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Definitions• Critical Temperature (Tc): Highest temperature at which a species can coexist

in two phase (liquid and vapor)• Critical Pressure (Pc): Pressure that corresponds to critical temperature

• Critical Point (Critical State) of a fluid: The critical point refers to the statewhen the fluid is at Tc and the corresponding critical pressure,Pc. Such a fluidcan still coexist, at Tc and Pc, as a liquid and vapor mixture.

• Reduce Pressure (Pr): This is the actual pressure of a fluid divided by its criticalpressure, Pr=P/Pc

• Reduce Temperature (Tr): This is the actual temperature of a fluid divided byits critical pressure, Tr=T/Tc

• Pitzer Acentric Factor : This factor (symbol ) is a parameter used in nonideal equations of state that takes into account the geometry and polarity of amolecule



Calculate the reduced temperature and pressure:



Non-ideal gases

• In reality molecules of a gas do interact, all real gases are nonideal.

• At, higher pressures and/or lower temperatures the impact of intermolecular interactions on gas behavior increases

•

Non ideal gas method must be used to account for the effect of these interaction on the relationship between P,V and T ( andrelated properties such as density) of a gas

• Below, the following five methods will be introduced: – Virial Equation of State – Van der Waals Equation of State – Soave-Redlich-Kwong (SRK) equation of state – Compressibility Factor Equation of State – Kay’s Rule (for non ideal gas mixtures)



Virial Equations of State• The virial expansion, also called the virial equation of state, is the most

interesting and versatile of the equations of state for gases..• The virial expansion is a power series in powers of the variable, n/V, and has

the form,

• The coefficient, B(T ), is a function of temperature and is called the "secondvirial coefficient. C (T ) is called the third virial coefficient, and so on.

• The expansion is, in principle, an infinite series, and as such should be valid for

all isotropic substances.• In practice, however, terms above the third virial coefficient are rarely used in

chemical thermodynamics.



Truncated virial equation (truncated at 2nd term)

V

B

RT

V P1

Pitzer Acentric Factors , ω , a parameter that reflects the geometry and polarity of a molecule



)( 1 B B

P

RT B

o

c

c

Estimate B using the following equations:

2.41

6.1

172.0139.0

422.0083.0

r

r

o

T B

T B



Example:

Two gram-moles of nitrogen is placed in a three literEstimate the tank pressure using;i) ideal gas equation of stateii) the virial equation of state truncated after the seTaking the second estimate to be correct, calculate terror that results form the use of the ideal gas equatsystems conditions



Van Der Waals Equation of StateBased on a modification of the ideal gas law Van Der Waals Constant

2

a

v Accounts for attractive forces between molecules

b Correction accounting for the volume occupied by the molecules themselves

The parameters a and b change from onegas to another but are independent of temperature



Soave-Redlich-Kwong (SRK) Equation of State

SOAVE-REDLICH-KWONG (SRK) EQUATION

A more accurate cubic EOS is the empirical SRK equation:

The parameters of the SRK EOS are calculated the following



COMPRESSIBILITY FACTORThe compressibility factor,Z is a useful thermodynamic property for modifiying the ideal gas law to account for the real gas behaviour

For ideal gas Z=1The value Z generally increase with pressure and decreases with temperature

At high pressures molecules are colliding more often, and at low temperatures they are moving less rapidly.



The procedure for using the generalized compressibility chart is as follows:

1. Find the critical pressure and the critical temperature for thefluid of interest( note: if the fluid is hydrogen or helium thesecritical values must be corrected)

2. Calculate the reduced pressure and temperature (note: alltemperatures used must be absolute)

3. Use the compressibility chart to determine Z



The generalized Compressibility Chart

100 gmoles of nitrogen is contained in a 5 litervessel at -20.6 0C. Estimate the pressure in the

cylinder.



EXAMPLE : What is the compressibility factor of nitrogen at 800 p



Example : A mountaineer on Mount Everest has a cylinder of supp The volume of oxygen is 3.0 L and there are 1071 g oxy The temperature outside is - 30˚C. Estimate the pressur the tank using compressibility factors.



NON IDEAL GAS MIXTURE-Gas contains more than one species



EXAMPLE :A mixture containing 30 mole% isobutane and 70 mole

a container at 500 atm and - 120˚C. What is the specificmixture?

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