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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