CHAPTER 9 MIXTURES

9.8 MIXTURES INGRAVITATIONAL ANDCENTRIFUGALFIELDS 274

Table 9.6 Expressions for the dependence of pressure factors of nonelectrolytes on pressure. The
approximate expressions assume the phase is incompressible, or the solute partial molar volume is
independent of pressure.

Substance Pressure factor at pressurep^0

Substanceiin a gas mixture, or the
pure gas

i(g)D

p^0

p

Substance i in a liquid or solid
mixture, or the pure liquid or solid

iDexp

(^) Zp 0
p
Vi
RT
dp
!
exp

Vi.p^0 p/
RT

Solvent A of a solution ADexp
(^) Zp 0
p
VA
RT
dp
!
exp

VA.p^0 p/
RT

Solute B, mole fraction or molality
basis
x;BDm;BDexp
(^) Zp 0
p
VB^1
RT
dp
!
exp

VB^1 .p^0 p/
RT

Solute B, concentration basis c;BDexp
"Zp 0
p

VB^1
RT
T^1

dp

exp

VB^1 .p^0 p/
RT

1:49at 100 bar. For a solution withVB^1 D 100 cm^3 mol^1 , we obtain the same values as
these forx;B,m;B, andc;B. These values demonstrate that it is only at high pressures
that the pressure factor differs appreciably from unity. For this reason, it is common to see
expressions for activity in which this factor is omitted:aiD (^) ixi,am;BD (^) m;BmB=m,
and so on.
In principle, we can specify any convenient value for the standard pressurep. For a
chemist making measurements at high pressures, it would be convenient to specify a
value ofpwithin the range of the experimental pressures, for examplepD 1 kbar,
in order that the value of each pressure factor be close to unity.

9.8 Mixtures in Gravitational and Centrifugal Fields

A tall column of a gas mixture in a gravitational field, and a liquid solution in the cell
of a spinning centrifuge rotor, are systems with equilibrium states that are nonuniform in
pressure and composition. This section derives the ways in which pressure and composition
vary spatially within these kinds of systems at equilibrium.

9.8.1 Gas mixture in a gravitational field

Consider a tall column of a gas mixture in an earth-fixed lab frame. Our treatment will
parallel that for a tall column of a pure gas in Sec.8.1.4. We imagine the gas to be divided
into many thin slab-shaped phases at different elevations in a rigid container, as in Fig.8.1
on page 195. We want to find the equilibrium conditions reached spontaneously when the
system is isolated from its surroundings.