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ChE Cal 2
Lecture set 1
byEngr. Rowie Carpio
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PHASE DIAGRAM
Introduction
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Phase diagram
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Phase diagram
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Phase diagram
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Phase diagram of water
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Phase diagram
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Phase diagram
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Definition of terms
Vapor pressure or equilibrium vapor pressure
or saturation pressure
is the pressure exerted by a vapor in thermodynamic
equilibrium with its condensed phases (solid or liquid) at agiven temperature in a closed system.
is an indication of a liquid's evaporation rate. It relates to thetendency of particles to escape from the liquid (or a solid).
corresponds to a point on the vapor-liquid curve for asubstance at a given temperature T.
is the pressure for a corresponding to temperature at which aliquid boils into its vapor phase.
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Definition of terms
Vapor pressure (continuation) a substance with a high vapor pressure at normal
temperatures is often referred to as volatile.
A highly volatile substance is much more likely to
be found as vapor than is a substance with lowvolatility, which is more likely to be in condensedphase (liquid or solid)
High vapor pressurehigh volatility
Low boiling pointhigh volatility Example: acetone is more volatile than liquid
water at room temperature
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Definition of terms
Vapor pressure (continuation) increases non-linearly with temperature (for any
substance)
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Definition of terms
Boiling point temperature or saturation temerature
corresponds to the temperature on the vapor-liquid equilibriumcurve for a substance at a given pressure
normal boiling point is the boiling point of a substance at P = 1 atm
Melting point or freezing point
corresponds to the temperature on the solid-liquid equilibriumcurve for a substance at a given pressure
Sublimation point
corresponds to the temperature on the solid-vapor equilibriumcurve for a substance at a given pressure
Triple point
the point at which solid, liquid and vapor phases can all co-exist
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Definition of terms
Critical point or critical state
the point at which the vapor-liquid equilibriumterminates.
at critical T , critical P and critical V
on the PT diagram corresponds to the highest P and Tat which two phases (liquid-vapor) can co-exist.
Supercritical fluid
any substance at a temperature and pressure aboveits critical point, where distinct liquid and gas phasesdo not exist.
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Definition of terms
Gas vs. VaporVapor
gaseous substance below its critical temperature
which can be condensed by compressing orincreasing the pressure.
Gas
or noncondensable gas
gaseous substance above its critical temperaturewhich cannot be condensed by compressing orincreasing the pressure.
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Estimation of Vapor pressure
In the absence of empirical data ( i.e. steam table),
vapor pressure can be estimated using the
following:
1. Antoine equation
2. Cox vapor pressure chart
3. Clausius-clapeyron
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Estimation of Vapor pressure
1. Antoine equation
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Estimation of Vapor pressure
2. Cox vapor pressure chart
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Estimation of Vapor pressure
3. Clausius-Clapeyron equation
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Estimation of Vapor pressure
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Estimation of Vapor pressure
Alternatively, Clausius-Clapeyron equation
If the Hvap is known, and is constant within the range of thetemperature given
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Note: Antoine equation is more accurate than Clausius-Clapeyron
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Gibbs phase rule
Degrees of freedom (DOF)
Is the number of intensive variables that mustbe specified (or fixed) to define a system.
DOF = 2+CP, C=number of components,P=number of phases
Intensive variablesdo not depend on the size of thesystem. Example: molar volume, density, temp,
pressure
Extensive variables depend on the size of the system.Example: mass, volume
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Gibbs phase rule
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Gibbs phase rule
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Application of Gibbs phase rule
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Application of Gibbs phase rule
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Application of Gibbs phase rule
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Application of Gibbs phase rule
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PHASE EQUILIBRIUM
Introduction
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Definition of term
Equilibrium
A condition in which all acting influences are
canceled by others, resulting in a stable,
balanced, or unchanging system.
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Phase equilibrium
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Phase Equilibrium
Why study?
Many processes in chemical engineering do notonly involve a single phase.
Example: brewing a cup of coffee or tea,
absorption of SO2,
distillation to recover methanol or ethanol from
aqueous solution from aqueous solution
L-L extraction
Adsorption
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Phase equilibrium systems
Solid-liquid
Solid-vapor
Gas-liquid
Vapor-liquid
Liquid-liquid
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GAS-LIQUID SYSTEMS - 1 condensable component
Example: Air-water system
System of multiple components of which only 1 may
condense at a given process conditions.
evaporation, drying, humidification involve
transfer of species from the liquid to the gas
phase.
condensation, dehumidification involve transferof species from the gas to the liquid phase
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GAS-LIQUID SYSTEMS - 1 condensable component
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Water molecules begin to evaporate, as
the mole fraction of water increase in the
gas phase, so as the partial pressure of
water. Eventually, the net amount of
water molecules entering to gas phase
approaches zero. Such that no change
occurs in the amount or concentration of
either phase. At such condition, the:
Gas phase is said to be saturated with
water, referred to as saturated gas
And, the water in the gas phase isreferred to as saturated vapor.
Note:
air (or any gas) can only hold so
much water vapor (or any vapor)
If the air (or any gas) and liquid water(or any liquid substance) are at
equilibrium, the air must besaturated
with water vapor .
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GAS-LIQUID SYSTEMS - 1 condensable component
RaoultsLaw for 1 condensable component.
For a condensable component i, at equilibrium (at saturation), the partialpressure of i in the gas mixture must equal the vapor pressure of the
pure i liquid at the temperature of the system.
Raoultslaw:
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Where,
Pi = partial pressure of the component i in the gas phase
yi = mole fraction of component i in the gas phaseP = total pressure of the gas mixture
pi* = vapor pressure of the component I as liquid at the temperature of the system.
The limiting case for a single condensable component
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GAS-LIQUID SYSTEMS - 1 condensable component
RaoultsLaw for 1 condensable component.
Raoultslaw:
Notes:
Pi = pi* , saturated gas
Pi < pi* , the vapor present in the gas is said to be superheated vapor
Dew point: if the superheated vapor is cooled at constantpressure, the temperature at which the first dew forms.
Degrees of superheat: Ti-Tdp ,
where, Ti = actual temperature,
Tdp= dew point temperature
.
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GAS-LIQUID SYSTEMS - 1 condensable component
Definition of term
Saturation A phase at equilibrium is saturated with a chemical species if it
holds as much of the species as it maximally can.
example, air at a given temperature and pressure will only hold somuch water vapor. If more water vapor were somehowintroduced into the air, condensation would occur and the extrawater vapor would come out of the air as liquid water.
In general, when a gas that is saturated with a species A is incontact with a liquid of pure A, the rate at which molecules of Aevaporate from the liquid into the gas equals the rate at whichmolecules of A from the gas condense into the liquid.
In general, when a gas that is saturated with a species A, it meanscontains all the species A it can hold (maximum) at the a given Tand P.
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GAS-LIQUID SYSTEMS - One condensable component
Definition of terms
Partial saturation is the condition at which the vapor is not in equilibrium
with the liquid phase, and the partial pressure of thevapor is less than the vapor pressure of the liquid at thegiven temperature.
Partial pressure In a mixture of gases, each gas has a partial
pressurewhich is the pressure that the gas would have ifit alone occupied the same volume at thesame temperature.
The total pressure of a gas mixture is the sum of thepartial pressures of each individual gas in the mixture.
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GAS-LIQUID SYSTEMS - 1 condensable component
Saturated Gas
Humidity
specific term use to refer to the air-water
vapor system.
Saturation
refers to any gas-vapor combination.
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Means of expressing saturation
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GAS-LIQUID SYSTEMS - 1 condensable component
Things to consider!!
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Example 1:
Use of Raoultslaw
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Example 2
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A stream of air at 100 deg C and 5260 mm Hg contains 10%water by volume. Calculate:
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Example 2
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A stream of air at 100 deg C and 5260 mm Hg contains 10%water by volume. Calculate:
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Example 2
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A stream of air at 100 deg C and 5260 mm Hg contains 10%water by volume. Calculate:
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Example 2
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A stream of air at 100 deg C and 5260 mm Hg contains 10%water by volume. Calculate:
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Example 2
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A stream of air at 100 deg C and 5260 mm Hg contains 10%water by volume. Calculate:
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Example 3
What is the minimum number of cubic meters of dry air
at 20oC and 100 kPa necessary to evaporate 6.0 kg of
ethyl alcohol if the total pressure remains constant at
100 kPa and the temperature remains 20
o
C?
Assume that the air is blown through the alcohol to
evaporate it in such a way that the exit pressure of the
air-alcohol mixture is at 100 kPa.
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Example 4
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Seatwork 1
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Seatwork 2
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Seatwork 3
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Seatwork 4
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Seatwork 5
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Seatwork 6
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Example 5
Calculate the volume of 150 Kg humid air at
30oC, 30% RH, at 1 atm
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Example 6
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Example 7