Essay > Module 3 Computation of the Compressibility Factor, Fugacity Coefficient, and Thermodynamic

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1 Name: Sofhia Marie B. Punzalan

Date Submitted: October 15, 2020

Section: 6L Module 3

Computation of the Compressibility Factor, Fugacity Coefficient, and Thermodynamic Equilibrium Constant of Gas-Phase Equilibria

I.

Introduction The ideal gas law holds good sufficiently at high temperatures and low pressures but as

the pressure increases and the temperature decreases, real gases deviates from the ideal gas law. This is because molecules of real gases interact with one another wherein repulsive forces between molecules aid expansion while attractive forces aid compression (Atkins 2006).

Several equations of state such as Redlich-Kwong, Benedict-Webb-Rubin, and Beattie Bridgeman equations have been proposed to represent the data of real gases more accurately (Rao 2004). To quantify the deviation of real gases from the ideal gas behavior, compressibility factor or compression factor, Z, has been introduced (Rao 2004). It is defined to be the ratio of the measured molar volume of a real gas to the molar volume of an ideal gas at a given pressure and temperature (Atkins 2006). The compressibility factor, Z, is given by equation 3.1. ⁄

[Eq’n 3.1]

For real gases, Z is always equal to 1 while for real gases, Z>1 at high pressures and Z<1 at intermediate pressures (Atkins 2006). The compressibility factor of a gas can also be expressed by using an infinite power expansion series of a virial equation (Bello 2017).

Another parameter that quantifies deviation of real gases from the ideal gas behavior is the fugacity coefficient, Φ, which depends on the temperature, pressure, and identity of the gas (Atkins 2006). It is simply the ratio of fugacity to pressure (see equation 3.2). As the pressure of

2 the gas approaches zero, the gas tends to behave perfectly where f and p will be more identical thus, Φ will be equivalent to 1.

[Eq’n 3.2] Fugacity (f) is the effective pressure of a real gas, which replaces the true pressure in an ideal gas equation (Atkins 2006). It is also equivalent to the effective concentration of a substance. Replacing the true pressure with fugacity in the molar Gibbs free energy equation and performing series of integrations will give a final equation (see eq’n 3.3), which when applied to different equations of state would determine the fugacity coefficient. For this module, the equations of state used were van der Waals (see equation 3.4) and Redlich-Kwong (see equation 3.5). ∫

[Eq’n 3.3]

( )

( )

[Eq’n 3.4]

( )

( )

[Eq’n 3.5]

There are two other methods that can be used to calculate the fugacity coefficient of real gases, which are Newton-Raphson method and Simpson’s method.

II.

Materials and Methods This module was divided into two parts which were, (1) determination of the

compression factor and fugacity coefficient of the gases, and (2) determination of the thermodynamic equilibrium constant of the equilibrium reaction. For the first part, three different methods were used to calculate fugacity coefficients of the assigned gas, nitrogen gas. The fugacity coefficients were determined at different temperatures: 600K, 800K, and 1000K and different pressures: 100 bar, 200 bar, and 300 bar. The reference pressure used was 1 bar and

3 the values of a and b were obtained from the table of gas constants provided by the instructor.

The first method performed was direct calculation method using van der Waals EOS and Redlich-Kwong EOS. The equations used were seen in equations ## and ##. They were evaluated using the assigned temperatures and pressures as well as the reference pressure. In that method, the total fugacity coefficients obtained were 18 (9 fugacity coefficients for each EOS).

The second method performed was Newton-Rapson method using van der Waals EOS. In this method, the compression factors were initially calculated and then their values were used to compute the fugacity coefficients. For this method, a total of 9 compression factor values and 9 fugacity coefficients were obtained. Lastly, the third method performed was Simpson’s method. In this method, values of compression factor (Z), pressure (P), and different temperatures (600K, 800K, 1000K) were used to calculate the fugacity coefficients. A total of 3 fugacity coefficients were obtained in this method.

The second part of the module

III.

Results

and

·

This must contain tables of derived data (do not show raw data) from calculations.

·

Tabulate

·

Make separate tables that compare experimental values with the literature values (show the

or

include

literature

values

Discussion

used

and

cite

references

percent

properly.

error).

·

Graphs should be included especially in cases where trends in data need to be illustrated

or

clarified.

·

Observe

proper

·

Show

·

Incorporate

·

Compare

the

presentation

theoretical

significance

of

tables

and

interpretation

answers derived/measured

values

and

graphs. of

to with

the

accepted

results. questions.

literature

values.

4 ·

Discuss

the

·

Apply

possible

·

Show limitations and inherent error of experimental procedure and apparatus.

·

Briefly

compare

·

Give

at

IV.

Summary

·

Summarize the important points in relation to the objectives of the exercise.

·

State any conclusions reached and comment on the validity of these conclusions.

V.

effects

of

any

approximation/assumption

corrections

to

results

the

method

used

two

applications

least

with

whenever

other

available

of

the

and

made. possible.

methods. experiment.

Conclusions

Sample

Calculations

·

Show

the

equations

used.

·

Show a complete calculation of one datum representative of the data contained in the

tables. ·

Show plotted values including results of linear regression whenever necessary.

·

VI.

Can

Literature

be

handwritten

or

typewritten.

Cited

https://books.google.com.ph/books?id=iYWiCXziWsEC&pg=PA59&dq=compressibility+factor&h l=en&sa=X&ved=2ahUKEwjX5_fZsJ3sAhWUQN4KHYfeCkIQ6AEwA3oECAIQAg#v=onepage& q=compressibility%20factor&f=false

https://books.google.com.ph/books?id=k3JQDwAAQBAJ&pg=PA191&dq=compressibilit y+factor+expansion+series&hl=en&sa=X&ved=2ahUKEwiU0ujBxJ3sAhUOqpQKHSI7CF8Q6AE wAHoECAUQAg#v=onepage&q=compressibility%20factor%20expansion%20series&f=false

5 https://www.google.com/search?tbm=bks&ei=wwd7X5f6OpSBQaHvauQBA&q=compressibility+factor+expansion+series&oq=compressibility+factor+expansio n+series&gs_l=psyab.3...5313117.5315842.0.5316065.17.17.0.0.0.0.153.1584.10j6.16.0....0...1c.1.64.psyab..1.1.102...33i10k1.0.FfJAKvQKN4k