Thermodynamics and Chemistry

CHAPTER 9 MIXTURES

9.4 LIQUID ANDSOLIDMIXTURES OFNONELECTROLYTES 246

system 1

(A+B+C)(g)

pDpACpBCpC

pA;fA

(A+B)(l)

xA

system 2

(A+C)(g)

pDpACpC

pA;fA

A(l)

Figure 9.5 Two systems with equilibrated liquid and gas phases.

solution of solvent A and solute B, whereas the liquid in system 2 is the pure solvent. In
system 1, the partial pressurepAin the equilibrated gas phase depends on the temperature
and the solution composition. In system 2,pAdepends on the temperature. BothpAand
pAhave a mild dependence on the total pressurep, which can be varied with an inert gas
constituent C of negligible solubility in the liquid.
Suppose that we vary the composition of the solution in system 1 at constant temper-
ature, while adjusting the partial pressure of C so as to keeppconstant. If we find that
the partial pressure of the solvent over a range of composition is given bypADxApA,
wherepAis the partial pressure of A in system 2 at the sameTandp, we will say that the
solvent obeysRaoult’s law for partial pressurein this range. This is the same as the origi-
nal Raoult’s law, except thatpAis now the vapor pressure of pure liquid A at the pressure
pof the liquid mixture. Section12.8.1will show that unlesspis much greater thanpA,
pAis practically the same as the saturation vapor pressure of pure liquid A, in which case
Raoult’s law for partial pressure becomes identical to the original law.
A form of Raoult’s law with fugacities in place of partial pressures is often more useful:
fADxAfA, wherefAis the fugacity of A in the gas phase of system 2 at the sameTand
pas the solution. If this relation is found to hold over a given composition range, we will
say the solvent in this range obeysRaoult’s law for fugacity.
We can generalize the two forms of Raoult’s law for any constituentiof a liquid mix-
ture:

piDxipi (9.4.2)

(Raoult’s law for partial pressure)

fiDxifi (9.4.3)

(Raoult’s law for fugacity)

Herexiis the mole fraction ofiin the liquid mixture, andpiandfiare the partial pressure
and fugacity in a gas phase equilibrated with pure liquidiat the sameTandpas the liquid
mixture. BothpAandfiare functions ofTandp.
These two forms of Raoult’s law are equivalent when the gas phases are ideal gas mix-
tures. When it is necessary to make a distinction between the two forms, this book will refer
specifically to Raoult’s law for partial pressure or Raoult’s law for fugacity.