Sahand University of Technology – Department of Chemical Engineering
Course Title: Mass and Energy Balance (1393.94.2)
Homework Number Two
Offer Date: 22/12/1393
to Return Before: 26/01/1394
1. A gas stream contains 18.0 mole% hexane and the remainder nitrogen. The stream flows
to a condenser, where its temperature is reduced and some of the hexane is liquefied. The
hexane mole fraction in the gas stream leaving the condenser is 0.0500. Liquid hexane
condensate is recovered at a rate of 1.50 L/min.
a) What is the flow rate of the gas stream leaving the condenser in mol/min? (Hint: First
calculate the molar flow rate of the condensate and note that rates at which C6H14 and
N2 enter the unit must equal the total rates at which they leave in the two exit
streams.)
b) What percentage of the hexane entering the condenser is recovered as a liquid?
2. Five pounds of bismuth (MW=200) is heated with one pound of sulfur to form Bi2S3
(MW=514). At the end of the reaction the mass is extracted and the free sulfur recovered
is 5% of the reaction mass. Determine
a) The limiting reactant.
2Bi  3S  Bi 2S 3
b) The percent excess reactant.
c) The percent conversion of sulfur to Bi2S3.
3. Your assistant reports the following experimental data for the exit Orsat gas analysis from
the combustion of a hydrocarbon oil in a furnace: CO2 11.8%; CO 5.0%%; H2 1.5%; O2 1.0%
and N2 by difference. The oil is being burned with 10% excess air. Would you compliment
him on his work?
4. Many chemicals generate emissions of volatile compounds that need to be controlled. In
the process shown in the accompanying figure, the CO in the exhaust is substantially
reduced by separating it from the reactor effluent and recycling the unreacted CO together
with the reactant. Although the product is proprietary, information is provided that the
fresh feed stream contains 40% reactant, 50% inert and 10% CO, and that on reaction 2
moles of reactant yield 2.5 moles of product. Conversion of the reactant to product is 73%
on one pass through the reactor, and 90% for the overall process. The recycle stream
contains 80% CO and 20% reactant. Calculate the ratio of moles of the recycle stream to
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Sahand University of Technology – Department of Chemical Engineering
Course Title: Mass and Energy Balance (1393.94.2)
Homework Number Two
Offer Date: 22/12/1393
to Return Before: 26/01/1394
moles of the product stream.
.
5. Consider the production of Formaldehyde from Methanol.
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CH 3OH  O 2  CH 2O  H 2O
2
Suppose that the percentage conversion is 20% of the Methanol at 30% excess air. Find the
composition of the product.
6. Methanol is produced from synthesis gas by the reaction:
CO  2H 2  CH 3OH
Since only 15 mole percent of the CO entering the reactor is convertor to methanol, a large
recycle of unreacted gases is necessary. The methanol produced is condensed and
separated from the unreacted gases. The ratio of H2 to CO in the fresh-feed gas stream to
the plant is exactly 2, the stoichiometric amount. Calculate the molar flow rates of fresh
feed and recycle required to produce 1000 gal/h of liquid methanol at 70 F when the
density is 49.3 lbm ft 3 (specific gravity = 0.791).
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Sahand University of Technology – Department of Chemical Engineering
Course Title: Mass and Energy Balance (1393.94.2)
Homework Number Two
Offer Date: 22/12/1393
to Return Before: 26/01/1394
7. Two methanol-water mixtures are contained in separate flasks. The first mixture contains
40.0 wt% methanol, and the second contains 70.0 wt% methanol. If 200g of the first
mixture is combined with 150g of the second, what are the mass and composition of the
product?
8. An aqueous solution of sodium hydroxide contains 20.0% NaOH by mass. It is desired to
produce an 8.0% NaOH solution by diluting a stream of the 20% solution with a stream of
pure water. Calculate the ratios (liters H2O/kg feed solution) and (kg product solution/kg
feed solution).
9. A liquid mixture containing 45.0% benzene (B) and 55.0% toluene (T) by mass fed to a
distillation column. A product stream leaving the top of the column (the overhead
product) contains 95.0mole% B, and a bottom product stream contains 8.0% of the
benzene fed to the column (meaning that 92% of the benzene leaves with the overhead
product). The volumetric flow rate of the feed stream is 2000L/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.
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Sahand University of Technology – Department of Chemical Engineering
Course Title: Mass and Energy Balance (1393.94.2)
Homework Number Two
Offer Date: 22/12/1393
to Return Before: 26/01/1394
10. The systems about which balances might be written are shown on the following
representation of the flowchart:
The outer boundary encompasses the entire process and has as input and output streams
all of the streams that enter and leave the process. Two of the interior boundaries
surround individual process units, and the third encloses a stream junction point.
11. The flowchart of a steady-state process to recover crystalline potassium chromate (K2CrO4)
from an aqueous solution of this salt is shown below.
Forty-five hundred kilograms per hour of a solution that is one-third K2CrO4 by mass is
joined by a recycle stream containing 36.4% K2CrO4, and the combined stream is fed into
an evaporator. The concentrated stream leaving the evaporator contains 49.4% K2CrO4:
this stream is fed into a crystallizer in which it is cooled (causing crystals of K 2CrO4 to come
out of solution) and then filtered. The filter cake consists of K2CrO4 crystals and a solution
that contains 36.4% K2CrO4 by mass: the crystals account for 95% of the total mass of the
filter cake. The solution that passes through the filter, also 36.4% K2CrO4, is the recycle
stream.
12. Acrylonitrile is produced in the reaction of propylene, ammonia, and oxygen:
The feed contains 10.0 mole% propylene, 12.0% ammonia, and 78.0% air. A fractional
conversion of 30.0% of the limiting reactant is achieved. Taking 100 mol of feed as a basis,
determine which reactant is limiting, the percentage by which each of the other reactants
is in excess, and the molar amounts of all product gas constituents for a 30% conversion of
the limiting reactant.
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Sahand University of Technology – Department of Chemical Engineering
Course Title: Mass and Energy Balance (1393.94.2)
Homework Number Two
Offer Date: 22/12/1393
to Return Before: 26/01/1394
13. Methane is burned with air in a continuous steady-state combustion reactor to yield a
mixture of carbon monoxide, carbon dioxide, and water. The reactions taking place are:
The feed to the reactor contains 7.80 mole% CH4, 19.4% O2, and 72.8% N2. The percentage
conversion of methane is 90.0%, and the gas leaving the reactor contains 8 mol CO2/mol
CO. Carry out a degree-of-freedom analysis on the process. Then calculate the molar
composition of the product stream using molecular species balances, atomic species
balances, and extents of reaction.
14. Propane is dehydrogenated to form propylene in a catalytic reactor:
The process is to be designed for a 95% overall conversion of propane. The reaction
products are separated into two streams: the first, which contains H2, C3H6, and 0.555% of
the propane that leaves the reactor, is taken off as product: the second stream, which
contains the balance of the unreacted propane and 5% of the propylene in the first
stream, is recycled to the reactor. Calculate the composition of the product, the ratio
(moles recycled)/(mole fresh feed), and the single-pass conversion.
15. Methane is produced in the reaction of carbon dioxide and hydrogen:
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Sahand University of Technology – Department of Chemical Engineering
Course Title: Mass and Energy Balance (1393.94.2)
Homework Number Two
Offer Date: 22/12/1393
to Return Before: 26/01/1394
The fresh feed to the process contains hydrogen, carbon dioxide, and 0.400 mole% inerts
(i). The reactor effluent passes to a condenser that removes essentially all of the methanol
and water formed and none of the reactants or inerts. The latter substances are recycled
to the reactor. To avoid buildup of the inerts in the system, a purge stream is withdrawn
from the recycle.
The feed to the reactor (not the fresh feed to the process) contains 28.0 mole%
CO2, 70.0 mole% H2, and 2.00 mole% inerts. The single-pass conversion of hydrogen is
60.0%. Calculate the molar flow rates and compositions of the fresh feed, the total feed to
the reactor, the recycle stream, and the purge stream for a methanol production rate of
155 kmol CH3OH/h.
16. One hundred mol/h of butane (C4H10) and 5000 mol/h of air are fed into a combustion
reactor. Calculate the percent excess air.
17. A hydrocarbon gas is burned with air. The dry-basis product gas composition is 1.5 mole%
CO, 6.0% CO2, 8.2% O2, and 84.3% N2. There is no atomic oxygen in the fuel. Calculate the
ratio of hydrogen to carbon in the fuel gas and speculate on what the fuel might be. Then
calculate the percent excess air fed to the reactor.
18. Three hundred gallons of a mixture containing 75.0 wt% ethanol and 25% water (mixture
specific gravity=0.877) and a quantity of a 40.0 wt% ethanol- 60% water mixture
(SG=0.952) are blended to produce a mixture containing 60.0 wt% ethanol. The object of
this problem is determine V40, the required volume of the 40% mixture.
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Sahand University of Technology – Department of Chemical Engineering
Course Title: Mass and Energy Balance (1393.94.2)
Homework Number Two
Offer Date: 22/12/1393
to Return Before: 26/01/1394
a) Draw and label a flowchart of the mixing process and do the degree-of-freedom
analysis.
b) Calculate V40.
19. Tank A containing 90% nitrogen is mixed with Tank B containing 30% nitrogen to get Tank
C containing 65% nitrogen. You are asked to determine the ratio of the gas used from Tank
A to that used from Tank B.
20. Consider the following process for recovering NH3 from a gas stream composed of N2 and
NH3. Flowing upward through the process is the gas stream, which can contain NH 3 and
N2 but not solvent S. and flowing downward through the device is a liquid stream which
can contain NH3 and liquid S but not N2.
The weight fraction of NH3 in the gas stream A leaving the process is related to the weight
fraction of NH3 in the liquid stream B leaving the process by the following empirical
relationship: WANH3 = 2WBNH3. Given the data shown in Figure, calculate the flow rates
and compositions of streams A and B.
21. The Figure shows a three-stage separation process. The ratio of P3/D3 is 3, the ratio of
P2/D2 is 1, and the ratio of A to B in stream P2 is 4 to1. Calculate the composition and
percent of each component in stream E. Hint: Although the problem comprises connected
units, application of the standard strategy of problem solving will enable you to solve it
without solving an excessive number of equations simultaneously.
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Sahand University of Technology – Department of Chemical Engineering
Course Title: Mass and Energy Balance (1393.94.2)
Homework Number Two
Offer Date: 22/12/1393
to Return Before: 26/01/1394
22. Sodium hydroxide is usually produced from common salt by electrolysis. The essential
elements of the system are shown in the Figure.
a) What is the percent conversion of salt to sodium hydroxide?
b) How much chlorine gas is produced per pound of product?
c) Per pound of product, how much water must be evaporated in the evaporator?
23. To save energy, stack gas from a furnace is used to dry rice. The flow sheet and known
data are shown in the Figure. What is the amount of recycle gas (in lb mol) per 100 lb of P
if the concentration of water in the gas stream entering the dryer is 5.20%?
24. In the process sketched below, Na2CO3 is produced by the reaction:
Na2S+CaCO3 → Na2CO3+CaS
The reaction is 90% complete on one pass through the reactor and the amount of CaCO3
entering the reactor is 50% in excess of that needed. Calculate on the basis of 1000 lb/h of
fresh feed:
(a) The lb of Na2S recycled, and
(b) The lb of Na2CO3 solution formed per hour.
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