first calculate the ebullioscopic constant of water

KE=

RTNBP^2 , 1 M 1

∆vapH 1

=

8. 314 × 373. 152 × 0. 018

40650

= 0. 513 kg K mol−^1.

From equation (7.35) we calculate the molar mass of the unknown substance

M=

0. 513 × 0. 001

0. 05 × 0. 1

= 0. 103 kg mol−^1 = 103g mol−^1.

(^1) If the solute dissociates,m 2 has to be replaced byναm 2 , whereνis the number of particles formed by the
dissociation of the molecule, andαis the degree of dissociation.