Concise Physical Chemistry

c12 JWBS043-Rogers September 13, 2010 11:27 Printer Name: Yet to Come

RAOULT’S LAW 183

0

TΔS

ΔH

ΔG

Α Β

XB

FIGURE 12.1 Entropy, enthalpy, and Gibbs free energy changes for ideal mixing atT>0.

selection of a single molecule might result in either A or B. Molecular disorder has

increased, hence entropy has also increased.

Uncertainty in random selection is greater for any mixture, but the maximum

uncertainty is at equal concentrationsA=B. All other ratios are less random. The

enthalpy and entropy of ideal mixing are shown as the middle and upper curves in

Fig. 12.1. The Gibbs free energy is
G=
H−T
S, so the null result for
H

causes the free energy change
Gto be exactly opposite to theT
Scurve at any

mole fractionXBand any temperature not equal to zero. Note that Fig. 12.1 could

equally well have been drawn withXAas the horizontal axis becauseXA+XB= 1

andXA= 1 −XB.

12.2 RAOULT’S LAW

A slightly less stringent requirement on the components of an ideal binary solution is

that the partial vapor pressure of its components be a linear function of concentration,

with the vapor pressure of the pure componentp◦Aas the slope of the function

pA=XAp◦A

The concentration is measured in terms of the mole fraction of the component labeled

A, and the variablepAis the vapor pressure of A in the solution. This rule is called

Raoult’s law. Raoult’s law is most easily understood by picking out the straight line

labeledpAin Fig. 12.2.

What is said of A is can also be said of B:

pB=XBp◦B