PHYSICAL CHEMISTRY IN BRIEF

CHAP. 7: PHASE EQUILIBRIA [CONTENTS] 217

For integration we need to know the temperature dependence of the enthalpy of melting of a
pureithcomponent, ∆fusHi.Tfiis the melting (fusion) temperature of a pureithcomponent.

7.9.3 Two-component systems with totally immiscible components

in the solid phase

The coexistence curve of a liquid mixture with crystals of component 2 (lineTf, 2 E in Figure
7.11) is given by the equation

lnγ(l) 2 x(l) 2 =

∫T

Tf, 2

∆fusH 2

RT^2

dT. (7.63)

and the coexistence curve of a liquid mixture with crystals of component 1 (line ETf, 1 ) by the
equation

lnγ 1 (l)x(l) 1 =

∫T

Tf, 1

∆fusH 1

RT^2

dT. (7.64)

The common solution of both equations gives the temperature and composition of the
eutectic point E [see7.9.1].

Note:Most organic substances do not mix in the solid phase.

• Ideal solubility
  If the liquid phase forms an ideal solution and the enthalpy of melting is independent
  on temperature, we have

−lnx(l) 1 =

∆fusH 1

R

(

1

T

−

1

Tf, 1

)

(7.65)

and similarly for the second part of the liquidus curve. From this it follows that:

1. The slope of the dependenceT–x 1 does not depend on substance 2.


2. Solubility increases with increasing temperature.


3. Of the two substances with roughly the same enthalpies of melting, the one with a
   lower temperature of melting will dissolve more.