5.23: Untitled Page 120
- Page ID
- 18253
Chapter 5
hydroxide leaves in the vapor stream, that none accumulates in the boiler, and that the temperature of the liquid entering and leaving the boiler is a constant.
Assume that the solid calcium hydroxide leaving the boiler is in equilibrium with the dissolved carbon dioxide, i.e., the boiler is an equilibrium stage. The solubility is often expressed as;
Equilibrium relation:
solubility = S g of Ca(OH) g of H O
2
2
however, a more precise description can be constructed.
In this problem you are asked to develop a general solution for the mass fraction of the suspended solid in the liquid stream leaving the boiler in terms of
and S. For = 0.50, 0.21, and 0.075, determine the mass fraction of suspended
solid when S .
3
2 5 10 .
Figure 5.29. Precipitation of calcium hydroxide in a boiler 5‐30. In problem 5‐29 an equilibrium relation between solid calcium hydroxide and dissolved calcium hydroxide was given by
Equilibrium relation:
solubility = S g of Ca(OH) g of H O
(1)
2
2
In Sec. 5.3.1 we expressed the general gas/liquid equilibrium relation for species A in terms of the chemical potential and for a solid/liquid system we would express Eq. 5‐24 as
Equilibrium relation:
( )
( )
(2)
A solid
A liquid
Two‐Phase Systems & Equilibrium Stages 221
For the process considered in Problem 5‐29, we assume that the solid phase is pure calcium hydroxide so that Eq. 2 takes the form
Equilibrium relation:
(O )
( )
(3)
A solid
A liquid
The description of phase equilibrium phenomena in terms of the chemical potential will be the subject of a subsequent course in thermodynamics; however, at this point one can illustrate how Eqs. 1 and 3 are related.
The development begins with a general representation for the chemical potential at some fixed temperature and pressure. This is given by ( )
(
F T , p, x , x , etc.)
(3)
A liquid
A
B
where x is the mole fraction of species A (calcium hydroxide) in the liquid A
phase. A Taylor series expansion about x 0 leads to (see Problem 5‐31) A
2
F
F
2
( )
F
( x )
( x ) .....
(4)
A liquid
x 0
A
2
A
A
x
A x
x
0
A
A
x 0
A
The first term in this expansion is zero and when the mole fraction of species A is small compared to one, x 1 , we can make use of a linear form of Eq. 4 given A
by
F
( )
( x )
A liquid
A
x
(5)
A x 0
A
In this problem you are asked to use Eq. 3 along with Eq. 5 and the approximation
c
A
x
,
when c c
(6)
A
A
B
cB
to derive Eq. 1. Here c represents the molar concentration of calcium A
hydroxide and c represents the molar concentration of water. In terms of B
species A and species B, it will be convenient to express the solubility in the form Equilibrium relation:
solubility = S
(7)
A
B
and note that this can be related to the molar form by use of c MW and A
A
A
c MW .
B
B
B