1. Reading Materials: Chapter 4
Describing Physical
Quantities
LECTURE 9
Chapter 4
CHEM ENG 1007

2. Objectives At the end of these lectures you should be able to:
Explain in your own words the meaning of gram-mole, lb-mole and kilogram-mole (Lecture 7)
Calculate two of the quantities mass (or mass flow rate), volume (or volumetric flow rate), and moles (or molars flow rate) from a knowledge of the third quantity for any species of known density and molecular weight. (Lecture 8)
Transform a material from one measure of concentration to another including mass/volume, moles/volume, ppm, ppb and molarity (Lecture 8)
Calculate the average molecular weight of the mixture
Convert the composition of a mixture from mass fraction (or mass percent) to mole fraction (or mole percent) and vice versa.
Chapter 4
CHEM ENG 1007

3. §4.2.3 Mixture Concentration
In the calculation of the mass fraction and mole fraction, the same units for mass and moles must be used in the numerator as in the denominator so that the calculated fraction is without units.
Summary:
Chapter 4
CHEM ENG 1007

4. Learning Check
Two compounds, one with a high molecular weight and one with a low molecular weight, each comprise 50 mole% of the same mixture. Which has the greater mass fraction in the mixture
Solution:
Answer: the stream that has higher molecular weight will have greater mass fraction.
Chapter 4
CHEM ENG 1007

5. Learning Check
A solution of salt dissolved in water is diluted with additional water. With each of the following variables, indicate whether the dilution process will cause the value of the variable to increase, decrease, or stay the same. Support your answer
Solution:
Chapter 4
CHEM ENG 1007

6. Average/Mean Molecular Weight
From mole fraction:
From mass fraction:
Chapter 4
CHEM ENG 1007

7. Illustration 7 Calculate the average molecular weight of air
(1) From its approximate molar composition of 79% N2, 21% O2
Solution:
Chapter 4
CHEM ENG 1007

8. Illustration 7 Calculate the average molecular weight of air
(2) From its approximate mass composition of 76.7 wt% N2, 23.3 wt% O2
Solution:
Chapter 4
CHEM ENG 1007

9. Illustration 7
(3) Assume we have 100 mol of air mixture, what is this amount in grams?
From (1) molar composition of 79% N2, 21% O2
Solution:
Chapter 4
CHEM ENG 1007

10. Illustration 7
(3) Assume we have 100 mol of air mixture, what is this amount in grams?
From (1) molar composition of 79% N2, 21% O2
Solution: (alternative method)
Chapter 4
CHEM ENG 1007

11. System Properties
Quantities necessary to describe the state or condition of a system.
Extensive properties: depend on the size of system
eg. weight, force, energy, flow rate
Intensive properties: are independent of the mass or size of system,
eg. temperature, pressure, density, viscosity, concentration, mass fraction, mole fraction, etc.
Chapter 4
CHEM ENG 1007

12. Learning Check
A solution of NaOH in water flows in a stream, and the mass flow rate of the stream suddenly increased. For each of the following properties of the stream, indicate whether the increase of the flow rate will cause the property to increase, decrease, or remain the same each case, explain your answer.
Solution:
Chapter 4
CHEM ENG 1007

13. Learning Check
A solution of NaOH in water flows in a stream, and the mass flow rate of the stream suddenly increased. For each of the following properties of the stream, indicate whether the increase of the flow rate will cause the property to increase, decrease, or remain the same each case, explain your answer.
Solution:
Chapter 4
CHEM ENG 1007

14. Example 4.5
From the acid-neutralization problem, the volumetric flow rate of the HCl solution coming from our manufacturing process is 11,600 L/hr, and the average molarity of HCl in that stream is M.
How many mol of HCl are in 88 m3 of the solution?
V = 88 m3; cHCl = M = mol/L; n = ? mol
Chapter 4
CHEM ENG 1007

15. Example 4.5
b) How many mole of HCl are flowing from the process per minute when the volumetric flow rate of the solution is 11,600 L/hr?
Chapter 4
CHEM ENG 1007

16. Example 4.5 What is the mass fraction of HCl in the solution?
V and c were given; xHCl=?
Chapter 4
CHEM ENG 1007

17. Illustration 8
A 2.25 L gas cylinder holds a mixture of hydrocarbons gases: methane, ethane and propane. The mass of the gas mixture in the cylinder is measured at 2.0 g. The mixture is at 25oC & 1 atm. Individual masses are given in the below table.
Constituent mi
(g of i)
CH4
1.0
C2H6
0.6
C3H8
0.4
Total
2.0
Chapter 4
CHEM ENG 1007

18. Illustration 8 a) Mass fraction of methane?
Same procedure for ethane and propane.
Constituent
(g of i/g total)
CH4
0.5 (i.e., 1/2)
C2H6
0.3 (i.e., 0.6/2)
C3H8
0.2 (i.e., 0.4/2)
Total
1.0
Chapter 4
CHEM ENG 1007

19. Illustration 8 b) Molecular weight of Propane? Very wrong!!!
Constituent
MW (g/mol)
CH4
16 (=12+4)
C2H6
30 (=2 x12+6x1)
C3H8
44 (=12x3+8x1)
Total -
Average
21.84
Very wrong!!!
Chapter 4
CHEM ENG 1007

20. Illustration 8 c) Mole fraction of ethane?
Same procedure for methane and propane.
Total number of moles is
Chapter 4
CHEM ENG 1007

21. Illustration 8 Check result by summing mole fractions? Constituentyi
CH4
0.682
C2H6
0.218
C3H8
0.099
Check result by summing mole fractions?
Thought Problem: Why don’t the mole fractions sum to 1?
Chapter 4
CHEM ENG 1007

22. Illustration 8 d) Average Molecular Weight? By mole fraction:
By mass fraction:
Chapter 4
CHEM ENG 1007

23. Illustration 8 e) Mass concentration of propane:
Apply same procedure for methane and ethane
Constituent Ci
(kg of i/m3)
CH4
0.444
C2H6
0.267
C3H8
0.178
Chapter 4
CHEM ENG 1007

24. §4.2.3 Conversion between mole fraction and mass fraction
Strategy for converting mass fractions/percentage to mole fractions/percentages
Assume a basis of 100 mass units
From the known mass fractions, calculate the mass of each species
Using the molecular weights, convert the mass into moles for each species
Compute the desired moles fractions or percentages.
Chapter 4
CHEM ENG 1007

25. §4.2.3 Conversion between mole fraction and mass fraction
Assume a basis of 100 moles
From the known mole fractions, calculate the number of moles of each species
Using the molecular weights, convert the moles into mass for each species
Compute the desired mass fractions or percentages.
Note: When performing such conversions, the best way is to tabulate your data
Chapter 4
CHEM ENG 1007

26. Example 4.6 Air has the following approximate mole%:
N2: mole%; O2: mole%; Ar: 0.94 mole%
Solution: Assume 100 mol of Air
Convert from mole to mass
Chapter 4
CHEM ENG 1007

27. Example 4.6 Hence, the total number of grams is
mT = = 2896 g
Chapter 4
CHEM ENG 1007

28. Example 4.6
Alternatively, we can set up our work as shown in the below table
Basis: 100 mol
Component yi ni
Mwi
mi (ni.Mwi) xi N2
0.7807
78.07 28
2186
0.7548 O2
0.2099
20.99 32
672
0.2320 Ar
0.0094
0.94
39.95 38
0.0131
Total 1
100
2896
0.9999
Chapter 4
CHEM ENG 1007