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VAPOUR LIQUID EQUILIBRIA& DEW POINT CALCULATIONSTHERMODYNAMICS II PROJECT

Group Members

Afnan Amjad

Haseeb Hayat

Hassan Raza

Malik Zeeshan Tariq

Muhammad Irfan

Muhammad Salman

Mudassir Sultan

Muhammad Zubair

CHE - 03


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Vapor-Liquid Equilibrium

Definition

Vaporliquid equilibrium (VLE) is a condition where a liquid and its vapor (gasphase) are in equilibrium with each other, a condition or state where the rate

ofevaporation (liquid changing to vapor) equals the rate of condensation (vapor

changing to liquid) on a molecular level such that there is no net (overall) vapor

liquid inter-conversion. A substance at vaporliquid equilibrium is generally referred

to as a saturated fluid. For a pure chemical substance this implies that it is at

its boiling point. The notion of "saturated fluid" includes saturated liquid (about to

vaporize), saturated liquidvapor mixture, and saturated vapor (about to condense).

ExplainationWhen a liquid such as water oralcohol is exposed to air in an open container, the

liquid evaporates. This happens because the distribution of speeds (and hence

kinetic energies) among molecules in a liquid is similar to that illustrated forgases,

shown again below.

At any given instant a small fraction of the molecules in the liquid

phase will be moving quite fast. If one of these is close to the surface and is traveling

upward, it can escape the attraction of its fellow molecules entirely and pass into the

gas phase. As the higherenergy molecules depart, the average energy of the

molecules in the liquid decreases and the temperature of the liquid falls. Heat energy

will be absorbed from the surroundings. Absorption of heat maintains the average

molecular speed in the liquid, so that, given enough time, all the liquid can
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evaporate. The heat absorbed during the entire process corresponds to

the enthalpy ofvaporization.

If the liquid is placed in a closed, rather than an open, container, we

no longer find that it evaporates completely. Once a certain partialpressure of gas

has been built up by the evaporation of liquid, no more change occurs, and theamount of liquid remains constant. The partial pressure attained in this way is called

the vapor pressure of the liquid. It is different for different liquids and increases with

temperature for a given liquid. So long as some liquid is present, the vapor pressure

is always the same, regardless of the size of the container or the quantity of liquid.

ExampleWe find that any size sample of water held at 25C will produce a vapor pressure of

23.8 mmHg (3.168 kPa) in any closed container, provided only that all the water

does not evaporate. On the macroscopic level, once the vapor pressure has been

attained in a closed container, evaporation appears to stop.

The

amount of vapor remains the same only because molecules are reentering the liquid

just as fast as they are escaping from it. The molecules of the vapor behave like any

other gas: They bounce around colliding with each other and the walls of the

container. However, one of these walls is the surface of the liquid. In most cases a

molecule colliding with the liquid surface will enter the body of the liquid, not have

enough energy to escape, and be recaptured.

When the liquid is first introduced into the container, there are very few molecules of

vapor and the rate of recapture will be quite low, but as more and more molecules

evaporate,
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The Chances of a recapture will become proportionately larger. Eventually the vapor

pressure will be attained, and the rate of recapture will exactly balance the rate of

escape. There will then be no net evaporation of liquid orcondensation of gas.

Once the vapor-liquid system has attained this state, it will appear on

the macroscopic level not to be undergoing any change in its properties. Theamount, the volume, the pressure, the temperature, the density, etc. of both liquid

and gas will all remain constant with time. When this happens to a system, it is said

to be in equilibrium state or to have attained equilibrium. Later, we will encounter

many other quite different examples of equilibrium, but they all have one property in

common. The lack of change on the macroscopic level is always the result of two

opposing microscopic processes whose rates are equal. The effect of each process

is to nullify the effect of the other. Since both microscopic processes are still in

motion, such a situation is often referred to as dynamic equilibrium.

The magnitude of the vapor pressure of a liquid depends mainly on two

factors:

The strength of the forces holding the molecules together

The temperature.

It is easy to see that if the intermolecular forces is weak, the vapor pressure will be

high. Weak intermolecular forces will permit molecules to escape relatively easily

from the liquid. The rate at which molecules escape will thus be high. Quite a

large concentration of molecules will have to build up in the gas phase before the

rate of reentry can balance the escape rate. Consequently the vapor pressure will be

large. By contrast, strong intermolecular forces result in a low escape rate, and only

a small concentration of molecules in the vapor is needed to balance it. The vapor

pressure of a liquid is quite a sensitive indicatorof small differences in intermolecular

forcesThe other major factor governing the magnitude of the vapor

pressure of a liquid is temperature. At a low temperature only a minute fraction of the

molecules have enough energy to escape from the liquid. As the temperature is

raised, this fraction increases very rapidly and the vapor pressure increases with it,

which makes sense given our previous discussion on temperature and gases. The

higher the temperature, the higher will be the increase of the energetic fraction ofmolecules. The result is a variation of vapor pressure with temperature. Note from

this figure how the vapor-pressure increase for a 10C increase in temperature is

larger at higher temperatures.
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Equilibrium between solid and vapor

(Sublimation curve)At the point B ice is in equilibrium with its Vapor. The pressure at B is the Vaporpressure of ice at the temperature at B. If this temperature at B is gradually raisedkeeping the volume constant, Vapor pressure of ice also increases. If the Vaporpressure of ice is plotted against temperature, the curve BO, the sublimation curve is

obtained. Along the curve BO, ice and water Vapor are in equilibrium with eachother.

The slope of the curve at any point is given by the Clapeyron.If the system is expanded isothermally, then this will decrease the pressure of theVapor phase. As at a given temperature, the solid-Vapor system has a fixed Vaporpressure, some ice will sublime to maintain the pressure. If the isothermal expansionis continued, more and more ice will sublime till the solid phase disappeared.

If, on the other hand, the system represented by point B is compressedisothermally, then some Vapor will condense to form ice in order to maintain the

pressure and prevent its increase. If the isothermal compression is continued, thenthe entire Vapor phase will disappear leaving only a solid phase in the system.


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These show that the regions above and below the curve BO represent solid andVapor phases, respectively.

Equilibrium between liquid, Vapor and solid water (ice)

The system at point B is gradually heated keeping the volume constant whentheVapour pressure of ice increases. A temperature is reached at which the Vaporpressure of ice becomes equal to that of liquid water maintained at the sametemperature. Then the solid water starts melting and the system consists of threephases, ice, water and Vapor, in equilibrium with each other. This is an invariantsystem (F=0) and the temperature and pressure of the system remain unchanged aslong as all the three phases are present together, is known as triple point. This pointfor water lies at 0.0075 and 4.6mmHg.

Equilibrium between liquid and Vapor(Vaporization curve)

The system at the triple point is gradually heated at constant volume; thetemperature and pressure do not change till the entire solid melts to give liquidwater. There are only 2 phases in the system liquid water and Vapor. If the heatingis continued at constant volume, the temperature and Vapor pressure of the systemvary along the curve OA. The curve

OA is known as the vaporization curve and along the curve OA liquid water and

Vapor are in equilibrium with each other. The slope of the curve OA at any point is

given by the Clapeyron equation. Mathematically,

If a system is subjected to isothermal expansion, then the pressure of the Vaporphase decreases, a small quantity of water evaporates to raise the pressure to avalue which is the Vapor pressure of liquid water at that temperature. As theisothermal expansion is continued, more and more liquid water evaporates till theentire liquid phase disappears and the system is made up of only Vapor.

Data Calculations

Following data are required and we find them by a series of calculations explained

later:

1. Partial Pressure

2. Composition of the mixture for which calculations are done


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In mixtures containing two or more components where their concentrations are

compared in the vapor and liquid phases, concentrations of each component are

often expressed as mole fractions. A mole fraction is number of moles of a given

component in an amount of mixture in a phase (either vapor or liquid phase) divided

by the total number of moles of all components in that amount of mixture in thatphase.

The equilibrium concentration of each component in the liquid phase is often

different from its concentration (or vapor pressure) in the vapor phase, but there is a

correlation. Such VLE concentration data is often known or can be determined

experimentally for vaporliquid mixtures with various components. In certain cases

such VLE data can be determined or approximated with the help of certain theories

such as Raoult's Law, Dalton's Law and/or Henry's Law.

Thermodynamics ExplanationFor pure systems having single component:

;

;

For multi-component systems:

;

;

Where P represents pressure, T represents temperature and G represents the

partial molar Gibbs free energy. Liq represents liquid state and vap is the vapour

state of the given component in the mixture.

Gibbs free energy is calculated by:

Where G is the extensive Gibbs free energy, and ni is the amount of substance of

component i.

Dew Point

Introduction

The dew point is the temperature below which the watervapor in a volume of humid air at a constant barometric pressure will condense into

liquid water. Condensed water is called dew when it forms on a solid surface.


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The dew point is a water-to-air saturation temperature. The dew point is associated

with relative humidity. A high relative humidity indicates that the dew point is closer

to the current air temperature. Relative humidity of 100% indicates the dew point is

equal to the current temperature and that the air is maximally saturated with water.

When the dew point remains constant and temperature increases, relative humiditydecreases.

When a liquid mixture begins to boil, the vapor does not normally have the same

composition as the liquid. The components with the lowest boiling point (i.e. the

more volatile) will preferentially boil off. Thus, as the liquid continues to boil, the

concentration of the least volatile component drops. This results in a rise in the

boiling point. The temperatures over which boiling occurs set the bubble and dew

points of the mixture.

The bubble and dew points can be defined as:

1. The bubble point is the point at which the first drop of a liquid mixture begins to

vaporize.

2. The dew point is the point at which the first drop of a gaseous mixture begins to

condense.

For a pure component, the bubble and dew point are both at the same temperature -

its boiling point. For example, pure water will boil at a single temperature (at

atmospheric pressure, this is 100C). For ideal mixtures (i.e. mixtures where there

are no significant interactions between the components), vapor-liquid equilibrium isgoverned by Raoult's Law and Dalton's Law.

Measurements

When the relative humidity is above 50% we can use the following formula:

and


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Considering the temperature in Celsius. RH represents the relative humidity.

Methods of Calculations

Calculating Bubble & Dew Points for Ideal Mixtures

Raoult's Law

Raoult's Law states that the partial pressure of a component, PA, is proportional to

its concentration in the liquid. So for component A,

PA=PoA.XA

Where

PA=partial pressure of component A

PoA= Vapour pressure of component A

XA= Liquid mole fraction of component A

Dalton's Law

Dalton's Law states that the total pressure is equal to the sum of the component

partial pressures. Thus for component A, its partial pressure, PA, is proportional to

its mole fraction in the gas phase

PA=YA.PTotal

Where

PTotal=Total System Pressure

yA=vapour mole fraction of component A

Dew Point Calculation

The dew point is the temperature at which a gas mixture will start to condense. For

an ideal mixture, we can use Dalton's and Raoult's Laws to calculate the dew point.

By combining the two equations, we can calculate the liquid mole fractions for a

given vapour composition, i.e.

XA=YA.PTotal/PoA

The pure component vapour pressures can then be used to calculate the liquid mole

fraction for each component, x, using the above equation. The sum of all the liquid

mole fractions should add up to 1 at the dew point. If the sum is greater than 1, the

temperature guess is too low. If the sum is less than 1, the temperature guess is toohigh. Adjust the temperature until the liquid mole fractions add up to 1.


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Example Calculation

Estimating the Dew Point

A gas has the following composition: 75mol% n-pentane, 20mol% n-hexane, 5mol%n-heptane. What is its Dew Point at atmospheric pressure (760 mmHg)?

The normal boiling points of pentane, hexane and heptane are 36C, 69C and 98C

respectively, so the dew point at atmospheric pressure will lie within this temperature

range. As a first guess, take a temperature of 40C.The vapour pressure of each

component can be estimated using their Antoine Equation (see our separate article).

So at 40C, the vapour pressure of each component is as follows:

Assuming ideal behaviour, the liquid mole fractions at the dew point can be

calculated using:

Thus

Adding the vapour mole fractions together gives: 0.857 + 0.074 + 0.006 = 0.937.

This is less than 1, meaning that 40C is below the bubble point. Re-guessing thetemperature at 50C, 45C, 42C and 41C


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Temperature40oC 50oC 45oC 42oC 41oC

yPentane 0.857 1.183 1.011 0.918 0.888

yHexane 0.074 0.107 0.089 0.080 0.077

yHeptane 0.006 0.009 0.008 0.007 0.006

Total 0.937 1.299 1.108 1.005 0.971

Dew point calculation with Raoult's law

We can also find dew point using modified form of Raoult's law which is given as

yAP= xAPA*(T)

Raoult's Law and for each component

yAP=xAPA*(T) Raoult's Law for component A

yBP=xBPB*(T) Raoult's Law for component B

by adding both equations we get

yA / PA*(T) + yB / PB*(T) = 1/P

We then find the composition from Raoult's Law

xA = yAP / PA*

Example

What is the dew point pressure of a mixture containing 40 mol% n-pentane and 60

mol% n-hexane at 121C and what is the composition of the first droplets of liquid

that begin to condense?

Solution

The vapor pressures are the same as in the above bubble-point problem because

the temperature is still 121C. However, now we want to eliminate x from the two

Raoult's Law equations because we know y values. Therefore we can use the

expression derived above:

yA / PA*(T) + yB / PB*(T) = 1/P = 0.4/3059 + 0.6/666 = 0.001032 / mm Hg

Thus,


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P = mm Hg/0.001032 = 969.3 mm Hg

We then find the composition from Raoult's Law

xA = yAP / PA* = (0.4)(969.3)/3059 = 0.127

Dew point calculation using modified Raoult's law with Gamma & pi:

We can also find dew point using modified Raoult's law with Gamma & phi. This is

given as

P=(Xi.gammai.Pisat)/phii

to find gamma,phi,Psat we use other complex equations and then put it in main

equation to find dew point pressure.

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