8/31/10
A mixture of methane and air is capable of being
ignited only if the mole % of methane is between 5 and
15 %. A mixture containing 9 mole % methane in air
flowing at a rate of 700 g/hr is to be diluted with pure
air to reduce methane to the lower flammability limit.
Find the mole fraction of O2 in the stream coming out,
n1.
Class 4
Monday, August 30th
9% CH4, 91% air
700 g/h
5% CH4 95 % air
Mixing Station
n1
air (mol/h)
9% CH4, 91% air
700 g/h
Mixing Station
5% CH4
95 % air
air (mol/h)
9% CH4, 91% air
700 g/h
Mixing Station
5% CH4
air (mol/h)
Plan:
a) Find average molecular wt, then moles of methan
b) Mass of methane coming in = mass of methane coming out in stream n1
c)  Moles of methane coming out in stream n1 = 5 % of n1
d) Can then solve for n1, and solve for moles of air in n1
e) Can solve for amount of pure air coming in but don’t need to
f) Find moles of oxygen in air then divide by total moles (n1)
1
8/31/10
9% CH4, 91% air
700 g/h
Mixing Station
5% CH4
air (mol/h)
A mixture containing 9 mole % methane in air flowing at a rate of 700 kg/hr is to be diluted with pure air to reduce methane to the lower flammability limit. The density of methane is lower than that of air. Therefore the density of the stream coming out will be:
a)  Lower than that of the methane stream coming in
b)  Higher than that of the methane stream coming in
c)  The same because of conservation of mass
9% CH4, 91% air
700 g/h
Mixing Station
5% CH4
air (mol/h)
What can be said about mass and mole fractions?
a) The mass fraction of a species is always greater than
the mole fraction of a species
b) The mole fraction of a species is always greater than
the mass fraction of a species
c) In a mixture of gases, the species that has the highest
mole fraction will have the highest mass fraction. d) In a mixture of liquids, the species that has the highest
mole fraction will have the highest mass fraction.
e) The relationship between mole and mass fraction
cannot be determined without additional information. 2
8/31/10
Section 3.4: Pressure
Temperature
Pressure = Force/Area
Therefore, units of:
lbf/in2
dynes/cm2
T(K) = T(oC) + 273.15
T (oF) = (9/5)[T(oC)] + 32
T(oR) = T(oF) + 460
oC
N/m2 (= Pa)
0
100
K
273
373
oF
oR
32
212
492
672
100K
180oF
Some Standard Conversions
1 atm = 1.01325 bars = 14.7 lbf/in2
= 760 mm Hg (at 0oC)
= 33.9 ft H2O (at 0oC)
= 1.01325 x 105 Pa
= 101.325 kPa
Sections 4 - 4.3a
Fundamentals of Material Balances
delta T:
100oC
180oR
delta oF or delta oR
-------------------------- = 1.8
delta oC or delta K
Batch or Semi-Batch Processing: All of the feed is
charged at the beginning and all of the product is
removed at some time later
Transient or unsteady state processes in which
process variables change with time
• Process Classification
• General Balance Equation
Continuous Processing:
The inputs and outputs flow continuously throughout
the duration of the process
• Flow Charts
Steady state processes in which process variables do
not change with time
3
8/31/10
General Balance Equation
Input + Generation - Output - Consumption = Accumulation
Input (enters through system boundaries)
Generation (produced within the system)
Output (leaves through system boundaries)
Consumption (consumed within the system)
Accumulation (buildup with the system)
Methane is a component of both the input and output
streams of a continuous process. When the mass flow rates
are measured, it is found that the mass flow rate in is less
than the mass flow rate out. Which part(s) of the general
balance equation could you keep in, assuming the
measurements are correct and the process does not leak?
I. GenerationII. Consumption III. Accumulation
a) I only
b) II and III only
c) I and III only
d) I and II only
e) I, II and III
For a continuous process at steady state, which term in
the general balance equation drops out?
a) Input
b) Generation
c) Output
d) Consumption
e) Accumulation
For a continuous process with no reaction, which term(s) drop
out?
I. Input
II. Generation
III. Output IV. Consumption V. Accumulation
a) I and II
b) II and III
c) II and IV
d) II, III and IV
e) I and III
4
8/31/10
Method of Solution (Approach) for Material Balance
Problems
1.  Draw a schematic for the process (flowchart) and label
all streams
2. Select a Basis (often given for you)
3. Write balances for the total mass (or moles) and for
each component, noting independent equations. For nonreactive processes up to N material balances may be
written, where N is the number of independent species
involved in the process.
4.  Solve the resulting system of equations
Careful: You can only write a total mole balance if there is
no reaction or if there is no change in total moles with the
reaction!
A distillation column separates components
based on their volatility. One or more
streams are fed to the column and two or
more product streams emerge, with the
overhead stream rich in the more volatile
substance. Consider a case where one
stream that is 3 weight % B and the rest C
and another stream that is 5300 kg/hr
containing only A and B are fed to a column.
Three product streams emerge: the
overhead is 100 % A. The bottom stream is
60 % B by weight and the rest C. The middle
stream, which is 1200 kg/h is 70 % A by
weight and the rest B and C.
Consider a case where one stream that is 3 wt %
B and the rest C and another stream that is 5300
kg/hr containing only A and B are fed to a column.
Three product streams emerge: the overhead is
100 % A. The bottom stream is 60 wt % B and the
rest C. The middle stream, which is 1200 kg/h is
70 wt % A and the rest B and C.
How many unknowns are there?
a) 4
c) 6
b) 5
d) 7
5
8/31/10
Consider a case where one stream that is 3 wt % B and the
rest C and another stream that is 5300 kg/hr containing
only A and B are fed to a column. Three product streams
emerge: the overhead is 100 % A. The bottom stream is 60
wt % B and the rest C. The middle stream, which is 1200
kg/h is 70 wt % A and the rest B and C.
How many material balances
may be written?
a) 1
c) 3
b) 2
d) 4
Consider a case where one stream that is 3 wt %
B and the rest C and another stream that is 5300
kg/hr containing only A and B are fed to a column.
Three product streams emerge: the overhead is
100 % A. The bottom stream is 60 wt % B and the
rest C. The middle stream, which is 1200 kg/h is
70 wt % A and the rest B and C.
How many unknowns must be
specified?
a)  2
c) 4
b) 3
d) 5
6