Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

Chapter 16 | 815

EXAMPLE 16–11 Composition of Different Phases of a Mixture

In absorption refrigeration systems, a two-phase equilibrium mixture of liquid

ammonia (NH 3 ) and water (H 2 O) is frequently used. Consider one such mix-

ture at 40°C, shown in Fig. 16–27. If the composition of the liquid phase is

70 percent NH 3 and 30 percent H 2 O by mole numbers, determine the com-

position of the vapor phase of this mixture.

Solution A two-phase mixture of ammonia and water at a specified temper-

ature is considered. The composition of the liquid phase is given, and the

composition of the vapor phase is to be determined.

Assumptions The mixture is ideal and thus Raoult’s law is applicable.

Properties The saturation pressures of H 2 O and NH 3 at 40°C are PH 2 O,sat

7.3851 kPa andPNH 3 ,sat1554.33 kPa.

Analysis The vapor pressures are determined from

The total pressure of the mixture is

Then the mole fractions in the gas phase are

Discussion Note that the gas phase consists almost entirely of ammonia,

making this mixture very suitable for absorption refrigeration.

yNH 3 ,gas side

PNH 3 ,gas side

Ptotal



1088.03 kPa

1090.25 kPa

0.9980

yH 2 O,gas side

PH 2 O,gas side

Ptotal



2.22 kPa

1090.25 kPa

0.0020

PtotalPH 2 OPNH 3 2.221088.031090.25 kPa

PNH 3 ,gas sideyNH 3 ,liquid side PNH 3 ,sat 1 T 2 0.70 1 1554.33 kPa 2 1088.03 kPa

PH 2 O,gas sideyH 2 O,liquid side PH 2 O,sat 1 T 2 0.30 1 7.3851 kPa 2 2.22 kPa

40 °C

yg,H 2 O =?

LIQUID

VAPOR

H 2 O + NH 3

yg,NH 3 =?

yf,H 2 O = 0.30

yf,NH 3 = 0.70

FIGURE 16–27

Schematic for Example 16–11.

SUMMARY

An isolated system is said to be in chemical equilibriumif no

changes occur in the chemical composition of the system.

The criterion for chemical equilibrium is based on the second

law of thermodynamics, and for a system at a specified tem-

perature and pressure it can be expressed as

For the reaction

where the n’s are the stoichiometric coefficients, the equilib-

rium criterioncan be expressed in terms of the Gibbs func-

tions as

which is valid for any chemical reaction regardless of the

phases involved.

nCgCnDgDnAgAnBgB 0

nAAnBB∆nCCnDD

1 dG (^2) T, P 0
For reacting systems that consist of ideal gases only, the
equilibrium constant KPcan be expressed as
where the standard-state Gibbs function change∆G(T) and
the equilibrium constant KPare defined as
and
Here,Pi’s are the partial pressures of the components in atm.
The KPof ideal-gas mixtures can also be expressed in terms
of the mole numbers of the components as
KP
NnCC NnDD
NnAA NnBB
a
P
Ntotal
b
¢n
KP
PnCC PnDD
PnAA PnBB
¢G 1 T 2 nCgC 1 T 2 nDgD 1 T 2 nAgA 1 T 2 nBgB 1 T 2
KPe¢G*^1 T2>RuT
cen84959_ch16.qxd 5/11/05 10:08 AM Page 815