Example 3.
3 Separation Process
A feed stream is flowing at a mass flow rate of 100 kg/min. The stream contains 20 kg/min
NaOH and 80 kg/min of water. The distillate flows at 40 kg/min and contains 5 kg/min
NaOH. Determine bottom stream mass flow rate and composition.
Solution Known quantities: Feed and distillate streams are fully specified (i.e., mass flow
rate and compositions are known).
Find: Bottom stream flow rate and compositions.
Analysis: The process-labeled flowchart is shown
Basis: 100 kg/min of the feed stream.
Total mass balance: 𝒎𝟏
𝟏
Component mass balance (NaOH):
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Dr.Firas Salim Mohammed Al-Ghulami
There are two simple linear algebraic equations with two unknowns (𝒎𝟑 , 𝒎𝑵𝒂𝑶𝑯 ),
solving for 𝒎𝟑 and 𝒎𝑵𝒂𝑶𝑯 :
Example 3.5 Concentrated Lemon Juice
The initial amount of pressed Lemon Juice contains 10% of total solids. It is desired to
increase to 20% of total solids by evaporation. The resulting concentrated juice consists of
20% total solids. Calculate the quantity of water that must be removed.
Solution Known quantities: Pressed juice mass and concentration, concentrated juice
solid concentration.
Find: The quantity of water to be removed.
Analysis: The process flow sheet is shown in
Basis: 100 kg of pressed juice.
0.10 × 100 kg = 0.2 × m3
m3 = 50 kg
Amount of water evaporated = 100 − 50 = 50 kg 61
Example 3.7 Methanol–Water Mixtures
Two methanol–water mixtures are mixed in a Stirred Tank. The first mixture contains 40.0
wt% methanol and the second one contains 70.0 wt% methanol. If 200 g/s of the first
mixture is combined with 150 g/s of the second one, what are the mass and composition of
the product?
Solution
Known quantities: Two methanol/water
mixtures with known compositions
are mixed together.
Find: The mass and composition of the product.
Analysis: The process-labeled flowchart is shown in
Basis: 200 g/s of the 40 wt% methanol (i.e., stream 1).
Component balance (methanol):
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Dr.Firas Salim Mohammed Al-Ghulami
Example 3.8 Synthesis of Strawberry Jam
To make strawberry jam, strawberries containing 15 wt% solids and 85 wt% water are
crushed. The crushed strawberries and sugar are mixed in a 4/5 mass ratio and the mixture is
heated to evaporate water. The residue contains one-third water by mass. Calculate the
amounts of strawberries needed to make 100 g of jam, and of evaporated water.
Solution Known quantities: Strawberries contain 15 wt% solids and 85 wt% water.
Find: Amount of strawberries needed to make 100 g of jam.
Analysis: The process-labeled flowchart is shown in
Basis: 100 g of jam is to be produced; m3 = 100 g.
Assumption: Steady state,
no reaction.
We have three components
(Solid, Water, and Sugar) so
three independent equations
can be written.
A relationship is given, which
can be expressed as 63
Dr.Firas Salim Mohammed Al-Ghulami
Material Balance Component balance (solid):
Relation:
Component balance (water):
Overall total mass balance:
Substituting m2 in terms of m1 using the relation,
Substituting m4 in terms of m1 using water mass balance equation,
Rearranging and solving for m1,
Substitute m1 = 47.6 g in the following equation:
Substitute m1 = 47.6 g and m4 = 7.1 g in the overall material balance equation:
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Dr.Firas Salim Mohammed Al-Ghulami
Example 3.13 Extraction
Hexane is used to extract seed oil from cleaned cotton seed. Raw cotton seed consists of
15 wt% cellulose material, 35 wt% protein meal, and 50 wt% oil. Calculate the composition
of oil extract obtained when 3 kg hexane is used per 1 kg mass raw seeds.
Known quantities: Raw seed composition, hexane/raw seed mass ratio.
Find: Composition of oil extract.
Analysis: The process-labeled flowchart is shown
Basis: 100 kg of raw cotton seeds
Component balance:
Protein meal: 0.35(100 kg) = m3
Cellulose: 0.15(100 kg) = m4
Oil: 0.50 (100 kg) = Xoil,5 m5
Hexane: 300 kg = (1 − Xoil,5) m5
Total mass balance:
100 kg + 300 kg = 35 kg + 15 kg + m5
Mass of the extracted oil = m5 = 350 kg 0.5(100 kg) = xoil,5 350 Xoil,5 = 0.143 65
Example 3.16 Evaporation Chamber
Three input streams are fed into an evaporation chamber to produce an output stream with
the desired composition. Liquid water, fed at a rate of 20.0 cm3/min, air (21 mol% O2, the
balance N2), and pure oxygen, fed at one-fifth of the molar flow rate of air stream. The output
gas is analyzed and is found to contain 1.5 mol% water. Draw and label a flowchart of the
process and calculate all unknown stream variables.
Known quantities: Feed stream composition and product water composition.
Find: All unknown stream variables.
Analysis: The process-labeled flowchart is shown
Basis: 20 Cm3/min of liquid water
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Relation:
Pure oxygen molar flow rate is one-fifth of the molar flow rate of air (stream 2):
Material Balance
Component balance (water):
Total overall mole balance:
Component balance (N2):
Oxygen mole fraction in product stream:
Check your answer against oxygen component balance:
After substitution: Substitute known quantities in the
component balance equation for oxygen:
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