Thermodynamics and Chemistry

CHAPTER 12 EQUILIBRIUM CONDITIONS IN MULTICOMPONENT SYSTEMS

12.4 COLLIGATIVEPROPERTIES OF ADILUTESOLUTION 375

which we can rewrite as

Åsol,AH

T^2

dT

Åsol,AV

T

dpD



@.A=T /

@xA



T;p

dxA (12.3.5)

(phases in

equilibrium)

HereÅsol,AH is the molar differential enthalpy of solution of solid or gaseous A in the
liquid mixture, andÅsol,AV is the molar differential volume of solution. Equation12.3.5is
a relation between changes in the variablesT,p, andxA, only two of which are independent
in the equilibrium system.
Suppose we set dpequal to zero in Eq.12.3.5and solve for dT=dxA. This gives us the
rate at whichTchanges withxAat constantp:



@T

@xA



p

D

T^2

Åsol,AH



@.A=T /

@xA



T;p

(12.3.6)

(phases in

equilibrium)

We can also set dTequal to zero in Eq.12.3.5and find the rate at whichpchanges withxA
at constantT:

@p
@xA



T

D

T

Åsol,AV



@.A=T /

@xA



T;p

(12.3.7)

(phases in

equilibrium)

Equations12.3.6and12.3.7will be needed in Secs.12.4and12.5.

12.4 Colligative Properties of a Dilute Solution

Thecolligative propertiesof a solution are usually considered to be:

1.Freezing-point depression: the decrease in the freezing point of the solution, com-

pared to pure solvent at the same pressure.

2.Boiling-point elevation: the increase in the boiling point of a solution containing

nonvolatile solutes, compared to pure solvent at the same pressure.

3.Vapor-pressure lowering: the decrease in the vapor pressure of a solution containing

nonvolatile solutes, compared to the vapor pressure of the pure solvent at the same

temperature.

4.Osmotic pressure: the increase in the pressure of the solution that places the solvent

in transfer equilibrium with pure solvent at the same temperature and pressure as the

original solution (page 373 ).

Note that all four properties are defined by an equilibrium between the liquid solution and a
solid, liquid, or gas phase of the pure solvent. The properties called colligative (Latin:tied
together) have in common a dependence on the concentration of solute particles that affects
the solvent chemical potential.
Figure12.3on the next page illustrates the freezing-point depression and boiling-point
elevation of an aqueous solution. At a fixed pressure, pure liquid water is in equilibrium
with ice at the freezing point and with steam at the boiling point. These are the temperatures