CHAPTER 1- INTRODUCTION CHE243-MATERIAL AND ENERGY BALANCE AND SIMULATION
CHAPTER 1- INTRODUCTION
INTRODUCTION TO ENGINEERING CALCULATION
• Units And Dimensions
• Conversion Of Units
• Systems Of Units
• Dimensional Homogeneity
PROCESSES AND PROCESS VARIABLES
• Concept Of Mass, Volume, Flowrate
• Chemical Composition
• Pressure And Temperature
2.0 UNIT & DIMENSION
Proper handling of units is an essential part of being an engineer
A measured or counted quantity has a numerical value and unit, eg. 2 meter, 4.29 kilograms.
A dimension is a property that can be measured, e.g – length, time, mass or temperature, or calculated by multiplying or dividing other dimensions, such as length/time (velocity).
Measurable unit are specific values of dimensions that have been defined by convention, custom, or law, e.g – grams for mass, seconds for time and centimeters for length.
3.0 CONVERSION OF UNITS
Equivalence between two expressions of the same quantity can be defined in terms of a ratio:
Factors Conversion
mm 100
cm 1
mm 10
cm 1
centimeter 1 per milimeters 10 cm 1
mm 10
milimeters 10 per centimeter 1 mm 10
cm 1
2
2
2
To convert a quantity expressed in terms of the unit to its equivalent in terms of another unit, multiply the given quantity by the conversion factor (new unit/old unit). Example:
1 g
1000 mg
36 mg = 0.036 g
4.0 SYSTEM OF UNITS
Base units – for mass, length, time, temperature, electrical current and light intensity.
Multiple units – defined as multiples or fractions of base units such as minutes, hours, and milliseconds, all defined in unit of seconds.
Derived units – (a) by multiplying and dividing base or multiple units
(cm2, ft/min) – preferred as compound unit.
(b) As defined equivalent to compound unit (eg. 1 lbf
32.174 lbm.ft/s2).
SYSTEM OF UNITS
SI unit – System International – meter (m) for length, kilogram (kg) for mass, seconds (s) for time and Kelvin (K) for temperature.
CGS system – Most identical to SI unit. Refer to Felder (pp. 11) Table 2.3-1.
American Engineering System – foot (ft) for length, pound-mass (lbm) for mass, seconds for time.
*Note: Refer to Felder (pp. 11)
Quantities can be added or subtracted only if their units are the same.
Rule – every valid equation must be dimensionally homogeneous; that is, all additive terms on both sides of equation must have the same dimensions.
*Note: Refer to Felder (pp. 20-22).
5.0 DIMENSIONAL
HOMOGENEITY
Consider the equation
D(ft)=3t(s)+4
1. If the equation is valid, what are the dimensions of the constants 3 and 4
2. If the equation is consistent in its units, what are the units of 3 and 4
3. Derive an equation for distance in meters in terms of time in minutes
5.0 DIMENSIONAL
HOMOGENEITY
You need to:
– Minimize production of unwanted byproducts
– Separate the good (product) from the bad
(byproducts)
– Recover the unused reactants
– Maximize profit, minimize energy
consumption, minimize impact on the
environment
Process: any operation or series of operations.
•The material enters a process = Input or Feed.
•The material which leaves the process = Output or
Product.
• It is common for process to consist of multiple steps.
These each steps is carried out in a process unit. Each of
process unit has associated with it a set of input and output
process stream.
•To design or analyze a process, we need to know the
amounts, compositions & condition of materials which enter
& leave the process.
6.0 MASS AND VOLUME
Density – mass per unit volume.
Specific volume – volume occupied by a unit mass of the substance
Specific gravity – ratio of the density of the substance to the density of a reference substance ref at specific condition:
Reference most commonly used for solid and liquid is water
at 4OC 1000 kg/m3
ref
SG
Calculate the density of mercury in lbm/ft3 and the volume in ft3 occupied by 215 kg of mercury. Given SG of mercury is 13.546 and density of water is 62.3 lbm/ft3.
Density of mercury….
392.843
ft
lbm
EXAMPLE 2
3ft5617.0
Volume of 215 kg mercury….
• Flowrate- the rate at which a material is transported through a process line is the flowrate of that material
• Can be expressed as- mass flowrate(mass/time) or volumetric flowrate (volume/time)
• Volumetric flowrate can be converted to mass flowrate if density of a fluid is known
MASS AND VOLUMETRIC FLOWRATE
..
// VmVm
• The mass flowaret of n-hexane (𝜌=0.659 g/cm3) in a pipe is 6.59 g/s. What is the volumetric flowrate of the hexane?
• The volumetric flowrate of CCl4(𝜌=1.595 g/cm3) in a pipe is 100.0 cm3/min. what is the mass flowrate of the CCl4?
EXAMPLE 3
s
cm3
0.10
min5.159
g
7.0 CHEMICAL COMPOSITION
Atomic weight – mass of an atom.
Molecular weight – sum of atomic weights of atoms that constitute a molecule of the compound, e.g O2 = 32 g/g-mol.
If a molecular weight of a substance is M, then there are M kg/kmol, M g/mol, and M lbm/lb-mole of this substance.
Molecular weight can be used as a conversion factor that relates the mass and the number of moles of a quantity of the substance.
1) Conversion Between Mass and Moles
How many of each of the following are contained in 100.0 g of CO2
(M=44.01)?
(1) mol CO2 (4) mol O (7) g O2
(2) lb-moles CO2 (5) mol O2
(3) mol C (6) g O
2CO mol 273.2)1(
EXAMPLE 4
2
3 CO mole-lb 10011.5)2(
C mol 273.2)3(
O mol 546.4)4(
2O mol 273.2)5(
gO7.72)6(
2O 7.72)5( g
7.0 CHEMICAL COMPOSITION
Mass Fraction:
Mole Fraction:
Percent by mass of A is 100xA
Percent by moles of A is 100yA
2) Mass & Mole Fraction and Molecular Weight
mass total
A of massAx
moles total
A of molesAy
A solution contains 15% A by mass (xA = 0.15) and 20 mole% B (yB = 0.20)
A kg 26
1) Calculate the mass of A in 175 kg of solution
EXAMPLE 5
2) Calculate the mass flowrate of A in a stream of solution flowing at a rate of 53 Ibm/h
h
AmIb8
A solution contains 15% A by mass (xA = 0.15) and 20 mole% B (yB = 0.20)
min
Bmol200
3) Calculate the molar flow rate of B in stream flowing at a rate of 1000 mol/min
EXAMPLE 5 CONT’D
A solution contains 15% A by mass (xA = 0.15) and 20 mole% B (yB = 0.20)
s
solution kmol140
4) Calculate the total solution flow rate that corresponds to a molar flow rate of 28 kmol B/s.
EXAMPLE 5 CONT’D
EXAMPLE 5 CONT’D
A solution contains 15% A by mass (xA = 0.15) and 20 mole% B (yB = 0.20)
5) Calculate the mass of the solution that contains 300 Ibm of A.
solutionmIb 2000
7.0 CHEMICAL COMPOSITION
A set of mass fractions may be converted to an equivalent set of mole fractions by:
(a) Assuming as a basis of calculation a mass of the mixture.
(b) Using the known mass fractions to calculate the mass of each component in the basis quantity; and converting this masses to moles;
(c) Taking the ratio of the moles of each component to the total number of moles.
3) Conversion from a Composition by Mass to Molar Composition
A mixture of gases has the following composition by mass:
Component Mass %
O2 16
CO 4.0
CO2 17
N2 63
What is the molar composition?
EXAMPLE 6
A researcher conducted an experiment on electrolysis of mixed brine. A mixture of gases was produced at the cathode. The composition (by weight) of the gases was as follows: 64% Chlorine (Cl2), 29% Bromine (Br2) and 7% Oxygen (O2). Using the ideal gas law, calculate the composition (by volume) of the gas mixture….
Given Molecular weight Br2 = 159.83, Cl2 = 70.91, O2 = 32.00
7.0 CHEMICAL COMPOSITION
Average molecular weight – (mean molecular weight of a mixture), Mav
Using mole fraction:
Using mass fraction:
4) Average molecular weight
ntallcompone
iiav MyMyMyM ...2211
ntallcompone i
i
av M
x
M
x
M
x
M...
1
2
2
1
1
Calculate the average molecular weight of air:
(1) From its approximate molar composition of 79 mol% N2, 21 mol%O2
(2) From its approximate composition by mass of 76.7 wt% N2, 23.3 wt% O2
EXAMPLE 7
84.28avM
7.0 CHEMICAL COMPOSITION
5) Concentration
Solution: a mixture of substance called solutes in another substance called solvent. Solvent: a dominant substance that is present in larger amount and so it dissolves or dilutes the solutes. Solute: a substance that are present in smaller amount and dissolves or distributes in a solvent. It could be more than one solute in a solution. • Particles of solutes are normally distributed uniformly throughout the solvent mass.
• This distribution of solutes in a solvent is known as concentration (conc) of solutes in the solution.
• The conc of solutes could be expressed as mass conc or molar concentration (molarity).
• Mass concentration of a solute A in solution (g/cm3, kg/m3, Ibm/ft3).
• Molarity of a solute A in solution (in mol/L or M).
• ppm & ppb are used to express the con of trace species that is present in a very dilute amount (very small amount) relative to other components in a mixture.
• For a solution in liq or solid phase
Concentration of a substance A in ppm
= mass of a substance a solute A in gmol
106 unit of solution
Concentration of a substance A in ppb
• = mass of a substance a solute A in gmol
109 unit of solution
7.0 CHEMICAL COMPOSITION
6) Parts per Million and Parts per Billion
• Pressure- ratio of a force to the area on which the force acts
• Unit : Ibf/in2 (psi) or dynes/cm2 or N/m2 [pascal (Pa)]
Pabsolute = Pgauge + Patmospheric
Typical value of Patmospheric at sea level are;
1atm = 14.696psi = 760mmHg = 101.325kPa
8.0 PRESSURE
AFP /
9.0 TEMPERATURE
Temperature – a measure of average kinetic energy possessed by the substance molecules.
The relationship to convert a temperature expressed in one unit to another:
15273CTKT o . 67459FTRT oO .
KT81RT O . 32CT81FT oO .
The conversion factor:
The conversion factors refer to temperature intervals, not temperatures.
K1
C1
R1
F1
K1
R81
C1
F81 O
O
OO
O
O
,,.
,.