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The Simplest Phase Equilibrium Examples and Some Simple Estimating Rules Chapter 3.
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Transcript of The Simplest Phase Equilibrium Examples and Some Simple Estimating Rules Chapter 3.
The Simplest Phase Equilibrium Examples and Some Simple Estimating Rules
Chapter 3
When is a system at equilibrium?
For a system to be at equilibrium there can be no spontaneous processes occurring within the system
1. Temperature
It must be at the same temperature as the surroundings
It must have a uniform temperature Steady state is not the same as
equilibrium
Steady State
0
x
T
0
t
T
At steady state different temperatures can exist at different points around the system, but the system does not change with time.
Equilibrium
0
x
T
0
t
T
At equilibrium the temperature is the same throughout the system, and the system does not change with time.
2. Energy
Mechanical Energy can be converted completely to some other form of mechanical energy
It can also be converted completely to heat by a frictional process
Heat can not be converted completely to energy by a frictional process
No moving parts
This means that a system at equilibrium can not have moving parts, because in real systems motion leads to friction – which is irreversible
Constant Pressure
In the absence of restraining gravity, spring, electrostatic, magnetic, osmotic, or surface forces, at equilibrium the system must be at uniform pressure
If it’s not, the pressure difference causes motion
3. No flow of electricity
Electricity flowing through a resistor causes the wire to heat up – the current is changed into heat, which is an irreversible process
Phase Equilibrium
First some definitions Gas – any substance in a gaseous state Vapor – a gas at a temperature below it’s
critical point That means it can condense if we raise the
pressure enough
Liquid-Vapor Phase Equilibrium Consider the liquid water – water
vapor equilibrium To be at equilibrium, the rate of water
molecules leaving the liquid must be the same as the rate of molecules returning to the liquid
Evaporation = condensation Vapor pressure of the liquid =
pressure of the vapor
If the system is not at equilibrium
The liquid either spontaneously boils to transfer mass into the vapor phase until equilibrium is attained, or…
The vapor condenses until the gas pressure equals the vapor pressure of the liquid.
Consider a more complicated system – where air is involved
Water + dissolved air
Air + water vapor
Frictionless piston
There is air dissolved in the water, and water vapor in the gas phase
Composition of Air and Water in Equilibrium at 20 0C and 1 atm
Gas Phase Liquid Phase
Mole fraction water
0.023 .999985
Mole fraction oxygen
0.205 5x10-6
Mole fraction nitrogen
0.772 10x10-6
Total 1.0 1.0The composition of the gas and liquid phases is different
What happens when you change the temperature?
More liquid evaporates, and goes into the vapor phase.
Less gas becomes soluble in the liquid phase
Increasing Complexity
When there is only one substance, the composition of both phases is the same (100%)
When we add additional components, the composition of each phase is different
Chemical Engineers use this fact in separation processes
It’s the basis of distillation columns, liquid extraction, drying operations and crystallization to name a few
How do you predict the composition in each phase of a multicomponent system?
Raoult’s law Henry’s law
Raoult’s Law – Partial Pressure
Pi is the partial pressure of component i
yi is the mole fraction of component i in the gas
P is the total gas pressure
PyP ii
Raoult’s Law – Partial Vapor Pressures
0iii PxP
Pi is the partial vapor pressure of component i
xi is the mole fraction of component i in the liquid
P0 is the pure component vapor pressure of component i
Pyi
Raoult’s Law
0iii PxPy
i
ii
y
PxP
0
And by extension
0 iiPxP
Fugacity
0iii PxPy
Partial Pressure Partial Vapor Pressure
Fugacity of the gas
For ideal gases and for ideal solutions
Fugacity of the liquid
Henry’s Law Used with gases above their critical
temperature For example, consider dissolving O2 in
water The O2 can’t exist as liquid at room
temperature, so we can’t use Raoult’s law
We don’t have a vapor pressure, so we use a “pseudo” vapor pressure called the Henry’s law constant
Henry’s Law
Henry’s Law is identical to Raoult’s law, except that the Henry’s law constant replaces the vapor pressure
iii HxPy
Which equation should I use?
Raoult’s Law deals with vapor-liquid equilibrium
Henry’s Law deals with gas-liquid equilibrium Gases usually do not dissolve in liquids
to any great extent
Problem Solving
Consider a system where water is in equilibrium at one atmosphere with air
0waterwaterwater PxPy
oxygenoxygenoxygen HxPy
nitrogennitrogennitrogen HxPy
We know P= 1 atm, the vapor pressure of water, and the Henry’s law constants for oxygen and nitrogen.
That gives us 3 equations and 6 unknowns!!!
Raoult’s law
Henry’s law
Henry’s law
But we know three more relationships We know that the sum
of the mole fractions in the liquid is 1
The sum of the mole fractions in the gas is 1
The ratio of oxygen gas to nitrogen gas
1 nitrogenoxygenwater yyy
1 nitrogenoxygenwater xxx
266.079.0
21.0
nitrogen
oxygen
y
y
There are lots of ways to solve these systems of equations
Spread Sheet MATLAB Calculator “solve” feature Paper, pencil and brain power
How do you find the vapor pressure and Henry’s law constant values?
Vapor Pressures Steam tables Antoine’s equation
Henry’s Law Constant Appendix A.3 Perry’s Handbook
Two Component Phase diagram
Liquid-Vapor Compositions of Benzene-Tolune at 1 atm
75
80
85
90
95
100
105
110
115
0 0.2 0.4 0.6 0.8 1
Mole fraction benzene
Te
mp
era
ture
, (C
)
Liquid
Vapor
2 phase
Liquid-Vapor Compositions of Benzene-Tolune at 1 atm
75
80
85
90
95
100
105
110
115
0 0.2 0.4 0.6 0.8 1
Mole fraction benzene
Te
mp
era
ture
, (C
)
A 40% benzene-60% toluene solution boils at 94 C, and is in equilibrium with a 64% benzene – 36% toluene vapor
Uses and Limits of Raoult’s and Henry’s Laws
1. In a dilute solution, Raoult’s law will probably apply to the solvent.
2. If the solvent and solute are chemically similar, Raoult’s law will probably apply to both, over the entire range of concentration.
3. If the solvent and solute interact chemically, Raoult’s law will probably do a poor job.
Uses and Limits of Raoult’s and Henry’s Laws
4. Henry’s law works well for most gases unless they interact chemically with the solvent.
5. Henry’s law works well for liquids that are immiscible in water, and only dissolve a small amount.
6. Henry’s law can be used for solvents besides water.
Uses and Limits of Raoult’s and Henry’s Laws
7. You can add a fudge factor, called the activity coefficient, to account for non-ideal behavior.