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INTRODUCTION TO MATERIAL BALANCES
155:201
9/9/08
Most problems you will solve in CBE 201 will look something like this:
A liquid mixture containing 45.0 wt% benzene (B) and 55.0% toluene (T) is fed to a distillation column
operating at steady state. Product streams emerge from the top and bottom of the column. The top
product stream contains 95.0 wt% B, and the bottom product stream contains 8% of the benzene fed to
the column. The volumetric flow rate of the feed stream is 2000 liters/h and the specific gravity of the
feed mixture is 0.872. Determine the mass flow rate of the overhead product stream and the mass flow
rate and composition (mass fractions) of the bottom product stream.
You can take two approaches to solving such problems:
1. Start writing and solving equations until all of the required quantities have been determined.
2. Draw and label a flow chart, outline a solution strategy, and
then
write equations and solve for the
required quantities.
Although the first approach will work for simple problems, and may initially seem easier, it will be
difficult or impossible to solve more complicated problems this way. Therefore, we will use the second
approach, even for easier problems, so that you’ll be used to it when the problems get harder.
STEPS IN A PROBLEM SOLUTION
Drawing and labeling a flow chart
The labeled flowchart for the above problem looks like this:
•
Process unit (e.g. distillation column) is represented by a box.
•
Input and output streams are represented by lines indicating direction of flow.
•
It is important that your flow chart be
completely
labeled. This means that you can write an
expression for the flowrate (continuous process) or amount (batch process) of each species in every
stream in terms of the numbers and variables written on the flow chart. To do this, you will need to
show one of the following for each stream:
o
Total mass or mass flow rate and mass fraction of each component
o
Total moles or molar flow rate and mole fraction of each component
o
Mass, mass flow rate, moles or molar flow rate of each component
•
Units must be shown for every number or variable.
•
If numerical values are unknown for any quantity, use an algebraic symbol and enclose its units in
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 Spring '09
 Buettner
 20%, 35%, Mass flow rate, 40%, 21 mole, 55.0%

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