Thermodynamics and Chemistry

CHAPTER 12 EQUILIBRIUM CONDITIONS IN MULTICOMPONENT SYSTEMS

12.8 LIQUID–GASEQUILIBRIA 407

following solubilities of gaseous Cl 2 in several dissimilar solvents at 0 C and a partial

pressure of1:01bar:xBD0:270in heptane,xBD0:288in SiCl 4 , andxBD0:298in

CCl 4. These values are similar to one another and close to the ideal valuepB=pBD

0:273.

12.8.5 Effect of temperature and pressure on Henry’s law constants

Consider the solution process B(g)!B(soln) for a nonelectrolyte solute B. The expression
for the thermodynamic equilibrium constant, with a solute standard state based on mole
fraction, is

KD

aB(sln)

aB(g)

D

x;B (^) x;BxB
fB=p

(12.8.28)

The Henry’s law constantkH,Bis related tofBandxBby

kH,BD

fB

(^) x;BxB

(12.8.29)

(see Table9.4), and is therefore related toKas follows:

kH,BD

x;Bp

K

(12.8.30)

(nonelectrolyte solute)

The pressure factorx;Bis a function ofTandp, andKis a function only ofT. The value
ofkH,Btherefore depends on bothTandp.
At the standard pressurepD 1 bar, the value ofx;Bis unity, and Eqs.12.1.13and
12.1.14then give the following expressions for the dependence of the dimensionless quan-
titykH,B=pon temperature:

d ln.kH,B=p/

dT

D

d lnK

dT

D

Åsol,BH

RT^2

(12.8.31)

(pDp)

d ln.kH,B=p/

d.1=T /

D

d lnK

d.1=T /

D

Åsol,BH

R

(12.8.32)

(pDp)

These expressions can be used with little error at any pressure that is not much greater than
p, say up to at least 2 bar, because under these conditionsx;Bdoes not differ appreciably
from unity (page 274 ).
To find the dependence ofkH,Bon pressure, we substitutex;Bin Eq.12.8.30with the
expression forx;Bat pressurep^0 found in Table9.6:

kH,B.p^0 /D

x;B.p^0 / p

K

D

p

K

exp

(^) Z
p^0
p

VB^1

RT

dp

!

(12.8.33)

We can use Eq.12.8.33to compare the values ofkH,Bat the same temperature and two
different pressures,p 1 andp 2 :

kH,B.p 2 /DkH,B.p 1 /exp

(^) Z
p 2
p 1

VB^1

RT

dp

!

(12.8.34)