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

where 
is the solubility. Expressing the pressure in bars and noting that the

unit of molar concentration is kmol of species iper m^3 , the unit of solubility

is kmol/m^3 · bar. Solubility data for selected gas–solid combinations are

given in Table 16–3. The product of solubilityof a gas and the diffusion

coefficientof the gas in a solid is referred to as the permeability,which is a

measure of the ability of the gas to penetrate a solid. Permeability is

inversely proportional to thickness and has the unit kmol/s · m · bar.

Finally, if a process involves the sublimationof a pure solid such as ice or

the evaporationof a pure liquid such as water in a different medium such as

air, the mole (or mass) fraction of the substance in the liquid or solid phase

is simply taken to be 1.0, and the partial pressure and thus the mole fraction

of the substance in the gas phase can readily be determined from the satura-

tion data of the substance at the specified temperature. Also, the assumption

of thermodynamic equilibrium at the interface is very reasonable for pure

solids, pure liquids, and solutions except when chemical reactions are

occurring at the interface.

Chapter 16 | 813

TABLE 16–3

Solubility of selected gases and

solids (from Barrer)

(for gas i, 
r–i,solid side/Pi,gas side)

Gas Solid TK kmol/m^3 · bar

O 2 Rubber 298 0.00312

N 2 Rubber 298 0.00156

CO 2 Rubber 298 0.04015

He SiO 2 298 0.00045

H 2 Ni 358 0.00901

EXAMPLE 16–8 Mole Fraction of Water Vapor Just over a Lake

Determine the mole fraction of the water vapor at the surface of a lake whose

temperature is 15°C, and compare it to the mole fraction of water in the lake

(Fig. 16–24). Take the atmospheric pressure at lake level to be 92 kPa.

Solution The mole fraction of water vapor at the surface of a lake is to be

determined and to be compared to the mole fraction of water in the lake.

Assumptions 1 Both the air and water vapor are ideal gases. 2 The amount

of air dissolved in water is negligible.

Properties The saturation pressure of water at 15°C is 1.7057 kPa (Table A–4).

Analysis There exists phase equilibrium at the free surface of the lake,

and thus the air at the lake surface is always saturated at the interface

temperature.

The air at the water surface is saturated. Therefore, the partial pressure of

water vapor in the air at the lake surface will simply be the saturation pres-

sure of water at 15°C,

The mole fraction of water vapor in the air at the surface of the lake is deter-

mined from Eq. 16–22 to be

Water contains some dissolved air, but the amount is negligible. Therefore,

we can assume the entire lake to be liquid water. Then its mole fraction

becomes

Discussion Note that the concentration of water on a molar basis is

100 percent just beneath the air–water interface and less than 2 percent

just above it even though the air is assumed to be saturated (so this is the

highest value at 15°C). Therefore, large discontinuities can occur in the con-

centrations of a species across phase boundaries.

ywater,liquid side
1.0 or 100 percent

yv

Pv

P



1.7057 kPa

92 kPa

0.0185 or 1.85 percent

PvPsat @ 15°C1.7057 kPa

yH 2 O,liquid side ≅ 1.0

Lake

15 °C

Air

92 kPa

yH 2 O,air side = 0.0185

Saturated air

FIGURE 16–24

Schematic for Example 16–8.

cen84959_ch16.qxd 5/11/05 10:08 AM Page 813