Material and Energy Balance Concept Inventory
Hanyak’s
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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.
Total moles in and out must balance for steady state and no reaction.
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.
Since unsteady state, you can not judge which option might apply.
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.
For a steady-state system with reaction, total moles may not be conserved.
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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.
Total mass (or weight) is conserved; thus, States 1, 2, and 3 must be equal in weight.
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 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.
The fireplace system boundary is semi-continuous. Air in, carbon depleted, and hot gas out.
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.
The house system boundary is semi-batch. No air in, carbon depleted, and hot gas out.
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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
No material in or out. Only energy in and out.
c. cannot tell
8. Is the above system for Problem D an isolated system?
a. yes
b. no
Energy in and out. An isolated system has no mat’l and energy transfer.
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
It is a batch system with respect to the material.
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
It is a batch system with respect to the material.
c. cannot tell
11. Is the system of Problem E at steady state with respect to the total energy in the system?
a. yes
Work in equals heat out.
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
The vapor and liquid phases are in equilibrium provided the
b. no
temperature and pressure of the system are constant with time.
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.
Equation 2 is the material balance, and Equation 4 accounts for the mixing effect.
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.
Because of the positive heat of solution, the temperature of the solution rises.
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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
E
F
? mol/s
5 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
By material balance for Streams D, H, and E and for Streams E, F, I, and K.
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.
Stream H by passes some process units. Stream K is a purge, because it allows chemical
compounds not to build up in Recycle I.
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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.
The exothermic reaction generates heat in the system, and thus increases the temperature.
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.
Only atoms are conserved during chemical reactions, not chemical compounds.
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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
The total mole balance must have a reaction term, since
b. Equation 1
moles may not be conserved during chemical reactions.
c. Equation 7
Eqn 1:
nF  nA  nE  1 RI  0
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
Equation 7 is not linear independent. Algebraically,
d. Equation 8
combining Eqs. 2 to 7 will give you the corrected Eq. 1.
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
–
nE ,WA
=
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
Equation 2 is the atom balance for the hydrogen atom.
b. Equation 4
The third term needs a 2, since 2 hydrogen atoms exist
c. Equation 1
in a molecule of H2O.
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.
Total mass is conserved during chemical reaction.
d. None of these.
Eq. 5 is part of math model, thus it is not a check.
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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
The more volatile component is the one with the lower boiling point,
c. cannot tell
which is Component A as shown on the TXY diagram.
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.
It is the temperature at which the first drop of liquid is
e. None of the above.
formed when a gas is cooled to the sat’d vapor curve.
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.
A vapor fraction of zero occurs at the bubble-point
e. None of the above.
temperature on the saturated liquid curve.
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 ).
Options (b) and (d) are the same thing. They
Both Options (a) and (c) above.
represent the combined total and Component A
Both Options (b) and (d) above.
material balances; that is, the reverse lever rule.
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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
Line Segment (bc) is the latent enthalpy change. It is horizontal
b. no
for a pure compound, but has a slope for a multi-component mixture.
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 .
Line Segment (ab) is the sensible enthalpy change for the liquid.
d. Line segment ab .
Thus, Line Segment (bc) is for when the liquid is boiling.
e. None of the above.
29. Does Line segment cd represent a sensible molar enthalpy change?
a. Yes
Line Segment (cd) is the sensible enthalpy change for the gas.
b. No
Line Segment (ab) is the sensible enthalpy change for the liquid.
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.
Rewrite model as log Y = log a + b log X,
d. Y versus log X.
a straight line relations for log Y versus log X.
e. None of the above.
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