CHAPTER 5
MULTI-PHASE SYSTEMS
Sem 1, 2015/2016
ERT 214 Material and Energy Balance / Imbangan Bahan
dan Tenaga
Outline
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Bubble point
Boiling point
Dew point
Raoult’s Law
Henry’s Law
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Virtually all commercial chemical processes involve
operations in which material is transferred from one
phase (gas, liquid, or solid) into another.
These multiphase operations include all phase-change
operations on a single species. such as freezing,
melting, evaporation, and condensation, and most
separation and purification processes, which are
designed to separate components of mixtures from
one another.
Examples of Multiphase
Separation Processes
• Brewing a cup of coffee.
Hot liquid water and solid ground coffee beans are contacted. Soluble constituents of the
beans are transferred from the solid phase to a liquid solution (coffee), and then the
residual solids (grounds) are filtered from the solution. The operation of dissolving a
component of a solid phase in a liquid solvent is referred to as leaching.
• Removal of sulfur dioxide from a gas stream.
If a fuel that contains sulfur is burned. The product gas contains sulfur dioxide. If the gas is
released directly into the atmosphere, the S02 combines with atmospheric oxygen to form
sulfur trioxide. The S03 in turn combines with water vapor in the atmosphere to form
sulfuric acid (H2S04), which eventually precipitates as acid rain.
To prevent this occurrence, the combustion product gas is contacted with a liquid solution in an
absorption or scrubbing process. The SO2 dissolves in the solvent and the clean gas that
remains is released to the atmosphere.
SINGLE-COMPONENT PHASE
EQUILIBRIUM
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Phase Diagrams
Estimation of Vapor Pressures
Phase Diagrams
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2.
3.
4.
At most temperatures and pressures, a single pure
substance at equilibrium exists entirely as a solid, liquid,
or gas; but at certain temperatures and pressures, two and
even all three phases may coexist.
Pure water is a
gas at 130°C and 100 mm Hg,
solid at -40°C and 10 atm,
but at 100°C and 1 atm it may be a gas, a liquid, or a
mixture of both,
at approximately 0.0098°C and 4.58 mm Hg it may be a
solid, a liquid, a gas, or any combination of the three.
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A phase diagram of a pure substance is a plot of one
system variable against another that shows the
conditions at which the substance exists as a solid. a
liquid, and a gas.
The most common of these diagrams plots pressure on
the vertical axis versus temperature on the horizontal
axis.
The boundaries between the single-phase regions
represent the pressures and temperatures at which
two phases may coexist.
Phase Diagrams of H20 and CO2
Several familiar terms may be defined with reference to
the phase diagram.
1. If T and P correspond to a point on the vapor-liquid equilibrium
curve for a substance, P is the vapor pressure of the substance
at temperature T, and T is the boiling point (more precisely, the
boiling point temperature) of the substance at pressure P.
2. The boiling point of a substance at P = 1 atm is the normal
boiling point of that substance.
3. If (T, P) falls on the solid-liquid equilibrium curve, then T is the
melting point or freezing point at pressure P.
4. If (T, P) falls on the solid-vapor equilibrium curve, then P is the
vapor pressure of the solid at temperature T, and T is the
sublimation point at pressure P.
5. The point (T, P) at which solid, liquid, and vapor phases can all
coexist is called the triple point of the substance.
6. The vapor-liquid equilibrium curve terminates at the critical
temperature and critical pressure (Tc and Pc). Above and to the
right of the critical point, two separate phases never coexist.
Phase Diagrams of H20
Notice that the phase transitions-condensation at point B and evaporation at point Dtake place at boundaries on the phase diagram; the system cannot move off these
boundaries until the transitions are complete.
Estimation of Vapor Pressures
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The volatility of a species is the degree to which the species tends to transfer
from the liquid (or solid) state to the vapor state.
At a given temperature and pressure, a highly volatile substance is much more
likely to be found as a vapor than is a substance with low volatility, which is more
likely to be found in a condensed phase (liquid or solid).
Separation processes such as distillation are used to separate more volatile
species from less volatile species by partially vaporizing liquid mixtures. The
vapor product is relatively rich in the more volatile feed components and the
residual liquid is rich in the components with lower volatility.
The vapor pressure of a species is a measure of its volatility: the higher the
vapor pressure at a given temperature, the greater the volatility of the species
at that temperature.
Engineers who design and analyze separation processes therefore need to know
the vapor pressures of process species as functions of temperature.
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It often happens that tabulated vapor pressure data are not available at
temperatures of interest, or they may not be available at all for a given species.
One solution to this problem is to measure p* at the desired temperatures. Doing so is
not always convenient, however, especially if a highly precise value is not required.
An alternative is to estimate the vapor pressure using an empirical correlation for
p*(T).
A relationship between p*, the vapor pressure of a pure substance, and T, the
absolute temperature, is the Clapeyron equation
T is
absolute
temperature
Vg specific molar volumes
(volume/mole) of gas (vapor)
the latent heat of
vaporization, or the
energy required to
vaporize one mole
of the liquid.
VI are the specific molar
volumes (volume/mole)
of liquid.
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Unless the pressure is extremely high, the specific volume of the liquid (Vl) is
negligible relative to that of the vapor (i.e., Vg - VI = Vg).
If we assume that this is the case, apply the ideal gas equation of state to the
vapor (so that Vg is replaced with RT/ p* ) and rearrange the resulting equation
with the aid of elementary calculus. We obtain
If the vapor pressure of a substance is measured at several temperatures and In
p* is plotted versus l/T (or p* is plotted versus l/T on semilog axes).
From Equation above, the slope of the resulting curve at a given temperature
equals
. This is the method most commonly used to determine heats of
vaporization experimentally.
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Suppose now that the heat of vaporization of a substance is independent of temperature (or nearly
so) in the temperature range over which vapor pressures are available.
Equation
may then be integrated to yield the Clausius-Clapeyron equation
where B is a constant that varies from one substance to another.
According to this equation, a plot of In p* versus 1/T (or a semilog plot of p* versus 1/T) should be a
straight line with slope
and intercept B.
If you know
and p* at a single temperature To, you can solve the Clausius-Clapeyron equation for B
and thereafter use this equation to estimate p* at any temperature close to To.
If you have p* versus T data, you can plot In p* versus 1/T and determine
the method of least squares.
and B graphically or by
EXAMPLE: Vapor Pressure Estimation
Using the Clausius-Clapeyron Equation
The vapor pressure of benzene is measured at two temperatures, with the
following results:
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Tl = 7.6°C,
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T2 = 15.4°C,
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P1* = 40mm Hg
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P2*= 60mm Hg
Calculate the latent heat of vaporization and the parameter B in the ClausiusClapeyron equation and then estimate p* at 42.2°C using this equation.
The vapor pressure of benzene is measured at two temperatures, with the following results:
Tl = 7.6°C,T2 = 15.4°C, P1* = 40mm Hg P2*= 60mm Hg
Calculate the latent heat of vaporization and the parameter B in the Clausius-Clapeyron equation and then estimate p* at 42.2°C using this
equation.
Clausius-Clapeyron equation
T1=280.8K;P1=40
The vapor pressure of benzene is measured at two temperatures, with the following results:
Tl = 7.6°C,T2 = 15.4°C, P1* = 40mm Hg P2*= 60mm Hg
Calculate the latent heat of vaporization and the parameter B in the Clausius-Clapeyron equation and then estimate p* at 42.2°C using this
equation.
T2=288.6K;P2=60
GAS-LIQUID SYSTEMS:
ONE CONDENSABLE COMPONENT
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A law that describes the behavior of gas-liquid systems over a wide range of conditions
provides the desired relationship.
If a gas at temperature T and pressure P contains a saturated vapor whose mole fraction
is Yi (mol vapor/mol total gas), and if this vapor is the only species that would condense
if the temperature were slightly lowered, then the partial pressure of the vapor in the
gas equals the pure-component vapor pressure pi* (T) at the system temperature.
This equation is a limiting case of Raoult's law.
It is the fundamental relation used in the analysis of equilibrated gas-liquid systems
containing one condensable component.
Example: Composition of a Saturated
Gas-Vapor System
Air and liquid water are contained at equilibrium in a closed chamber at
75°C and 760 mm Hg. Calculate the molar composition of the gas phase.
MULTICOMPONENT
GAS-LIQUID SYSTEMS
MULTICOMPONENT
GAS-LIQUID SYSTEMS
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Gas-liquid processes that involve several components in each phase
include many chemical reactions, distillation, and transfer of one or
more species from a gas to a liquid (absorption or scrubbing) or vice
versa (stripping).
Variables can then be determined using equilibrium relationships for the
distribution of components between the two phases.
In this section we define several such relationships and illustrate how they
are used in the solution of material balance problems like using:
Vapor Liquid Equilibrium Data
Roult’s Law and Henry Law
Vapor-Liquid Equilibrium Data
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The best way to evaluate equilibrium
compositions is from tabulated data.
Perry's Chemical Engineers' Handbook, pp. 2-76
through 2-89, gives partial pressures of vapors over
various liquid solutions.
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Try NEXT EXAMPLE which illustrates the use of such
data
Example: Absorption of SO2
A gas stream consisting of 100 lb-mole/h of an SO2air mixture containing 45 mole% SO2 is contacted
with liquid water in a continuous absorber at 30°C.
The liquid leaving the absorber is analyzed and
found to contain 2.00 g of SO2 per 100 g of H20.
Assuming that the gas and liquid streams leaving the
absorber are in equilibrium at 30°C and 1 atm,
calculate the fraction of the entering SO2 absorbed
in the water and the required water feed rate.
A gas stream consisting of 100 lb-mole/h of an SO2-air mixture containing 45 mole% SO2 is contacted
with liquid water in a continuous absorber at 30°C. The liquid leaving the absorber is analyzed and
found to contain 2.00 g of SO2 per 100 g of H20.
Assuming that the gas and liquid streams leaving the absorber are in equilibrium at 30°C and 1 atm,
Gas Stream (out):
Y air
YH2O
YSO2
Gas Stream (in):
Liquid Stream (in):
Liquid Stream (out)
Gas Stream (out):
Y air=0.727
YH2O=0.0416
YSO2=0.232
Gas Stream (out):
Y air=0.727
YH2O=0.0416
YSO2=0.232
Mass fraction=mass SO2/total mass (100+2)
Raoult's Law & Henry's Law
Raoult's Law:
P is the vapor pressure of pure liquid A at temperature T
YA is the mole fraction of A in the gas phase.
Raoult's law is an approximation that is generally valid when XA is close to I (that is
when the liquid is almost pure A).
It is also sometimes valid over the entire range of compositions for mixtures of
similar substances, such as paraffinic hydrocarbons of similar molecular weights.
Note: When XA = I (that is, when the liquid is pure A) -Raoult's law reduces to the
expression PA = P*A(T) given previously for systems with only one condensable
component
Henry's Law
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where HA(T) is the Henry's law constant for A in a specific solvent.
Henry's law is generally valid for solutions in which XA is close to 0 (dilute
solutions of A) provided that A does not dissociate. ionize, or react in the
liquid phase.
The law is often applied to solutions of non-condensable gases.
Values of Henry's law constants (or closely related quantities) are given for
several gases in water on pp. 2-125 through 2-128 of Perry's Chemical
Engineers' Handbook.
A gas-liquid system in which the vapor-liquid equilibrium relationship for every
volatile species is either Raoult's law or Henry's law is said to exhibit ideal
solution behavior.
An ideal liquid solution is a mixture of liquids that exhibits ideal solution
behavior at equilibrium
Example:
Raoult's Law and Henry's Law
Use either Raoult's law or Henry's law to solve the
following problems.
1. A gas containing 1.00 mole% ethane is in contact
with water at 20.0°C and 20.0 atm. Estimate the
mole fraction of dissolved ethane.
2. An equimolar liquid mixture of benzene (B) and
toluene (T) is in equilibrium with its vapor at 30.0°C.
What is the system pressure and the composition of
the vapor?
1. A gas containing 1.00 mole% ethane is in contact with
water at 20.0°C and 20.0 atm. Estimate the mole fraction of
dissolved ethane.
Solved using Henry’s Law
Mole fraction, Xethane = ???
YethaneP=Xethane*Hethane (at T=20oC)
2. An equimolar liquid mixture of benzene (B) and toluene (T) is in
equilibrium with its vapor at 30.0°C. What is the system pressure and the
composition of the vapor?
Solved using Raoult's Law:
simple empirical
equation that
correlates vapor
pressuretemperature
data
APPENDIX B (PAGE 640 –Antoine Equation Constant (to find vapor
pressure at temperature (T)
Benzene:
A=6.89272
B=1203.531
C=219.888
Touluene:
A=6.95805
B=1346.773
C=219.693
Vapor-Liquid Equilibrium
Calculations for Ideal Solutions
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When a liquid is heated slowly at constant pressure, the temperature at
which the first vapor bubble forms is the bubble-point temperature of the
liquid at the given pressure.
When a gas (vapor) is cooled slowly at constant pressure, the
temperature at which the first liquid droplet forms is the dew-point
temperature at the given pressure.
Calculating bubble-point and dew-point temperatures can be a complex
task for an arbitrary mixture of components.
However, if the liquid behaves as an ideal solution (one for which
Raoult's or Henry's law is obeyed for all components) and the gas phase
can also be considered ideal, the calculations are relatively straight
forward.
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Suppose an ideal liquid solution follows Raoult's law and contains species A, B, C
...with known mole fractions XA, XB, Xc ....
If the mixture is heated at a constant pressure to its bubble-point temperature Tbp,
the further addition of a slight amount of heat will lead to the formation of a vapor
phase.
Since the vapor is in equilibrium with the liquid, and we now assume that the
vapor is ideal (follows the ideal gas equation of state), the partial pressures of
the components are given by Raoult's law,
where P~ is the vapor pressure of component i at the bubble-point temperature.
Moreover, since we have assumed that only A, B, C, ... are present in the system, the
sum of the partial pressures must be the total system pressure, P; hence,
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The pressure at which the first vapor forms when a liquid is decompressed
at a constant temperature is the bubble-point pressure of the liquid at the
given temperature.
Above equation can be used to determine such a pressure for an ideal
liquid solution at a specific temperature, and
The mole fractions in the vapor in equilibrium with the liquid can then
be determined as
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The dew-point temperature of a gas (vapor) may be found using a method
similar to that for bubble-point temperature estimation.
Again, suppose a gas phase contains the condensable components A, B, C,
... and a non-condensable component G at a fixed pressure P.
Let Yi be the mole fraction of component i in the gas. If the gas mixture is
cooled slowly to its dew point, Tdp, it will be in equilibrium with the first liquid
that forms. Assuming that Raoult's law applies, the liquid-phase mole fractions
may be calculated as
At the dew point of the gas mixture, the
mole fractions of the liquid components
(those that are condensable) must sum to 1:
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The value of Tdp can be found by trial and error once expressions for p;(T) have been
substituted.
The composition of the liquid phase may then be determined from Equation
Liquid mole fractions may then be calculated from this
equation with Tdp replaced by the system temperature, T.
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The dew-point pressure, which relates to condensation brought about by increasing
system pressure at constant temperature. can be determined by solving
for P:
THANK YOU
Mid Term Exam 1
(up to Chapter 3 ONLY)
27 Oct 2015
DKD3