ERT 206/4 THERMODYNAMICS SEM 1 (2012/2013) Dr. Hayder Kh. Q. Ali
[email protected] 1 Slide 2 The Nature of Equilibrium The
Phase rule. VLE Quantitative Behavior Raoults Law VLE by Modified
Raoults Law 2 Slide 3 3 In this chapter we first discuss the nature
of equilibrium, and then consider two rules that give the number of
independent variables required to determine equilibrium states.
Then a qualitative discussion of vapor/liquid phase behavior.
Introduce the simplest formulations that allow calculation of
temperatures, pressures, and phase compositions for systems in
vapor/liquid equilibrium. The first, known as Raoult's law, is
valid only for systems at low to moderate pressures and in general
only for systems comprised of chemically similar species. A
modification of Raoult's law that removes the restriction to
chemically similar species is treated. Finally the calculations
based on equilibrium ratios or K-values are considered. Slide 4
Phase equilibrium Application Distillation, absorption, and
extraction bring phases of different composition into contact. Both
the extent of change and the rate of transfer depend on the
departure of the system from equilibrium. Quantitative treatment of
mass transfer the equilibrium T, P, and phase compositions must be
known. 4 Slide 5 The nature of equilibrium A static condition in
which no changes occur in the macroscopic properties of a system
with time. At the microscopic level, conditions are not static. The
average rate of passage of molecules is the same in both
directions, and no net interphase transfer of material occurs. An
isolated system consisting of liquid and vapor phases in intimate
contact eventually reaches a final state wherein no tendency exists
for change to occur within the system. Fixed temperature, pressure,
and phase composition 5 Slide 6 Phase rule vs. Duhems theorem (The
number of variables that is independently fixed in a system at
equilibrium) = (the number of variables that characterize the
intensive state of the system) - (the number of independent
equations connecting the variable): Phase rule: Duhems rule: for
any closed system formed initially from given masses of prescribed
chemical species, the equilibrium state is completely determined
when any two independent variables are fixed. Two ? When phase rule
F = 1, at least one of the two variables must be extensive, and
when F = 0, both must be extensive. 6 Slide 7 7 VLE: QUALITATIVE
BEHAVIOR Vapor/Liquid equilibrium (VLE) is the state of coexistence
of liquid and vapor phases. In this qualitative discussion, we
limit consideration to systems comprised of two chemical species,
because systems of greater complexity cannot be adequately
represented graphically. When N = 2, the phase rule becomes F = 4 -
. Since there must be at least one phase ( = 1), the maximum number
of phase-rule variables which must be specified to fix the
intensive state of the system is three: namely, P, T, and one mole
(or mass) fraction. All equilibrium states of the system can
therefore be represented in three dimensional P-T- composition
space. Within this space, the states of pairs of phases coexisting
at equilibrium (F = 4 - 2 = 2) define surfaces. A schematic
three-dimensional diagram illustrating these surfaces for VLE is
shown in Fig. below: Slide 8 8 Slide 9 9 This figure shows
schematically the P-T-composition surfaces which contain the
equilibrium states of saturated vapor and saturated liquid for a
binary system: The under surface contains the saturated-vapor
states; it is the P-T-yl surface. The upper surface contains the
saturated-liquid states; it is the P-T-xl surface. These surfaces
intersect along the lines UBHC2 and RKAC1, which represent the
vapor pressure-vs.-T curves for pure species 1 and 2. Slide 10 10
Because of the complexity of Fig. 10.1, the detailed
characteristics of binary VLE are usually depicted by
two-dimensional graphs. The three principal planes, each
perpendicular to one of the coordinate axes. A vertical plane
perpendicular to the temperature axis is outlined as ALBDEA. The
lines on this plane form a P-x 1 -y 1 phase diagram at constant T.
A horizontal plane perpendicular to the P axis is identified by
HIJKLH. Viewed from the top, the lines on this plane represent a
T-x 1 -y 1 diagram at constant P. Slide 11 11 Slide 12 12 The third
plane, vertical and perpendicular to the composition axis, is
indicated by MNQRSLM, this is the P-T diagram. At points A and B in
Fig. 10.3 saturated-liquid and saturated-vapor lines intersect. At
such points a saturated liquid of one composition and a saturated
vapor of another composition have the same T and P, and the two
phases are therefore in equilibrium. Slide 13 13 Slide 14 14 Slide
15 Within this space, the states of pairs of phases coexisting at
equilibrium define surfaces. The subcooled-liquid region lies above
the upper surface; the superheated-vapor region lies below the
under surface. UBHC 1 and KAC 2 represent the vapor pressure-vs.-T
curves for pure species 1 and 2. C 1 and C 2 are the critical
points of pure species 1 and 2. L is a bubble point and the upper
surface is the bubblepoint surface. Line VL is an example of a tie
line, which connects points representing phases in equilibrium. W
is a dewpoint and the lower surface is the dewpoint surface. Pxy
diagram at constant T Txy diagram at constant P PT diagram at
constant composition 15 Slide 16 Fig 10.8 16 Slide 17 Fig 10.9 17
Slide 18 18 Simple models for VLE When thermodynamics is applied to
vapor liquid equilibrium, the goal is to find by calculation the
temperatures, pressures, and compositions of phases in equilibrium.
Slide 19 Raoults law: the vapor phase is an ideal gas (apply for
low to moderate pressure) the liquid phase is an ideal solution
(apply when the species that are chemically similar) where xi is a
liquid-phase mole fraction, yi is a vapor-phase mole fraction, and
Pi sat is the vapor pressure of pure species i at the temperature
of the system. The product yi P on the left side of Eq. is known as
the partial pressure of species i 19 Slide 20 20 Ideal-solution
behavior is often approximated by liquid phases wherein the
molecular species are not too different in size and are of the same
chemical nature although it provides a realistic description of
actual behavior for a small class of systems, it is valid for any
species present at a mole fraction approaching unity, provided that
the vapor phase is an ideal gas. Slide 21 21 Dewpoint and
Bubblepoint Calculations with Raoult's Law Engineering interest
centers on dewpoint and bubblepoint calculations; there are four
classes: In each case the name suggests the quantities to be
calculated: either a BUBL (vapor) or a DEW (liquid) composition and
either P or T. Thus, one must specify either the liquid-phase or
the vapor-phase composition and either T or P. Slide 22 Binary
system For bubblepoint calculation For dewpoint calculation 22
Slide 23 23 Slide 24 Binary system acetonitrile (1)/nitromethane(2)
conforms closely to Raoults law. Vapor pressures for the pure
species are given by the following Antoine equations: (a) Prepare a
graph showing P vs. x 1 and P vs. y 1 for a temperature of 75C. (b)
Prepare a graph showing t vs. x 1 and t vs. y 1 for a pressure of
70 kPa. (a) BUBL P At 75C e.g. x 1 = 0.6 At 75C, a liquid mixture
of 60 mol-% (1) and 40 mol-% (2) is in equilibrium with a vapor
containing 74.83 mol-% (1) at pressure of 66.72 kPa. Fig. 10.11 24
Slide 25 Fig. 10.11 25 Slide 26 (b) BUBL T, having P = 70 kPa
Select tt vs. x 1 t vs. y 1 Fig. 10.12 26 Slide 27 VLE modified
Raoults law Account is taken of deviation from solution ideality in
the liquid phase by a factor inserted into Raoults law: The
activity coefficient, f (T, x i ) 27 Slide 28 28 Slide 29 For the
system methanol (1)/methyl acetate (2), the following equations
provide a reasonable correlation for the activity coefficients: The
Antoine equations provide vapor pressures: Calculate (a): P and {y
i } for T = 318.15 K and x 1 = 0.25 (b): P and {x i } for T =
318.15 K and y 1 = 0.60 (c): T and {y i } for P = 101.33 kPa and x
1 = 0.85 (d): T and {x i } for P = 101.33 kPa and y 1 = 0.40 (e):
the azeotropic pressure and the azeotropic composition for T =
318.15 K (a) for T = 318.15, and x 1 = 0.25 29 Slide 30 (b): for T
= 318.15 K and y 1 = 0.60 An iterative process is applied, with
Converges at: (c): for P = 101.33 kPa and x 1 = 0.85 A iterative
process is applied, with Converges at: 30 Slide 31 (d): for P =
101.33 kPa and y 1 = 0.40 A iterative process is applied, with
Converges at: 31 Slide 32 (e): the azeotropic pressure and the
azeotropic composition for T = 318.15 K Define the relative
volatility: Azeotrope Since 12 is a continuous function of x 1 :
from 2.052 to 0.224, 12 = 1 at some point There exists the
azeotrope! 32 Slide 33 VLE from K-value correlations A convenient
measure, the K-value: the lightness of a constituent species, i.e.,
of its tendency to favor the vapor phase. When Ki is greater than
unity, species i exhibits a higher concentration in the vapor
phase; when less, a higher concentration in the liquid phase, and
is considered a "heavy" constituent. 33 Slide 34 The Raoults law:
The modified Raoults law: 34 Slide 35 Fig 10.13 35 Slide 36 Fig
10.14 36 Slide 37 For a mixture of 10 mol-% methane, 20 mol-%
ethane, and 70 mol-% propane at 50F, determine: (a) the dewpoint
pressure, (b) the bubblepoint pressure. The K-values are given by
Fig. 10.13. (a) at its dewpoint, only an insignificant amount of
liquid is present: (b) at bubblepoint, the system is almost
completely condensed: 37 Slide 38 Flash calculations A liquid at a
pressure equal to or greater than its bubblepoint pressure flashes
or partially evaporates when the pressure is reduced, producing a
two-phase system of vapor and liquid in equilibrium. Consider a
system containing one mole of nonreacting chemical species: The
moles of liquid The moles of vapor The liquid mole fraction The
vapor mole fraction 38 Slide 39 The system acetone (1)/acetonitrile
(2)/nitromethane(3) at 80C and 110 kPa has the overall composition,
z 1 = 0.45, z 2 = 0.35, z 3 = 0.20, Assuming that Raoults law is
appropriate to this system, determine L, V, {x i }, and {y i }. The
vapor pressures of the pure species are given. Do a BUBL P
calculation, with {z i } = {x i } : Do a DEW P calculation, with {z
i } = {y i } : Since P dew < P = 110 kPa < P bubl, the system
is in the two-phase region, 39
