Material and Energy Balance Concept Inventory
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Problem A. Consider the process system depicted below with five process streams (A, B, C, etc).
C
mol/s
A
mol/s
process unit
D
mol/s
B
mol/s
E
mol/s
1. If the system above for Problem A is at steady state and no chemical reactions are
occurring within the system, which one of the following statements is true about the
molar flow rates?
a. Stream A is equal to Stream C.
b. Streams A plus B are equal to Stream C.
c. Streams A plus B are equal to Streams C plus D.
d. Steams A plus B are equal to Streams C plus D plus E.
e. None of the above.
2. If the system above for Problem A was just being started up, which one of the following
statements is true about the molar flow rates?
a. Stream A is equal to Stream C.
b. Streams A plus B are equal to Stream C.
c. Streams A plus B are equal to Streams C plus D.
d. Streams A plus B are equal to Streams C plus D plus E.
e. None of the above.
3. If the system above for Problem A is at steady state and the following chemical reaction
for compounds S, T, U, V, and W is occurring within the system:
1S + 1T

1U + 1V + 1W
which one of the statements below is true about the molar flow rates?
a. Stream A is equal to Stream C.
b. Streams A plus B are equal to Stream C.
c. Streams A plus B are equal to Streams C plus D.
d. Streams A plus B are equal to Streams C plus D plus E.
e. None of the above.
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Problem B. As shown in the diagrams below, a piece of paper is burned in a bell jar that is
isolated from its surroundings. Paper and air exist in State 1. The paper is ignited and allowed
to burn as shown in State 2. Ashes are left as shown in State 3.
(1) paper
(2) fire
(3) ashes
4. If everything has been weighed in each state of Problem B, what conclusion can you
draw?
a. State 1 would have the larger weight.
b. State 2 would have the larger weight.
c. State 3 would have the larger weight.
d. None of the above.
Problem C. Seven logs are burning in the fireplace of a house in winter with the chimney open.
All the windows and doors in the house are tightly shut. Answer the following two questions
about the burning process.
5. If the system boundary is drawn around the fireplace, the burning operation is what kind
of process?
a. Continuous process.
b. Batch process.
c. Semi-batch process.
d. Semi-continuous process.
e. None of them.
6. If the system boundary is drawn around the house, the burning operation is what kind of
process?
a. Continuous process.
b. Batch process.
c. Semi-batch process.
d. Semi-continuous process.
e. None of them.
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Problem D. Consider the system below. The motor driven stirrer delivers work to the liquid in the
vessel. This work is transformed into internal energy with attendant rise in temperature. Heat is
transferred through the walls of the container to the surroundings.
work in
heat out
7. Is the above system for Problem D an open system?
a. yes
b. no
c. cannot tell
8. Is the above system for Problem D an isolated system?
a. yes
b. no
c. cannot tell
Problem E. Suppose that a situation is reached at which the temperature of the stirred liquid in the
diagram of Problem D attains constancy and heat is being transferred to the surroundings at a constant
rate. If this constant temperature within the system is at 40ºC, and the boiling point of the liquid
(hydrogen fluoride) is 19.4ºC, answer the following questions:
9. In Problem E, are there any changes in the mass inventory for the system as a result of the high
temperature?
a. yes
b. no
c. cannot tell
10. Is the system of Problem E at steady state with respect to the materials in the system?
a. yes
b. no
c. cannot tell
11. Is the system of Problem E at steady state with respect to the total energy in the system?
a. yes
b. no
c. cannot tell
12. If the system for Problem E is assumed to be at steady state, does this imply that the system is at
equilibrium?
a. yes
b. no
c. cannot tell
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Problem F. An engineering student is conducting an experiment using a beaker containing one
liter of alcohol and a beaker containing one liter of water. The alcohol and water are poured into
a four-liter beaker to form the solution mixture. The student writes the following relationships in
her lab notebook about the experiment:
Eq. 1:
Vsoln
=
Valc
Eq. 2:
ρsolnVsoln
=
ρalcValc
Eq. 3:
Vsoln
=
usoln Asoln t
Eq. 4:
Vsoln
=
Valc
+
+
Vwat
+
ρwatVwat
Vwat
+
ΔVmixing
where V is volume; ρ is density;
u is velocity; A is area; t is time.
13. Which of the above relationships for Problem F are true for the experimental process?
a. Equations (1) and (2)
b. Equations (1) and (3)
c. Equations (2) and (4)
d. Equations (1), (2), (3) and (4)
e. None of the above equations.
14. The student conducts a similar mixing experiment for Problem F but uses sodium
hydroxide pellets and water, both of which are at ambient conditions. Which one of the
following statements is true immediately after the solution is created?
a. The solution is at ambient conditions.
b. The temperature of the solution is greater than ambient.
c. The temperature of the solution is less than ambient.
d. None of the above.
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Problem G. Consider the system depicted below of process streams (A, B, C, etc.) and process
units. The whole system operates at steady state, and chemical reactions may or may not be
occurring.
15 mol/s
30 mol/s
A
B
C
I
K
H
5 mol/s
J
some process units
30 mol/s
D
5 mol/s
E
F
? mol/s
G
5 mol/s
15. The number of moles per second in Stream F of Problem G is:
a. 10 mol/s
b. 25 mol/s
c. 15 mol/s
d. 20 mol/s
e. none of the above
16. In Problem G, which one of the following pairs represents the bypass stream and purge
stream, respectively?
a. Streams G and K.
b. Streams K and H
c. Streams I and K
d. Streams K and I
e. Streams H and K.
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Problem H. Consider the reactor system depicted below with a feed and product stream. The
system operates adiabatically and at steady state, and a highly exothermic reaction is occurring.
feed
mol/s
reactor unit
product
mol/s
17. In Problem H, which one of the following statements is true about the outlet temperature
of the product stream?
a. It is equal to the inlet temperature.
b. It is less than the inlet temperature.
c. It is greater than the inlet temperature.
d. None of the above statements is true.
18. When solving the energy balance for the reactor in Problem H, the molar enthalpies of
each process stream are calculated relative to selected reference conditions, at which the
reference enthalpies are set arbitrarily to zero for convenience? Which one of the
following selections of reference temperatures and pressures can be used in the energy
balance for the reactor?
a. The product-stream temperature and pressure for each chemical compound.
b. 25ºC and 1 atm for each chemical compound.
c. The feed-stream temperature and pressure for each chemical compound.
d. 25ºC and 1 atm for the atoms that make up the chemical compounds.
e. Any temperature and pressure because the reference enthalpies cancel each other
out.
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Problem I. An engineering student is confronted with solving the following problem. One
hundred g-moles per hour of pure ethane gas is burned with 50% excess air. The percentage
conversion of the ethane is 80 mol%. The only products of the combustion reaction are carbon
dioxide and water. What are the total and chemical component flow rates of the exhaust stream?
The student has created the following conceptual model, which is correct:
Process Diagram
Assumptions
TF  ?
PF  ?
F
1.
2.
3.
4.
TE  ?
nF  100 mol / h
PE  ?
xF , ET  1.0
Continuous process
Steady state
Air is just O2 and N2
T’s and P’s not needed
nE  ?
xE , ET  ?
E
reactor
xE ,O 2  ?
Given:
xE , N 2  ?
TA  ?
80 mol% conversion of ET
50% excess air
xE ,CD  ?
PA  ?
nA  ?
xE ,WA  ?
A
Find:
xA,O 2  0.21
nE and nE , j ' s in g-mol/h
xA, N 2  0.79
2 C2H6 + 7 O2  4 CO2 + 6 H2O
Reaction 1:
The student has decided to model the combustion operation using mole balances. He has
developed the following mathematical model:
(1)
n F  n A
–
n E
(2)
n F
–
n E , ET
–
(3)
0.21n A
–
n E ,O 2
–
(4)
0.79 n A
–
n E ,N 2
(5)
–
n E ,CD
+
(6)
–
n E ,W A
+
=
n E , ET  n E ,O 2  n E , N 2  n E ,CD  n E ,W A
n E
(7)
1
4 R1
6 R
1
0
=
0
=
0
=
0
=
0
=
0
(8)
(n F  n E , ET ) / n F  0.80
(9)
 7 mol O2 

0.21 n A  1.50 n F 
2
mol
ET


where
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2 R1
7 R
=
R1 is the extent of reaction for the combustion in g-rxns/h.
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19. In Problem I, which one of the equations in the above mathematical model based on
mole balances is incorrect?
a. Equation 4
b. Equation 1
c. Equation 7
d. Equation 3
e. All equations are correct as written.
20. For the proposed mathematical model based on mole balances in Problem I above, the
degrees of freedom is zero, when it should be one. Which non-material balance equation
must be dropped from the mathematical model?
a. Equation 9
b. Equation 1
c. Equation 7
d. Equation 8
Another student has decided to model the combustion operation in Problem I using atom
balances instead of mole balances. She has developed the following mathematical model:
(1)
2 n F
–
2 n E , ET
–
1 n E ,CD
=
0
(2)
6 nF
–
6 n E , ET
–
n E ,W A
=
0
(3)
2 (0.21n A )
–
2 n E , O 2
–
2 n E ,CD
=
0
(4)
2 (0.79 n A )
–
2 n E , N 2
=
0
(5)
n E
=
n E , ET  n E ,O 2  n E , N 2  n E ,CD  n E ,W A
(6)
(n F  n E , ET ) / n F  0.80
(7)
 7 mol O2 

0.21 n A  1.50 n F 
2
mol
ET


–
1n E ,W A
21. In Problem I, which one of the equations in the above mathematical model based on
atom balances is incorrect?
a. Equation 2
b. Equation 4
c. Equation 1
d. Equation 6
e. All equations are correct as written.
22. In Problem I, what is the most likely equation to be used as a “check” on the numerical
answers that would be calculated for the unknown variables using the mathematical
model based on atom balances?
a. The total mole balance.
b. The mixture equation for Stream E (i.e., Equation 5)
c. The total mass balance.
d. None of these.
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Problem J. The temperature-composition (TXY) diagram for the binary system of chemical
components A and B is given below. A gas process stream containing 50 mole percent of chemical
component A is being cooled at a constant pressure of 2 atm.
2 atm
Pressure =
a
T1
T2
f
T3
b
g
T4
h
c
d
T5
j
e
T6
0
0.1
0.2
0.3
XA
0.4
0.5
ZA
0.6
0.7
0.8
0.9
1
YA
Mole Fraction of Component A
23. For the binary mixture in Problem J, is Compound B the more volatile component?
a. yes
b. no
c. cannot tell
24. For the binary mixture in Problem J, the temperature labeled as T3 is called what?
a. The super-heated vapor temperature.
b. The bubble-point temperature.
c. The sub-cooled liquid temperature.
d. The dew-point temperature.
e. None of the above.
25. For the binary mixture in Problem J, what is the vapor fraction for the temperature labeled as T5?
a. The vapor fraction is 1.
b. The vapor fraction is 0.5.
c. The vapor fraction is 0.87.
d. The vapor fraction is 0.
e. None of the above.
26. For the binary mixture in Problem J, the vapor fraction for the temperature labeled as T4 is
defined by which of the following relationships.
a. Line segment cd divided by line segment bd .
b.
c.
d.
e.
f.
Line segment gc divided by line segment gh .
( T4 – T5 ) divide by ( T3 – T5 ).
( ZA – XA ) divide by (YA – XA ).
Both Options (a) and (c) above.
Both Options (b) and (d) above.
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Problem K. A process stream was heated in the laboratory to change it from a sub-cooled liquid to a
superheated vapor. The heating operation is depicted in the diagram below.
130
d
120
110
100
c
90
b
80
70
a
60
0
10
20
30
40
50
60
70
80
90
100
Enthalpy Change as the Stream is heated, kJ/mol
27. Is the process stream in Problem K a multi-component mixture of chemical compounds?
a. yes
b. no
c. cannot tell
28. What line segment in Problem K represents the latent heat of vaporization?
a. Line segment cd .
b. Line segment bcd .
c. Line segment bc .
d. Line segment ab .
e. None of the above.
29. Does Line segment cd represent a sensible molar enthalpy change?
a. yes
b. no
c. cannot tell
Problem L. An engineering student has conducted an experiment in the laboratory to investigate the
relationship between variables X and Y. In her laboratory notebook, she has written Y  a X b to model
that relationship, where a and b are constants. Her notebook contains 20 experimental data points.
30. She should plot what against what, in order to verify that a linear relationship exists?
a. Y versus X.
b. log Y versus X.
c. log Y versus log X.
d. Y versus log X.
e. None of the above.
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