1. Fundamentals of Chemical Engineering - II
CHPE204
PREREQUISITE: CHPE202
Dr. Ir. Yasir Ali

2. Chapter 1
Single-Phase Systems

3. LIQUID AND SOLID DENSITIES
When you heat a liquid or a solid it normally expands (i.e., its density decreases).
In most process applications, however, it can be assumed with little error that solid and liquid densities are independent of temperature.
Similarly, changes in pressure do not cause significant changes in liquid or solid densities; these substances are therefore termed incompressible.

4. LIQUID AND SOLID DENSITIES
In most process applications, however, it can be assumed with little error that solid and liquid densities are independent of temperature.

5. LIQUID AND SOLID DENSITIES

6. EXAMPLE: Determination of a Solution Density

8. IDEAL GASES The Ideal Gas Equation of State
The ideal gas equation of state can be derived from the kinetic theory of gases by assuming that gas molecules have a negligible volume, exert no forces on one another, and collide elastically with the walls of their container.
The equation usually appears in the form:

9. IDEAL GASES The Ideal Gas Equation of State
What are the conditions for a gas to behave as predicted by the ideal gas?
The major ones are:
1. The molecules of an ideal gas do not occupy any space; they are infinitesimally small.
2. No attractive forces exist between the molecules so that the molecules move completely independently of each other.
3. The gas molecules move in random, straight-line motion and the collisions between the molecules, and between the molecules and the walls of the container, are perfectly elastic.

10. IDEAL GASES The Ideal Gas Equation of State Solution
EXAMPLE: Use of Standard Conditions to Calculate Volume from Mass
Calculate the volume, in cubic meters, occupied by 40 kg of CO2 at standard conditions assuming CO2 acts as an ideal gas.
Solution
Basis: 4O kg of CO2
40 kg CO2
1 kg mol CO2
22.42 m3 CO2
44 kg CO2
= 20.4 m3 CO2 at S.C
Notice in this problem how the information that m3 at S.C = 1 kg mol is applied to transform a known number of moles into an equivalent number of cubic meters.
An alternate way to calculate the volume at standard conditions is to use Equation (5-2.1).

11. IDEAL GASES The Ideal Gas Equation of State
EXAMPLE: Calculation of R using the standard conditions
Find the value for the universal gas constant R to match the following combination of units: For 1 gmol of ideal gas when the pressure is in atm. the volume is in cm3, and temperature is in K.

12. IDEAL GASES The Ideal Gas Equation of State
In many processes going from an initial state to a final state, you will find it convenient to use the ratio of the ideal laws in the respective states, and thus eliminate R as follows (the subscript 1 designates initial state, and the subscript 2 designates the final state)
OR:
Note that Equation (13.2) involves ratios of the same variable. This result has the convenient feature that the pressures may be expressed in any system of units you choose, such as kPa, inHg, mmHg. atm and so on, as long as the same units are used for both conditions of pressure.
Similarly, the ratio of the absolute temperatures and ratio of the volumes results in ratios that are dimensionless. Note how the ideal gas constant R is eliminated in taking the ratios.

13. IDEAL GASES The Ideal Gas Equation of State
EXAMPLE: Application of the Ideal Gas Law to Calculate a Volume
Calculate the volume occupied by 88 lb of CO2 at 15 OC and a pressure of 32.2 ft of water.
Solution
The final volume can be calculated via Equation (13.2) in which both R and (n1/n2) cancel out:

14. IDEAL GASES The Ideal Gas Equation of State
Assume that the given pressure is absolute pressure.
Basis: 88 lb of CO2

15. IDEAL GASES The Ideal Gas Equation of State
Now, using Equation (5-2.1), insert the given values, and perform the necessary calculations
Basis: 88 lb of CO2

16. IDEAL GASES
EXAMPLE: The Ideal Gas Equation of State
One hundred grams of nitrogen is stored in a container at 23.0 ºC and 3.00 psig.
Assuming ideal gas behavior, calculate the container volume in liters.
Verify that the ideal gas equation of state is a good approximation for the given conditions.
SOLUTION
The ideal gas equation of state relates absolute temperature, absolute pressure, and the quantity
of a gas in moles. We therefore first calculate:

17. IDEAL GASES

18. IDEAL GASES Standard Temperature and Pressure
Doing PVT calculations by substituting given values of variables into the ideal gas equation of state is straightforward, but to use this method you must have on hand either a table of values of R with different units or a good memory. A way to avoid these requirements is to use conversion from standard conditions.
For an ideal gas at an arbitrary temperature and pressure ,

19. IDEAL GASES

20. EXAMPLE: Conversion from Standard Conditions
Butane (C4H10) at 360 ºC and 3.00 atm absolute flows into a reactor at a rate of 1100 kg/h. Calculate the volumetric flow rate of this stream using conversion from standard conditions.
SOLUTION
As always, molar quantities and absolute temperature and pressure must be used.

21. EXAMPLE: Effect of T and P on Volumetric Flow Rates

22. EXAMPLE: Standard and True Volumetric Flow Rates
The flow rate of a methane stream at 285 ºF and 1.30 atm is measured with an orifice meter. The calibration chart for the meter indicates that the flow rate is 3.95×10 SCFH (standard cubic feet per hour [ft3 (STP)/h]). Calculate the molar flow rate and the true volumetric flow rate of the stream.
SOLUTION

23. Virial Equations of State

24. Virial Equations of State

25. EXAMPLE: The Truncated Virial Equation
Two gram-moles of nitrogen is placed in a three-liter tank at –150 ºC. Estimate the tank pressure using the ideal gas equation of state and then using the virial equation of state truncated after the second term. Taking the second estimate to be correct, calculate the percentage error that results from the use of the ideal gas equation at the system conditions.
SOLUTION

27. THE COMPRESSIBILITY FACTOR EQUATION OF STATE
The compressibility factor of a gaseous species is defined as the ratio

28. EXAMPLE: Tabulated Compressibility Factors
Fifty cubic meters per hour of methane flows through a pipeline at 40.0 bar absolute and K.
SOLUTION
From the given reference, z = at 40.0 bar and K. Rearranging Equation 5.4-2c yields

29. The Law of Corresponding States and Compressibility Charts
It would be convenient if the compressibility factor at a single temperature and pressure were the same for all gases, so that a single chart or table of z( T, P) could be used for all PVT calculations.
An alternative approach is presented in this section. We will show that z can be estimated
for a species at a given temperature T and pressure P with this procedure:
Look up (e.g., in Table B.1) the critical temperature Tc, and critical pressure Pc, of the species.
Calculate the reduced temperature Tr= T/Tc, and reduced pressure Pr= P/Pc .
Look up the value of z on a generalized compressibility chart which plots z versus Pr for specified values of Tr.

30. The basis for estimating in this manner is the empirical law of corresponding states, which holds that the values of certain physical properties of a as—such as the compressibility factor depend to great extent on the proximity of the as to its critical state. The reduced temperature and pressure provide a measure of this proximity; the closer Tr and Pr are to 1, the closer the gas is to its critical state. This observation suggests that a plot of z versus Tr and Pr should be approximately the same for all substances.
The below Figure shows a generalized compressibility chart for those fluids having a critical compressibility factor of 0.27

31. A generalized compressibility chart for those fluids

32. The procedure for using the generalized compressibility chart for PVT calculations is as follows:

33. Fig. 5.4-2 Generalized compressibility chart, low pressures

36. EXAMPLE: The Generalized Compressibility Chart
One hundred gram-moles of nitrogen is contained in a 5-liter vessel at 20 6 C. Estimate the pressure in the cylinder..
SOLUTION
From Table B.1, the critical temperature and pressure of nitrogen are

38. Nonideal Gas Mixtures
Whether an analytical or graphical correlation is used to describe nonideal gas behavior, difficulties arise when the gas contains more than one species. Consider, for example, the SRK equation of state (Equation 5.3-7)
We will illustrate PVT calculations for mixtures with a simple rule developed by Kay that utilizes the generalized compressibility charts.

39. EXAMPLE: Kay’s Rule
A mixture of 75% H2 and 25% N2 (molar basis) is contained in a tank at 800 atm and – 70 C.
Estimate the specific volume of the mixture in L/mol using Kay’s rule.
SOLUTION