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Water enters a tank at a rate of 4.00 kg/s and is
withdrawn at a rate of 2 kg/s. The tank is initially half
full. What should the general balance be?
Class 5
a) Input = Output
b) Input – Output = Accumulation
c) Input – Output – Consumption = 0
d) Input = Accumulation
Wednesday, September 1st
Procedure for Material Balance Calculations (pp. 101 & 102)
• Select a Basis of Calculation
• Draw a Flowchart; Identify known entities and label
unknowns as variables
• Degree of freedom analysis
• Express problem statement in terms of labeled variables
• Work in terms of moles or mass; not volume. Use
consistent units
• Write Material Balance Equations (total and N-1 individual
species or N species)
• Solve the Governing System of Equations
• Calculate requested quantities
• Scale the problem as appropriate
Basis of Calculation
• Select an amount (mass or moles) or a mass or molar
flow rate of a stream or a stream component as a Basis
of Calculation; all unknown variables are then
considered to be consistent with this basis.
• If a stream amount or flow rate is given in a problem
statement, it is usually most convenient to use this
quantity as a Basis of Calculations
• If no stream amounts or flow rates are known, assume
one as a Basis of Calculation. Choose an amount of a
stream with a known composition!
• If mass fractions are known – choose total mass as the
Basis
• If mole fractions are known, choose total moles as the
Basis
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9/2/10
Degree of freedom Analysis
# of unknowns
- # of equations we can write
= degrees of freedom
DOF = 0
DOF > 0
DOF < 0
system solvable
need more info to solve
overspecified
One thousand kilograms per hour of a mixture containing
equal parts by mass of methanol and water is distilled.
Product streams leave the top and the bottom of distillation
column. The flow rate of the bottom stream is measured and
found to be 673 kg/h, and the overhead stream is analyzed
and found to contain 96.0 wt% methanol.
a) Draw and label flowchart and do degree of freedom
analysis.
Equations we can write
Material balances (one for each independent species)
Process specifications
Physical properties and laws
Physical constraints
Energy balance
Can also assume a basis if no stream is given
• Select a Basis of Calculation
• Draw a Flowchart; Identify known entities and label
unknowns as variables
• Do degree of freedom analysis
YAY!!!!
One thousand kilograms per hour of a mixture containing equal parts by mass
of methanol and water is distilled. Product streams leave the top and the bottom
of distillation column. The flow rate of the bottom stream is measured and found
to be 673 kg/h, and the overhead stream is analyzed and found to contain 96.0
wt% methanol.
b) Calculate mass and mole fractions of methanol and molar
flow rates of methanol and water in the bottom product
stream.
• Express problem statement in terms of labeled variables
Calculate mass and mole fractions of methanol and
molar flow rates of methanol and water in the bottom
product stream.
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9/2/10
• Write Material Balance Equations
• Solve the Governing System of Equations
• Calculate requested quantities
A stream of air that is saturated with acetone enters a
condenser where 80 % of the acetone is condensed. The
flow rate into the condenser is 100 g/min. Consider air to be
one species. Find the flow rate of the gas stream leaving
the condenser and the mole fractions of air and acetone in
this stream. How many degrees of freedom are there?
a) 0
b) 1
c) 2
d) 3
Calculate mass and mole fractions
of methanol and molar flow rates of
methanol and water in the bottom
product stream.
A stream of air that is 10 mole % acetone enters a
condenser where 80 % of the acetone is condensed. The
flow rate into the condenser is 100 g/min. Consider air to be
one species. Find the flow rate of the gas stream leaving
the condenser and the mole fractions of air and acetone in
this stream. How many degrees of freedom are there?
a) 0
b) 1
c) 2
d) 3
An aqueous solution of HCl contains 15 % HCl by mass.
It is desired to produce a 5% HCl solution by diluting a
stream of the 15 % solution with pure water. Calculate
liters of H2O/kg feed solution and kg product solution/kg
feed solution.
Do same problem assuming that you need to make 100
kg of the 5 % solution.
Plan:
Change flow in to moles.
Do overall balance and acetone balance.
Find mole fractions in gas stream from condenser.
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9/2/10
An aqueous solution of HCl contains 15 % HCl by mass. It is
desired to produce a 5% HCl solution by diluting a stream of the
15 % solution with pure water. Calculate liters of H2O/kg feed
solution and kg product solution/kg feed solution.
An aqueous solution of HCl contains 15 % HCl by mass. It is
desired to produce a 5% HCl solution by diluting a stream of the
15 % solution with pure water. Calculate liters of H2O added/kg
feed solution and kg product solution/kg feed solution.
How many DOF’s?
a) 0
b) 1
c) 2
d) 3
An aqueous solution of HCl contains 15 % HCl by mass.
It is desired to produce a 5% HCl solution by diluting a
stream of the 15 % solution with pure water.
Do same problem assuming that you need to make 100
kg of the 5 % solution.
4