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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.