Chapter 3. Process Variables
1. What is a chemical process?
Adapted from Wikipedia:
 A chemical process is a method or means of somehow changing one or
more chemicals.
 In an "engineering" sense, a chemical process is a method intended to be used
in manufacturing to change the composition of chemical(s) or material(s), using
technology similar or related to that used in chemical plants.
 Chemical process may sometimes involve only one step, but often multiple steps,
referred to as unit operations. Chemical processes can be illustrated generally via
process flow diagrams (to be covered in the next Chapter).
Which variables characterize the operations of chemical processes?
Primary Dimensions: Mass, Temperature, Mole
Secondary Dimensions: Volume, Density, Pressure, Flow rate, Mass/Mol fraction,
Molecular Weight, Concentration, etc.
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2. Mass, Volume, Density, etc.
Note that mass of a substance is independent of its temperature & pressure, but its
volume depends on these variables!
i. Density: Mass per unit volume
 = mass/volume = m/V ( kg/m3, g/cm3, lbm/ft3)
ii. Specific Volume: Volume per unit mass
𝑉 = volume/mass = m/V ( m3/kg, cm3/g, ft3/lbm)
iii. Specific Gravity: Ratio of the density of a substance to the density of a reference
substance
SG =  / ref ( Dimensionless)
 Reference substance for solids&liquids is usually water at 4 oC.
𝜌𝐻2𝑂 4𝑜 𝐶 = 1.000 g/cm3 = 1000. kg/m3 = 62.43 lbm/ft3
Ex. SG = 0.6 (20o/4o) means that SG of a substance at 20 oC is 0.6𝜌𝐻2 𝑂 4𝑜 𝐶 .See Ex. 1
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3. Mass and Volumetric Flow Rate
The rate at which a material is transported through a process line.
For an incompressible fluid, e.g. liquid:
• Mass flow rate is constant.
• Volumetric flow rate is constant.
• Velocity will change due to changes in
Flow rate may be expressed as a
Cross Sectional Area.
i. Mass flow rate: Mass/time (𝑚  kg/h, g/s, lbm/s)
𝑚 = 1.5 kg/s means that every second 1.5 kg of fluid pass through the cross-section.
Independent of temperature & pressure!
ii. Volumetric flow rate: Volume/time = Velocity×Area/time ( m3/h, L/s, ft3/s)
𝑉 = 1.5 L/s means that every second 1.5 L of fluid pass through the cross-section.
May change w.r.t. temperature & pressure!
𝑚 = 𝜌𝑉
See Ex. 2
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Ex. 2.(iv) Liquid water flowing through the pipe on the L.H.S.
• Mass flow rate is 5.0 kg/s
• Cross sectional area is 0.250 m2 at the
enterance, and 0.500 m2 at the exit.
Find the volumetric flow rate and velocity at the
enterance and the exit
Volumetric flow rate is constant along the pipe, since
water is assumed to be constant at 1.00 kg/L.
𝑚
5.0 kg/s
𝑉=
=
= 5.0 L/s = 5.0×10-3 m3/s
water 1.00 kg/L
3
𝑣𝑒𝑛𝑡𝑒𝑟𝑎𝑛𝑐𝑒 =
5.0×10−3 𝑚 𝑠
= 0.020 m/s
2
0.250 𝑚
10−3
Animation taken from:
https://www.youtube.com/watch?v=k8IRxT1sM6s
𝑚3
5.0 ×
𝑣𝑒𝑥𝑖𝑡 =
0.500 𝑚2
Mass and Energy Balances - Chapter II
𝑠
= 0.010 𝑚/𝑠
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4. Chemical Composition
i. Variables related to pure substances: Atomic & Molecular Weight, Mole, etc.
Atomic weight (atomic mass unit  amu  u  Da) of an element is the mass of an
atom on a scale that assigns 12C a mass of exactly 12.
Molecular weight of a compound is the sum of the atomic weights of the atoms
that constitute a molecule of the compound.
Atomic oxygen (O) has an atomic weight of 15.9994 u (6 s.f.), while molecular
oxygen (O2) has a molecular weight of 31.9988 u (6 s.f.).
A gram-mole (g-mole, or mol)/lb-moles of a species (atomic or molecular) is the
amount of that species whose mass in grams/lbm is numerically equal to its
molecular weight.
Mass of 1 g-mole O2 is equal to 32 g. Mass of 1 lb-mole O2 is equal to 32 lbm.
One g-mole of any species contains approximately 6.021023 (Avagadro’s
number) molecules of that species.
See Ex. 3
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ii. Variables related to solutions: Mass/mol fraction, Average MW, ppm, etc.
A solution is a homogenous mixture of of two or more components, whether solid,
liquid, or gaseous.
Process streams sometimes contain one substance, but often consists of solutions.
The most fundamental way of characterizing a solution is via mass/mol fraction of its
components.
𝑀𝑎𝑠𝑠 𝑜𝑓 𝐴
Mass fraction: 𝑥𝐴 =
𝑇𝑜𝑡𝑎𝑙 𝑀𝑎𝑠𝑠
𝑀𝑜𝑙𝑒𝑠 𝑜𝑓 𝐴
Mol fraction: 𝑦𝐴 =
𝑇𝑜𝑡𝑎𝑙 𝑀𝑜𝑙𝑒𝑠
≡
≡
𝑘𝑔 𝑔 𝑜𝑟 𝑙𝑏𝑚 𝐴
(used generally for solids&liquids)
𝑘𝑔 𝑔 𝑜𝑟 𝑙𝑏𝑚 𝑇𝑜𝑡𝑎𝑙
𝑘𝑚𝑜𝑙 𝑔−𝑚𝑜𝑙 𝑜𝑟 𝑙𝑏−𝑚𝑜𝑙𝑒𝑠 𝐴
(used generally for gases)
𝑘𝑚𝑜𝑙 𝑔−𝑚𝑜𝑙 𝑜𝑟 𝑙𝑏−𝑚𝑜𝑙𝑒𝑠 𝑇𝑜𝑡𝑎𝑙
The percent by mass and mole percent of A are 100xA and 100yA, respectively.
Ex. 4
Pg. 68
Mass and Energy Balances - Chapter II
Solution on board
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Ex. 5
Pg. 68
Solution on board
Average Molecular Weight of a mixture, denoted with 𝑀 (kg/kmol,lbm/lb-mole), is
the ratio of the mass of a sample of the mixture divided by the molecular weight of
the species.
For a mixture with n species, taking yi as the mol fraction of ith component, and
Mi as the molecular weight of ith component:
𝑛
𝑀 = 𝑦1 𝑀1 + 𝑦2 𝑀2 + ⋯ =
𝑦𝑖 𝑀𝑖
𝑖=1
Or, taking xi as the mass fraction of ith component
1
𝑥1
𝑥2
=
+
+⋯=
𝑀 𝑀1 𝑀2
See Ex. 6
Mass and Energy Balances - Chapter II
𝑛
𝑖=1
𝑥𝑖
𝑀𝑖
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Concentration of a component in a solution is the amount of that component per
unit volume of the solution.
• Mass concentration  m/V ( kg/m3, g/cm3, lbm/ft3)
Note that mass concentration is similar to density, but applies to solutions.
• Molar concentration  mol/V ( kmol/m3, g-mol/cm3, lb-mol/ft3)
If molar concentration is given in g-mol/L, then it is called Molarity.
Ex. 7
3-3.5 pg. 52
Parts per Million (ppm) and Parts per Billion (pbm) are used to express the
concentration of trace species, i.e. species present in very small (minute) amounts.
Especially used for environmentally hazardous species.
ppm (= yi106) and pbm (= yi109) may refer to mass or mol fractions, depending on
how concentration is reported. Recall that it is customary to use mass fractions for
solids&liquids, and mol fractions for gases. See Ex. 8
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