Peng-Robinson Case

Peng-Robinson: Program I

Introduction:

For this program, We are determine to find the density of argon for the temperature 160Kand the pressure range from 1 atm to 100 atm by the Peng-Robinson equation of state.

Peng-Robinson Equation of State:

By definition of equation of state, it is an equation that shows the relationship between each values of pressure, volume, and temperature of a quantity of a substance. From the Peng-Robinson Equation of State, the equation is

P=RT/(v-b)-(a(T))/( v(v+b)+b(v-b))

The Peng-Robinson Equation of State is also written as

Z³-(1-B)Z²+(A-3B²-2B)Z-(AB-B²-B³)=0

Where Z is the compressibility factor of pressure, volume, universal gas constant, and temperature.

Compressiblity Factor: PV/RT=Z

Our universal gas constant for this program is 0.08205atm*L/(mol*K).

Now we are going to find the Z factor and density of Argon.

Data (Ar (P=40 atm):

We are going to use the list of given values for Argon. We have P:40atm, T: 160K ,w:-0.004, Tc: 150.8K,Pc:48.1 atm, and R: 0.08205 atm*L.

Our P is our pressure, T is our temperature, ɯ is our acentric factor, Tcis our temperature constant, Pc is our pressure constant, and R is our universal gas constant.

Peng-Robinson Parameters for Ar:P(atm=40)

P= 40 atm

T= 160K

ɯ = -0.004

Tc= 150.8 K

Pc= 48.1 atm

R= 0.082205 (atm*L/(mol*K)

Calculations (Ar: 40atm):

We are going to use Microsoft Excel to solve for the other values, which are a,A,B,Z,a,a(Tc),f,g,Tr.

Then, using the Equation 1, we are going to calculate the compressibility and then calculate density and the density data by using the Solver.

After the calculation of density and density data, we will calculate the percent error.

The equations to plug in for each value are:

A=aP/(R²T²)

B=bP/(RT)

Z=Pv/(RT)

a= a(Tc)*f(Tr,ɯ)

a(Tc)=0.45724*R²T²c/Pc

f=1+g(1-Tr^½)