ChE Calculations

MOLARITY, MOLALITY, CONCENTRATION
1. How many mg/L are equivalent to 1.2% solution of a substance in water?

2. You purchased a tank with a volume of 2.1f 3. You pump the tank out and add first 20lb
of carbon dioxide and then 10lb of nitrogen. What are their molarities?
3. Find the molarity of a 50% triethanomine (C6H5NO3) solution if its density is 1.05kg/L.
4. Concentrated HCl has a density of 1.24 g/mL and has a molarity of 16M. Determine its
molality.
5. A solution in water contains 1.704kg of nitric acid per kg of water, and the solution has a
specific gravity of 1.382 at 20˚C. How many kg of nitric acid per cubic meter of solution
at 20˚C are there?
6. In the production of a drug having a molecular weight of 192, the exit stream from a
reactor flows at a rate of 10.5L/min. The drug concentration is 41.2% in water, and the
specific gravity of the solution is 1.024. Calculate the concentration of the drug (kg drug
per L solution) in the exit stream and the flow rate of the drug in kmol/min.
7. A solution was prepared by mixing equal masses of ethanol (SG=0.79) and water.
Assuming volume is additive, determine the specific gravity of the resulting solution.
8. Given that a nitric acid solution contains 1.704 kg HNO 3 / kg H2O, and has a specific
gravity of 1.382 at 20˚C, determine the following:
a) lbs HNO3 / lb solution
b) Molarity
c) Molality
9. A 0.5M aqueous solution of sulfuric acid flows into a process unit at a rate of
1.25m3/min. The specific gravity of the solution is 1.03. Calculate the mass concentration
of sulfuric acid in kg/m3 and the mass flowrate of sulfuric acid in kg/s.
10. 27lb of chlorine gas is used for treating 750,000gal of water each day. The chlorine used
up by the microorganisms in the water is measured to be 2.6mg/L. What is the residual
or excess chlorine concentration in the treated water?
GAUGE AND ABSOLUTE PRESSURE

1. A pressure gauge on a Welder’s tank gives a reading of 22.4psig. The barometric
pressure is 28.6inHg. Calculate the absolute pressure in the tank in psi, inHg, Pa, and f
H2O.
2. What is the gauge pressure at a depth of 4.5mi below the surface of the sea if the water
temperature averages 60˚F? Give your answer in psi. The specific gravity of sea water at
the given temperature is 1.042 and is assumed to be independent of pressure.
3. The pressure gauge on a tank of carbon dioxide used to fill water soda bottles reads
51psig. At the same time the barometer reads 28inHg. What is the absolute pressure in
the tank in psia?
4. In a double effect evaporator plant, the second effect is maintained under vacuum of
745torr. Find the absolute pressure in bar.
5. A manometer uses kerosene, SG=0.82, as a fluid. A reading of 5in of a manometer is
equivalent to how many mmHg?
6. A solvent storage tank 15m high contains styrene (C 8H8, SG=0.909). A pressure gauge
fixed at the bottom of the tank is to be used to determine the level of styrene.
Determine the gauge pressure when the tank is full of styrene.
7. What will the gauge pressure be at the bottom of the tank if a 15m high tank contains
10m hexane (SG = 0.659) and 4m water?
8. A large storage tank contains oil having a density of 917kg/m 3. The tank is 3.66m tall and
is open to the atmosphere where the barometric reading is in atm. The tank is filled with
oil to a depth of 3.05m and also contains 0.61m of water. Calculate the pressure exerted
at the bottom of the tank.
9. The diameter and height of a vertical cylindrical tank are 5f and 6f respectively. It is full
up to 75% height with carbon tetrachloride, the density of which is 1.6kg/L. Find its mass
in kg and the pressure exerted at the bottom of the tank.
10. The great Boston Molasses flood occurred on January 15, 1919. In it, 2.3M gallons of
crude molasses flowed from a 30f high storage tank that raptured, killing 21 people and
injuring 150. The estimated specific gravity of crude molasses in the tank is 1.4. What
was the mass of molasses in the tank in lb and the pressure at the bottom of the tank in
psi?
MASS AND MOLAR COMPOSITIONS

1. Calculate the mass and mole fractions of the respective components in NaClO 3.
2. Given that a nitric acid solution contains 1.704 kg HNO 3 / kg H2O, and has a specific
gravity of 1.382 at 20˚C, determine the mass percent of HNO 3.
3. The specific gravity of a solution of KOH at 15˚C is 1.0824 and contains 0.813lb KOH per
gal of solution. What are the mass fractions of potassium hydroxide and water in the
solution?
4. Concentrated HCl has a density of 1.24 g/mL and has a molarity of 16M. Determine the
mass and mole percent of HCl.
5. You purchased a tank with a volume of 2.1f 3. You pump the tank out and add first 20lb
of carbon dioxide and then 10lb of nitrogen. What is the molar composition of the gas
mixture in the tank?
6. A gas mixture contains 40lbs oxygen, 25lbs sulfur dioxide, and 30lbs sulfur trioxide. What
is the molar composition of the mixture?
7. The feed to an ammonia synthesis reactor contains 25% nitrogen and the balance
hydrogen. The flowrate of the stream is 3000kg/hr. Calculate the rate of flow of nitrogen
into the reactor in kg/hr.
8. A mixture of gases is analyzed and found to contain the following: 12% carbon dioxide,
6% carbon monoxide, 27.3% methane, 9.9% hydrogen, and 44.8% nitrogen. What is the
mass in lb of 3lbmol of this mixture?
9. Cracked gas from a petroleum refinery has the following composition by volume: 45%
methane, 10% ethane, 25% ethylene, 7% propane, 8% propylene, and 5% butane. What
is the average molecular weight of the cracked gas and the mass percent of propane?
10. A gaseous fuel is referred to analyze on a mole basis: 20% methane, 5% ethane, and the
remainder carbon dioxide. Calculate the following:
a) Analysis in mass percent
b) Analysis in volume percent
c) Mole fraction of each element
d) Average molecular weight
DIMENSIONAL HOMOGENEITY
1. Prove that the following equation for flow through a rectangular weir is dimensionally
consistent where q is the volumetric flowrate, L is the crest height, h is the water head in
f, and g is the acceleration due to gravity.
2 g ¿0.5
q=0.415(L−0.2 h) h1.5 ¿
2. The thermal conductivity k of a liquid metal is projected via the empirical equation:
B
T
k =A
Where k is in W/mK and A & B are constants. What are the units of A and B?
3. In 1916 Nusselt derived a theoretical relation for predicting the coefficient of heat
transfer between a pure saturated vapor and a colder surface:
3 2 1
k ρ gγ 4
h=0.943 ( Lμ ∆ T)
Where h is the mean heat transfer coefficient in BTU/hr-f2-R, k is the thermal
conductivity in BTU/hr-f-R, ρ is the density in lbm/f3, g is the acceleration of gravity,
4.17x108f/hr2, γ is the enthalpy change of evaporation in BTU/lb, L is the length of
tube in f, and ΔT is the temperature difference in R. What are the units of the constant
0.943?
4. The density of a certain liquid is given an equation of the following form:
ρ= ( A+ BT ) ecP
Where ρ is the density in g/cm3, T is the temperature in K, and P is the pressure in atm.
a) If the equation is dimensionally consistent, what are the units of A, B, and C?
b) In the units above, A=1.096, B=0.00086, and C=0.000953. Find A, B, and C if the
density is expressed in lb/f3, T in R, and P in psi.
5. The specific heat of toluene is given by the following equation:
−2
Cp=20.869+5.293 ×10 T
Where Cp is in BTU/lbmol-˚F and T is in ˚F. Express the equation in cal, mol, and K.
6. The heat capacity of sulfuric acid in a handbook has the units J/mol-K and is given by the
relation:
−1
Cp=139.1+1.56 ×10 T
Modify the formula so that the resulting expression yields the heat capacity with the
associated units of BTU/lbmol-R with T in R.
7. Vapor pressure of benzene in the temperature range of 280.65K (7.5˚C) to 377.15K
(104˚C)can be calculated using the Antoine’s Equation:
1211
lnP=6.9057−
T +220.8
Where P is the vapor pressure in torr and T is the temperature in ˚C. Convert the
equation to SI units.
8. Your handbook showed that the microchip etching roughly follows the relation:
d=16.2 ( 1−e−0.021t )
With t<200s and d is in micrometers.
a) What units are associated with the numbers 16.2 and 0.021?
b) Convert the relation so that d will be in inches and t is in minutes.
9. A particular equation is as follows:
ft
( )
D ( ft )=4+ 0.5t ( s ) +7 x 2
s
a) What are the units of 4, 0.5, and 7 for the equation to be dimensionally
homogenous?
b) If all distance units are to be in meters and al time units are to be in minutes,
what is the new equation relating the distance to t and x?
10. The velocity in a pipe in turbulent flow is expressed by the following equation:
1
τ 2
u=k () ρ
Where τ is the shear stress in N/m2 at the pipe wall, ρ is the density of the fluid in kg/m 3,
u is the velocity in m/s, and k is a coefficient. You are asked to modify the equation so
that the shear stress can be introduced in the units of τ which are lbf/f2, and the density
ρ for which the units are lbm/f3 so that the velocity u comes out in the units of f/s. Give
the final equation in terms of u, τ, and ρ so a reader will know that American
Engineering units are involved in the equation.
MIXING
1. Ammonia is a gas for which reliable analytical methods are available to determine its
concentration in other gases. To measure flow in a natural gas pipeline, pure ammonia
gas is injected into the pipeline at a constant rate of 72.3kg/min for 12min. Five miles
downstream from the injection point, the steady-state ammonia concentration is found
to be 0.382% by weight. The gas upstream from the point of ammonia injection contains
no measurable ammonia. How many kg of natural gas are flowing through the pipeline
per hour?
2. Water pollution in the Hudson River has claimed considerable attention, especially
pollution from sewage outlets and industrial wastes. To determine accurately how much
effluent enters the river is quite difficult because to catch and weigh the material is
impossible, weirs are hard to construct, and so on. One suggestion that has been offered
is to add a tracer of Br ion to a given sewage stream, let it mix well, and sample the
sewage stream afer it mixes. On one test of the proposal you add 10lb/hr of NaBr for
24hrs to a sewage stream with essentially no Br in it. Somewhat downstream of the
introduction point a sampling of the sewage stream shows 0.012% NaBr. The sewage
density is 60.3lb/f3 and the river water density is 62.4lb/f 3. What is the flowrate of the
sewage in lb/min?
3. A stream containing 25% ethanol in water is to be diluted with a second stream
containing 10% ethanol in water to form a product solution containing 17% ethanol.
Calculate the ratio of the mass flow of the solution that consists of 17% ethanol to that
with 25% ethanol.
4. A manufacturer of briquettes has a contract to make briquettes for barbecuing that are
guaranteed to not contain over 10% moisture and 10% ash. The basic material used has
this analysis: 12.4% moisture, 16.6% volatile combustible matter, 57.5% carbon, and
13.5% ash. To meet the specifications at their limits the manufacturer plans to mix with
the base material a certain amount of petroleum coke that has this analysis: 8.2% VCM,
88.7% C, and 3.1% moisture. How much petroleum coke must be added per 100lb of the
base material?
5. It is desired to make a nitrating acid containing 47.5% nitric acid and 48% sulfuric acid by
mixing concentrate sulfuric and nitric acid solutions. If 91.5% nitric acid is used, calculate
the % sulfuric acid solution required and the amount of each solution to make 15 metric
tons of the nitrating acid.
6. A water solution containing 10% acetic acid is added to a water solution containing 30%
acetic acid flowing at a rate of 20kg/min. The product P of the combination leaves at a
rate of 100kg/min. What is the composition of P?
7. Salted butter is produced in a continuous butter-making machine by adding slurry of salt
to butter. The slurry contains 60% of salt and 40% of water by weight. If the final
composition of the butter is to be 15.8% moisture and 1.4% salt, on a basis of 100kg of
produced butter, estimate the original percent moisture content of butter prior to
salting, assuming original butter contains no salt.
8. It is required to make 100kg mixed acid containing 60% sulfuric acid, 32% nitric acid, and
8% water by blending the spent acid containing 11.3% nitric acid, 44.4% sulfuric acid,
and 44.3% water, aqueous 90% nitric acid solution, and aqueous 98% sulfuric acid
solution. All percentages are by mass. Calculate the quantity of the concentrated sulfuric
acid required for blending.
9. A liquid adhesive consists of a polymer dissolved in a solvent. The amount of polymer in
the solution is important to the application. An adhesive dealer receives an order for
3000lb of an adhesive solution containing 13% polymer by weight. On hand are 500lb of
10% solution and very large quantities of 20% solution and pure solvent. Calculate the
weight of each that must be blended together to fill this order. Use all of the 10%
solution.
10. A polymer blend is to be formed from three compounds whose compositions and
approximate formula are listed in the following table. Determine the percentages of
each compound A, B, and C to be introduced into the mixture to achieve the desired
composition.
Composition % at A % at B % at C % at Product
(CH4)x 25 35 55 30
(C2H6)x 35 20 40 30
(C3H8)x 40 45 5 40
FILTRATION
1. Whole milk contains around 4.5% fat. Skimmed milk is prepared by the removal of some
of the fat from whole milk. The skimmed milk is found to contain 0.1% fat. It is desired to
prepare100kg of skimmed milk. Assuming that the fat only was removed to make the
skimmed milk, calculate the mass of the removed fat.
2. A saturated solution of salt is made by agitating an excess of the salt in water and then
filtering off the solution. If 1kg of water will dissolve 0.2kg of salt, and if 0.5kg of the
solution will adhere to ever kg of dry salt, calculate:
a. How much solution can be filtered off when 500kg of water is mixed with 250kg of
salt?
b. How much salt can be removed if the remaining wet salt were thoroughly dried?
3. Saturated solution of a salt is made by agitating 600kg salt in 1200kg water. The salt is
soluble to the extent of 0.25kg per kg water. On filtration, 0.4kg of the solution adheres
to every kg of undissolved salt. Calculate the weight of the filtrate and the kg of dry salt
recovered on the drying of the wet filter cake.
DRYING
1. A cereal product containing 55% water is made at a rate of 500kg/hr. You need to dry the
product so that it contains only 30% water. How much water has to be evaporated per
hour?
2. Sludge is wet solids that result from the processing in municipal sewage systems. The
sludge has to be dried before it can be composted or otherwise handled. If a sludge
containing 70% water and 30% solids is passed through a dryer, and the resulting
product contains 25% water, how much water is evaporated per ton of sludge sent to the
dryer?
3. Water pulp containing 85% water is dried until it contains 8% water. Water is removed @
Php400/ton of product. Calculate the drying cost per 100lb water removed.
4. Wet sugar that contains 20% water is sent through a dyer in which 75% of the water
content is removed. On a basis of 100kg feed, calculate the mass fraction of dry sugar in
the wet sugar that leaves the dryer and the amount of water removed per kg of wet
sugar leaving the dryer.
5. A wet paper pulp is found to contain 71% water. Afer drying it is found that 60% of the
original water content has been removed. Calculate the composition of the dried pulp
and the mass of water removed per kilogram of wet pulp.
6. A dairy produces casein which when wet contains 23.7% moisture. They sell this for
$8/100lb. They also dry this casein to produce a product containing 10% moisture. Their
drying costs are $0.8/100lb water removed. What should be the selling price of the dried
casein to maintain the same margin of profit?
7. Raw potatoes are composed of about 25% starch and 75% water. Before frying, raw
potatoes are peeled and then washed. Assume that 8% of the weight of the potatoes is
lost in the peeling. Potatoes are then dried to 7% total water content. What is the mass
of dried potatoes produced from each 100kg of raw potatoes?
8. Wet t-shirts are being dried from a moisture content of 45% (wet basis) to a moisture
content of 25% (dry basis) by passing hot air through a drier. The fresh air contains 2%
water and the outlet air contains 15% water. Part of the outlet air is recycled to the drier,
and the air that enters the drier is 5% water. Calculate the recycle ratio.
EVAPORATION
1. In a textile mill, an evaporator system concentrates weak liquor containing 4% caustic
soda by mass to produce lye containing 25% solids. Calculate the evaporation of water
per 100kg feed in the evaporator.
2. A multiple-stage evaporator concentrates a weak NaOH solution from 3% to18% and
processes 2 tons of feed per day. How much product is made per day? How much water
is evaporated per day?
3. It is desired to prepare a sweetened concentrated orange juice. The initial pressed juice
contains 5% solids, and it is desired to increase its amount to 10% by evaporation.
Calculate the quantity of water that must be removed based on 100kg of initial pressed
juice.
4. Wet sugar that contains 1/5 water by mass is conveyed through an evaporator in which
85% of the entering water is vaporize. Taking a basis of 100kg feed, calculate the mass
fraction of water in the wet sugar leaving the evaporator, and the mas ratio of the vapor
to the product.
5. A triple effect evaporator is fed with 1000lbs of a 5% salt solution to be concentrated to
40% solution. If the amount of water evaporated from the 1 st effect is 375lbs and from
the 2nd effect is 1.5 times that of from the third effect, calculate the weight of water
evaporated from the latter two effects.
6. Seawater containing 3.5% salt passes through a series of 10 evaporators. Roughly equal
quantities of water are vaporized in each of the 10 units and then condensed and
combined to obtain a stream of fresh water. The brine leaving each evaporator but the
tenth is fed to the next evaporator. The brine leaving the tenth evaporator contains 5%
salt. Calculate the % yield of fresh water from the process and the weight percent of salt
in the solution leaving the fourth evaporator.
DISTILLATION
1. In a typical distillation column, a 35% ethanol solution is separated into a distillate with
85% ethanol and a waste stream containing 5% ethanol. Determine the ratio of the
distillate to the feed as well as the ratio of the distillate to the waste.
2. A liquid mixture of benzene and toluene contains 55% benzene by mass. The mixture is
to be partially evaporated to yield a vapor containing 85% benzene and a residual liquid
containing 10.6% benzene by mass. Calculate the mass of the distillate and bottom
streams.
3. A 1000kg feed containing 10% ethanol in water is sent to a distilling column. 10% of this
feed vaporizes in the distillate with an ethanol concentration of 60%. Calculate the
composition of the bottom stream and the weight of alcohol lost there.
4. A liquid mixture containing 45% benzene and 55% toluene by mass is fed to a distillation
column. A product stream leaving the top of the column contains 95% benzene by mole,
and a bottom product stream contains 8% of the benzene fed to the column. The
volumetric flowrate of the feed stream is 2000L/hr 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 of the bottom product stream.
5. Dilute alcohol from fermenting vats contain 11.15% ethanol. The distillate contains 95%
ethanol whole the bottom contains 0.5% ethanol. As distillation proceeds, a side stream
containing 40% ethanol is removed. The total recovery of ethanol in the distillate and in
the side stream is 96.5%. On the basis of 1000kg of feed, calculate the amounts of the
bottom, distillate, and side stream.
6. A feed stream to a distillation column, flowing at a rate of 1200kg/hr, contains a gaseous
mixture of ethanol, ethanol, and propanol. The feed contains 20% methanol. The
distillate contains 90% of the methanol and 60% of the ethanol contained. All of the
400kg/hr of propanol fed to the process ends in the bottom of the column. Calculate the
bottom stream mass flowrate.
7. A hydrocarbon feed consisting of a mixture of 20% propane, 30% propylene, 20%
isopentane and 30% pentane is fractioned at a rate of 1000kg/hr into a distillate that
contains all the propane and 78% of the isopentane in the feed. The mole fraction of
propylene in the distillate is 0.378. The bottom stream contains all the pentane fed to
the unit. Determine the flowrate of the bottom streams.
8. In a gas separation plant, the feed to the process has the following constituents:
Component Mole %
C3 1.9
i-C4 51.5
n-C4 46
C5+ 0.6
The flow rate is 5804kmol/day. If the overhead and bottom streams leaving the process
have the following compositions, what are the flow rates of the overhead and bottom
streams in kmol/day?
Component Mole % at Overhead Mole % at Bottom
C3 3.4 0
i-C4 91.34 1.04
n-C4 5.26 97.6
C5+ 0 1.36
9. In a distillation column, there are 2 input streams, A and B. Stream B is fed at a rate of
1000kg/hr, containing equal masses of benzene and toluene. The mass flowrate of
stream A is unknown, but it is known that it contains equimolar benzene and methanol.
Three output streams are observed. The topmost output stream contains only methanol.
The middle output stream flowing at a rate of 1000kg/hr, contains 70% benzene, 20%
toluene, and the balance methanol by mole. The bottom output stream contains only
benzene and toluene, and it is determined that it contains 33% toluene by mole.
Calculate the mass flow rate of stream A, the topmost output stream, and the bottom
output stream.
10. A liquid mixture containing 30% benzene, 25% toluene, and the balance xylene is fed to
a distillation column. The bottoms product contains 98% xylene and no benzene, and
96% of the xylene in the feed is recovered in this stream. The overhead product is fed to
a second column. The overhead product from the second stream contains 97% of the
benzene in the feed to this column. The composition of this stream is 94% benzene and
the balance toluene. Calculate the percentage of the toluene in the process feed that
emerges in the bottom product of the second column.
EXTRACTION
1. Liquid extraction is an operation used to separate the components of a liquid mixture of
two or more species. In the simplest case, the mixture contains two components: a
solute (A) and a liquid solvent (B). The mixture is contacted in an agitated vessel with a
second liquid solvent (C) that has two key properties: A dissolves in it, and B is
immiscible or nearly immiscible with it. Some of the A transfers from B to C, and then
the B-rich phase (the raffinate) and the C-rich phase (the extract) separate from each
other in a settling tank. If the raffinate is then contacted with fresh C in another stage,
more A will be transferred from it. This process can be repeated until essentially all of
the A has been extracted from the B. In a given process, acetic acid is extracted from a
mixture of acetic acid and water into hexanol, a liquid immiscible with water. 400g/min
of an 11.5% acetic acid solution is contacted with fresh hexanol, creating a raffinate
containing 0.5% acetic acid, and an extract phase containing 9.5% acetic acid. Calculate
the mass flow rates of hexanol, raffinate, and extract.
2. A tannery extracts mangrove bark containing 4% moisture, 37% tannin, and 23% soluble
non-tannin material. The residue removed from the extraction tank contains 62%
moisture, 2.8% tannin, and 0.9% soluble non-tannin material. What percentage of the
tannin in the original bark remains unextracted in the residue?
3. Salt in crude oil must be removed before the oil undergoes processing in a refinery. The
crude oil is fed in a extraction unit where fresh water fed to the unit mixes with the oil
and dissolves a portion of the salt contained in the oil. The product oil, containing some
salt but no water, being less dense than water, can be removed at the top of the washer.
If the spent wash water contains 15% salt and the crude oil contains 5% salt, determine
the concentration of salt in the washed oil product if the ratio of initial crude oil to water
used is 4 is to 1.
CRYSTALLIZATION
1. The solubility of sodium bicarbonate is 9.6g per 100g water @ 293.15K, and 16.4g per
100g water @ 330.15K. If a saturated solution of sodium bicarbonate @ 330.15K is
cooled to 293.15K, what percentage of the dissolved salt crystallizes out?
2. If 100g of sodium sulfate are dissolved in 200g of water and the solution is cooled until
100g of decahydrates crystallize out, find the composition of the mother liquor.
3. A chemist attempts to prepare some very pure crystals of borax (sodium tetraborate
decahydrate) by dissolving 100g sodium tetraborate in 200g of water. He the carefully
cools the solution until some borax particles crystallize out. Calculate the amount of
sodium tetraborate removed in the crystals per 100g of total initial solution, if the
residual solution @ 328.15K afer the crystals were removed contains 12.4% sodium
tetraborate.
4. 1000kg of a 40% magnesium sulfate solution is sent to a crystallizer where it is cooled to
293.15K. The wet crop, magnesium sulfate heptahydrate, plus adhering solution is later
sent to a drier producing anhydrous magnesium sulfate. If the solubility of magnesium
sulfate @ 293.15K is 5kg per 100kg solution, and if 10% of the mother liquor adheres to
the crop, calculate the amount of anhydrous magnesium sulfate produced and the
amount of water removed from the dryer.
5. The solubility of barium nitrate at 100˚C is 34g/100g of water and at 0˚C is 5g/100g of
water. If you start with 100g of barium nitrate and make a saturated solution with water
at 100˚C, how much water is required? Additionally, if the saturated solution is cooled to
0˚C, how much barium nitrate is precipitated out of the solution? The precipitated
crystals carry along with them on their surface 4g of water per 100g of crystals.
6. A saturated solution of sodium carbonate at 30˚C is sent to a crystallizer where it is
cooled to 12˚C. The stream containing the saturated solution is discarded as waste, while
the other stream containing decahydrate crystals with adhering solution is sent to a drier
to produce anhydrous sodium carbonate. With 1000kg of saturated solution at 30˚C and
5% of the mother liquor adhering to the crystals, calculate the weight of anhydrous
crystals exiting the drier.
Temperature 0 10 20 30
(˚C)
Solubility
7 12.5 21.5 38.8
(g/100g H2O)
7. A tank holds 10,000kg of a saturated solution of sodium bicarbonate at 60˚C. You want
to crystallize 500kg of sodium bicarbonate without any accompanying water from this
solution. To what temperature must the solution be cooled?
Temperature (˚C) Solubility (g NaHCO3/100g H2O)
60 16.4
50 14.45
40 12.7
30 11.1
20 9.6
10 8.15
8. One ton of a 30% solution of sodium carbonate in water is slowly cooled to 20˚C. During
the cooling, 10% of the water originally present is evaporated. The carbonate
precipitating out forms decahydrate crystals. If the solubility of anhydrous sodium
carbonate at 20˚C is 2.15lb/100lb of water, what weight of decahydrate crystallizes out?
9. 1000kg of a 30% solution of sodium carbonate in water is cooled slowly to 293K. During
cooling, a portion of water is evaporated and removed. 700kg of decahydrate crystals
are formed in this process. What percent of total water in the feed is evaporated? The
solubility of anhydrous sodium carbonate at 293K is 21.5kg/100kg water.
10. A water solution contains 60% Na2S2O2 together with 1% soluble impurity. Upon cooling
to 10˚C, pentahydrates crystallize out. The solubility of this hydrate of 1.4lb
pentahydrate/lb free water. The crystals removed carry as adhering solution 0,06lb
solution/lb crystals. When dried to remove the remaining water from the solution, the
final dry pentahydrate crystal must not contain more than 0.1% impurity. To meet this
specification, the original solution, before cooling, is further diluted with water. On the
basis of 100lb of the original solution, calculate the amount of water added before
cooling, and the % recovery of the Na2S2O2 in the dried hydrated crystals.
MATERIAL BALANCE WITHOUT REACTION (MULTIPLE UNITS)

1. In the feedstock preparation section of a plant manufacturing natural gasoline,
isopentane is removed from butane-free gasoline. A feed containing 80% pentane and
20% isopentane is fed to an isopentane extraction column where two product streams
emerge, one containing pure isopentane and the other containing pure pentane. Part of
the butane-free feed bypasses the tower and is mixed with the pentane product stream,
hence creating a final product containing 90% pentane and 10% isopentane. What
fraction of the butane-free gasoline is passed through the isopentane tower?
2. A stream containing 5.15% chromium is contained in the wastewater from a metal
finishing plant. The wastewater stream is fed to a treatment unit that removes 95% of
the chromium in the feed and recycles it to the plant. The residual liquid stream leaving
the treatment unit is sent to a waste lagoon. The treatment unit has a maximum
capacity of 4500kg/hr. If wastewater leaves the finishing plant at a rate higher than the
capacity of the treatment unit, the excess bypasses the unit and combines with the
residual liquid leaving the unit, and the combined stream goes to the waste lagoon.
Assuming that wastewater leaves the plant at a rate of 6000kg/hr, calculate the flowrate
of liquid to the waste lagoon, and the mass fraction of Cr in this liquid.
3. Fresh feed containing 20% KCl enters an evaporation process, wherein it is first mixed
with a recycle containing 60% KCl before entering the evaporator, producing a gross feed
which contains 40% KCl. Upon evaporation, 60kg of water is released to the atmosphere,
while the product, containing 60% KCl, is split into a product stream and a recycle
stream. Calculate the recycle ratio.
4. Fresh air containing 4% water vapor is to be cooled and dehumidified to a water content
of 1.7% water. A stream of fresh air is combined with a recycle stream of previously
dehumidified air and passed through the cooler. The blended stream entering the unit
contains 2.3% water. In the air conditioning unit, some of the water in the feed stream is
condensed and removed as liquid. A fraction of the dehumidified air leaving the cooler is
recycled and the remainder is delivered to a room. Taking 100mol of dehumidified air
delivered to the room as a basis of calculations, calculate the moles of fresh feed, moles
of water condensed, and moles of dehumidified air recycled.
5. 4,500kg/hr of a solution that is 1/3 potassium chromate by mass is joined by a recycle
stream containing 36.4% potassium chromate, and the combined stream is fed into an
evaporator. The concentrated stream leaving the evaporator contains 49.4% potassium
chromate. This stream is fed into a crystallizer in which it is cooled and then filtered. The
filter cake consists of potassium chromate crystals and a solution that contains 36.4%
potassium chromate 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% potassium chromate, is the
recycle stream. Calculate the rate of evaporation, the rate of production of crystalline
potassium chromate, the feed rates that the evaporator and the crystallizer must be
designed to handle, and the recycle ratio.
6. To save energy, stack gas from a furnace, containing 4.73% water, is used to dry rice from
75% to 95% rice. The exiting wet gas contains 9.31% water, and is split into two streams.
One is recycled back to the inlet air, and the other is purged. What is the recycle ratio if
the gas entering the dryer contains 5.2% water?
7. The fresh feed to a process is 10,000lb/hr of a 40% aqueous NaOH solution. The fresh
feed is combined with the recycled filtrate from a crystallizer, and fed to the evaporator
where water is removed to produce a 50% NaOH solution, which in turn is fed to the
crystallizer. The crystallizer produces a filter cake that is 95% NaOH crystals and 5%
solution that itself contains 45% NaOH. The filtrate also contains 45% NaOH.
a. Determine the flowrate of water removed by the evaporator, and the recycle rate for
this process.
b. Assume that the same production rate of NaOH flakes occurs, but the filtrate is not
recycled. What would the total feed rate of 40% NaOH have to be then? Assume that
the product solution from the evaporator still contains 50% NaOH.
8. A material containing 75% water and 25% solid is fed to a granulator at a rate of
4000kg/hr. The feed is premixed in the granulator with recycled product from a dryer,
which follows the granulator, to reduce the water concentration of the overall material
fed into the granulator to 50% water and 50% solid. The product that leaves the dryer is
16.7% water. In the dryer, air is passed over the solid being dried. The air entering the
dryer contains 3% water by weight, and the air leaving the dryer contains 6% water by
weight. Determine the recycle ratio and the rate of air flow to the dryer on a dry basis.
9. 10,000kg/hr of a 20% potassium nitrate solution is mixed with a stream of recycled
mother liquor before being fed to an evaporator. The evaporator temperature is 300
degrees, and the exiting stream contains 50% potassium nitrate. It is then fed to a
crystallizer, where it is cooled to 100 degrees in order to crystallize the potassium
nitrate. The crystals contain 96% potassium nitrate, while the recycled mother liquor has
a solubility of 0.6kg potassium nitrate per kg water. Determine the mass flowrate of the
recycle stream.
10. Blue vitriol, copper sulfate pentahydrate (249.55g/mol), is obtained from an evaporator-
crystallizer process from an aqueous solution of this salt. The fresh feed to the process
contains 30% copper sulfate. The wet crop contains 15kg of the crystal per kg of
saturated solution from the crystallizer operating at 0˚C. The mother liquor obtained
from the crystallizer is recycled to join the fresh feed. In the evaporator, the combined
feed loses 50% of its water content. The evaporator has a capacity of 100kg/s. Solubility
of copper sulfate (159.55g/mol) at 0˚C is 14.3kg in 100kg water. Calculate the recycle
ratio, the composition of the solution leaving the evaporator, and the weight of
anhydrous crystals formed.
MATERIAL BALANCE WITH REACTION (SINGLE UNIT)

1. The chlorination of methane occurs by the following reaction:
CH 4 +Cl2 →CH 3 Cl+ HCl
You are asked to determine the product composition if the conversion of the limiting
reactant is 67% and the feed composition in mole percent is 40% methane, 50%
chlorine, and 10% nitrogen.
2. Phenol can be manufactured by reacting chlorobenzene with NaOH.
C6 H 5 Cl+ NaOH →C 6 H 5 OH + NaCl
To produce 1000kg of phenol, 1200kg of NaOH and 1320kg of chlorobenzene are used.
Determine the % excess, % conversion, and the % yield.
3. Formaldehyde is produced by oxidizing methane using air. A side reaction is the
combustion of methane to form carbon dioxide. The reactions are as follows:
CH 4 +O2 → HCHO+ H 2 O
CH 4 +2O 2 →CO 2 +2 H 2 O
100mol/hr of methane at 25˚Cis fed to a reactor, and there is a 30% conversion to
formaldehyde. 20% of the remaining methane participates in the side reaction to form
carbon dioxide. Air at 100˚C is fed at the rate of 500mol/hr. What is the molar flow rate
of methane and water vapor in the product stream?
4. A bioreactor is a vessel in which biological reactions are carried out involving enzymes,
microorganisms, and/or plant and animal cells. In the anaerobic fermentation of grain,
the yeast Saccharomyces Cerevisiae digests glucose from plants to form the products
ethanol and propenoic acid by the following overall reactions:
C6 H 12 O6 →2 C 2 H 5 OH +2 CO2
C6 H 12 O6 →2 C 2 H 3 CO2 H+ 2 H 2 O
In a process, a tank is initially charged with 4000kg of a 12% solution of glucose in water.
Afer fermentation, 120kg of carbon dioxide have been produced and 90kg of unreacted
glucose remain in the broth. What are the weight percentages of ethanol and propenoic
acid in the broth at the end of the fermentation process? Assume that none of the
glucose is retained by the microorganisms.
5. Formaldehyde is produced industrially by the catalytic oxidation of methanol by the
following reaction:
1
CH 3 OH + O2 → HCHO + H 2 O
2
Unfortunately, under the conditions used to produce formaldehyde at a profitable rate, a
significant portion of the formaldehyde can react with oxygen to produce carbon
monoxide and water:
1
HCHO+ O2 →CO+ H 2 O
2
Assume that methanol and twice the stoichiometric amount of air needed for complete
oxidation of the methanol are fed to the reactor, 90% conversion of the methanol
results, and a 75% yield of formaldehyde occurs. Determine the composition of the
product gas leaving the reactor.
6. Consider a continuous, steady-state process in which the following two reactions take
place:
C6 H 12+ 6 H 2 O →6 CO +12 H 2
C6 H 12+ H 2 → C6 H 14
In the process 250 moles of hexene and 800 moles of water are fed into the reactor each
hour. The yield of hydrogen is 40% and the selectivity of the first reaction compared to
the second reaction is 12. Calculate the molar flow rates of all five components in the
output stream.
7. Semenov described some of the chemistry of alkyl chlorides. The two reactions of
interest for this problem are:
Cl2 +C 3 H 6 →C 3 H 5 Cl+ HCl
Cl2 +C 3 H 6 →C 3 H 6 Cl 2
The species recovered afer the reaction takes place for some time are listed in the given
table:
Species Cl2 C3 H 6 C3H5Cl C3H6Cl2 HCl
Moles 141 651 4.6 24.5 4.6
Based on the product distribution in the table, assuming that the feed consisted of only
chlorine and propene, calculate the moles of chlorine and propene that entered the
reactor, the fractional conversion of propene, the selectivity of allyl chloride (C 3H5Cl)
relative to propylene chloride (C3H6Cl2), the % yield of allyl chloride expressed in grams
of allyl chloride per gram of propene fed to the reactor, and the extent of the two
reactions.
8. Two well-known gas phase reactions take place in the dehydration of ethane:
C2 H 6 → C 2 H 4 + H 2
C2 H 6 + H 2 → 2 CH 4
Given the product distribution measured in the gas phase reaction of ethane as follows:
Component ethane ethylene hydrogen Methane
Mole % 27 33 13 27
Calculate the % conversion of ethane, the selectivity of ethylene relative to methane, the
yield of ethylene expressed in kmol ethylene produced per kmol ethane, and the extent
of the two reactions.
9. Ethanol is produced by the hydration of ethylene according to the following reaction:
C2 H 4 + H 2 O→ C2 H 5 OH
However, some of the products are converted in the following side reaction:
C2 H 5 OH → ( C 2 H 5 )2 O+ H 2 O
The feed to the reactor contains ethylene, steam, and nitrogen. The effluent analysis is
as follows:
Component C2 H 4 H2 O C2H5OH (C2H5)2O N2
Mole % 39.12 45.08 2.95 0.27 12.58
Calculate the % conversion of ethylene, % yield of ethanol, and maximum fractional
conversion of the excess reactant.
10. Chlorobenzene (C6H5Cl), an important solvent and intermediate in the production of
many other chemicals, is produced by bubbling chlorine gas through liquid benzene in
the presence of ferric chloride catalyst. In an undesired reaction, the product is further
chlorinated to dichlorobenzene, and in a third reaction the dichlorobenzene is
chlorinated to trichlorobenzene. The feed to a chlorination reactor consists of essentially
pure benzene and a technical grade of chlorine gas (98% by weight, the balance being
gaseous impurities with an average molecular weight of 25). The liquid output from the
reactor contains 65% benzene, 32% chlorobenzene, 2.5% dichlorobenzene, and 0.5%
trichlorobenzene. The gaseous output contains only HCl and the impurities that entered
with the chlorine. Calculate the percentage by which benzene is fed in excess, the
fractional conversion of benzene, the fractional yield of chlorobenzene, and the mass
ratio of the gas feed to the liquid feed.
MATERIAL BALANCE WITH REACTION (MULTIPLE UNITS)

1. Alkyl halides are used as an alkylating agent in various chemical transformations. The
alkyl halide ethyl chloride can be prepared by the following chemical reaction:
2C 2 H 6+Cl 2 → 2 C2 H 5 Cl +H 2
In a reaction process, fresh ethane and chlorine gas and recycled ethane are combined
and fed into the reactor. A test shows that if 100% excess chlorine is mixed with ethane,
a single-pass optimal conversion of 60% results, and of the ethane that reacts, all is
converted to products and none goes into undesired products. You are asked to calculate
the fresh feed concentrations required for operation, and the moles of ethyl chloride
produced per mole of ethane in the fresh feed.
2. The reaction of ethyl-tetrabromide with zinc dust proceeds as follows:
C2 H 2 Br 4 +2 Zn →C 2 H 2+2 ZnBr2
Based on one pass through the reactor, 80% of the ethyl-tetrabromide is reacted and the
remainder recycled. On the basis of 1000kg of ethyl-tetrabromide fed to the reactor per
hour, calculate how much acetylene is produced per hour in kg, the rate of recycle in
kg/hr, the feed rate necessary for Zn to be 20% in excess, and the mole ratio of ZnBr 2 to
C2H2 in the final products.
3. Pure propane is dehydrogenated catalytically in a continuous process to obtain propene.
All of the hydrogen formed is separated from the reactor exit gas with no loss of
hydrocarbon. The hydrocarbon mixture is then fractionated to give a product stream
containing 88% propene and 12% propane and a recycle stream containing 70% propane
and 30% propene. The single pass conversion from the reactor is 25%, and 1000kg of
fresh propane is fed per hour. Calculate the mass flow rates of the product and recycle
streams per hour.
4. In a simplified process to make ethylene dichloride (C 2H4Cl2) from ethylene and chlorine
gas, 90% conversion of ethylene occurs on each pass through the reactor. The overhead
stream from the separator contains 98% of the chlorine entering the separator, 92% of
the entering ethylene, and 0.1% of the entering ethylene dichloride. 5% of the overhead
from the separator is purged, while the bottom stream is the final product. Calculate the
flow rate and the composition of the purge stream.
5. Acetic acid is to be generated by the addition of 0% excess sulfuric acid to calcium
acetate. The reaction is:
Ca( Ac )2+ H 2 SO 4 → CaSO 4 +2 HAc
The reaction goes to 90% completion based on a single pass through the reactor. The
unused calcium acetate is separated from the products of the reaction and recycled. The
HAc is separated from the remaining products. Find the amount of recycle per hour
based on 1000kg of calcium acetate fed to the reactor per hour, and also calculate the
kilograms of HAc manufactured per hour.
6. Nitroglycerine, a widely used high explosive, when mixed with wood flour is called
dynamite. It is made by mixing high-purity glycerine with nitration acid, which contains
50% sulfuric acid, 43% nitric acid, and 7% water by weight. The reaction is:
C3 H 8 O3+ HNO 3 → C3 H 5 O3 ( NO2 )3 +3 H 2 O
The sulfuric acid does not take part in the reaction but is present to catch the water
formed. Conversion of the glycerine in the nitrator is complete, and there are no side
reactions, so all of the glycerine fed to the nitrator forms nitroglycerine. The mixed acid
entering the nitrator contains 20% excess nitric acid to assure that all of the glycerine
reacts. Afer nitration, the mixture of nitroglycerine and spent acid goes to a separator.
He nitroglycerine is insoluble in he spent acid, and its density is less, so it rises to the
top. It is carefully drawn off as a product stream and sent to wash tanks for purification.
The spent acid is withdrawn from the bottom of the separator and is sent to an acid
recovery tank where nitric and sulfuric acid is separated. The sulfuric acid – water
mixture is concentrated and sold for industrial purposes. He recycle stream to the
nitrator is a 70% solution of nitric acid in water. He product stream is 96.5%
nitroglycerine and 3.5% water by weight. If 1000kg of glycerine per hour are fed to the
nitrator, calculate the mass flow rate of the product stream, the fresh feed, the sulfuric
acid-water mixture (and its weight composition), and the recycle stream.
7. Methanol is synthesized from carbon monoxide and hydrogen in a catalytic reactor. The
fresh feed to the process contains 32% carbon monoxide, 64% hydrogen and 4%
nitrogen. This stream is mixed with a recycle stream in a ratio 5mol recycle / 1mol fresh
feed to produce the feed to the reactor, which contains 13% nitrogen. A low single-pass
conversion is attained in the reactor. The reactor effluent goes to a condenser from
which two streams emerge: a liquid product stream containing essentially all the
methanol formed in the reactor, and a gas stream containing all the carbon monoxide,
hydrogen, and nitrogen leaving the reactor. The gas stream is split into two fractions:
one is removed from the process as a purge stream, and the other is the recycle stream
that combines with the fresh feed to the reactor. For a basis of 100mol/hr fresh feed,
calculate the production rate of methanol, the molar flow rate and composition of the
purge gas, and the overall and single-pass conversions.
8. In the famous Haber process to manufacture ammonia, the reaction is carried out at a
pressure of 800 to 1000atm at 500 to 600˚C using a suitable catalyst. Only a small
fraction of the material entering the reactor reacts on one pass, so recycle is needed.
Also, because the nitrogen is obtained from the air, it contains almost 1% rare gases that
do not react. The rare gases would continue to build up in the recycle until their effect
on the reaction equilibrium would become adverse so a small purge stream is used. The
fresh feed composed of 75.16% hydrogen, 24.57% nitrogen, and 0.27% argon is mixed
with the recycle gas and enters the reactor with a composition of 79.52% hydrogen. The
gas leaving the ammonia separator contains 80.01% hydrogen and no ammonia. The
product ammonia contains no dissolved gases. Per 100 moles of fresh feed, calculate the
moles of recycle and purge, as well as the single pass conversion of hydrogen.
9. Methanol is synthesized in a catalytic reactor using CO and H 2. However, a side reaction
is observed to occur which leads to the formation of formaldehyde, H 2CO. The fresh feed
to the process contains 30% mol CO, 60% mol H 2 and 10% mol N2. The combined feed
stream to the reactor, containing 22% mol N 2, consists of 4 mol recycle per mol of fresh
feed. In the reactor, 9 moles of CH 3OH is produced per mole H 2CO. The reactor effluent
gas goes to the condenser where two streams emerge: a gas containing all CO, H 2 and N2
and a liquid stream CH3OH and H2CO. The gas stream is split into two fractions: one
stream is purged and the other is combined with fresh feed to the reactor. Calculate the
fraction of CO in the purge stream, single pass conversion with respect to CO and overall
conversion with respect to CO.
10. Ethylene oxide is produced by the catalytic oxidation of ethylene:
2C 2 H 4 +O2 → 2C 2 H 4 O
An undesired competing reaction is the combustion of ethylene:
C2 H 4 +3 O2 → 2 CO2 +2 H 2 O
The feed to the reactor contains 3 moles of ethylene per mole of oxygen. The single-pass
conversion of ethylene is 20%, and for every 100 moles of ethylene consumed in the
reactor, 90 moles of ethylene oxide emerges in the reactor products. A multiple-unit
process is used to separate the products. Ethylene and oxygen are recycled to the
reactor, ethylene oxide is sold as a product, and carbon dioxide and water are discarded.
Assuming a quantity of 100kmol of reactor feed as basis for calculations, calculate the
molar flowrates of ethylene and oxygen in the fresh feed, the production rate of
ethylene oxide, and the overall conversion of ethylene.
COMBUSTION OF GASEOUS FUELS
CASE I
1. Pure ethane is burned completely in 20% excess air. Air is supplied at 25˚C and 740torr
and is substantially dry. Calculate:
a. Orsat analysis of the products of combustion (10.81% CO2, 3.78% O2, 85.41% N2)
b. Kg of dry air supplied / kg of fuel gas (19.23)
c. Cubic meters of air / kg ethane (16.75)
d. Cubic meters of the products of combustion measured at 400˚C and 100kPa per
kg ethane (40.11)
e. Partial pressure of water in the products of combustion (13.95kPa)
2. Coal Gas at 15˚C, 760torr, and saturated with water vapor is burned in a furnace to
generate heat to a Water-Tube Boiler. Air with 60% RH is supplied at a rate of 5.7 m 3/m3
coal gas and enters at the same temperature and pressure as the coal gas. The coal gas
analyzes 1.4% CO2, 2.7% C2H2, 0.7% O2, 5.8% CO, 53.2% H2, 29.6% CH4, and 6.6% N2. The
molar ratio of CO2 to CO in the stack gas is 10:1. All the H 2 in the fuel is burned to water.
The stack gas leaves at 400˚C and 100kPa. Calculate:
a. % excess (27.19)
b. Orsat analysis of the stack gas (7.24% CO2, 0.72% CO, 5.23% O2, 86.81% N2)
c. Cubic meters stack gas per cubic meter of coal gas (15.19)
d. Dew point of the stack gas (58.8˚C)
3. Carbureted water gas is produced in the same way as blue water gas but in the presence
of cracked oil vapors in a carburetor. A typical gas analysis shows 4.7% CO 2, 7.8% C2H4,
0.3% O2, 36.5% H2, 35.5% CO, 8.6% CH4, and 6.6% N2. If this gas is burned in 104.34m 3 air
at 30˚C, 101kPa, and 60% RH per kmol fuel, calculate:
a. % excess (12.18%)
b. Orsat analysis of the stack gas (400˚C, 760torr) if 85% of C burns to CO 2 and all H2
burns to H2O (13.45% CO2, 2.37% CO, 3.47% O2, 80.71% N2)
4. A gaseous fuel containing 70% C, 20% H, 5% O, 3% N, and 2% S is burned to supply heat
in a certain manufacturing process. Air is supplied at atmospheric pressure, 300K, 80%
RH, and at a volumetric flowrate of 100cubic meters per kmol of fuel. The stack gases
leave at 1000K and at 2kPa gauge. Assuming complete combustion with S forming sulfur
dioxide, calculate:
a. % excess (11.32)
b. Complete analysis of the stack gas (16.82% CO 2, 5.12% H2O, 0.48% SO2, 2.26% O2,
75.32% N2)
c. Volume ratio between the stack gas and the air (3.34)
CASE II
1. A pure saturated hydrocarbon is burned with excess air. Orsat analysis of the products of
combustion shows 9.08% CO2, 1.63% CO, 5.28% O2, and no free H2. Calculate:
a. The formula of the hydrocarbon (C3H8)
b. % excess (24.99)
c. Kg dry air / kg of hydrocarbon (19.52)
2. A pure saturated hydrocarbon is burnt with excess air. Orsat analysis of the stack gas
shows 7.9% CO2, 1.13% CO, 0.24% H2, 5.33% O2, and 85.4% N2. Air is substantially dry.
The stack gases leave at 750mmHg pressure. Calculate:
a. % excess (25.73)
b. Formula of the hydrocarbon (CH4)
c. Kg air/kg fuel (21.58)
d. Dew point of the stack gas (54.21˚C)
3. Bottled gases are the liquefied petroleum gases propane and butane. If a sample of this
gas is burned in excess air, a burner gas of the following analysis is obtained: 8.62% CO 2,
1.38% CO, 6.45% O2, and 83.55% N2. Calculate:
a. % excess (35.02)
b. Composition of this bottle gas (55.05% propane)
4. A mixture of a saturated hydrocarbon and N 2 is burned in excess air supplied at 25˚C,
740torr and 90% RH. An Orsat analysis of the stack gas shows 7.6% CO 2, 2.28% CO,
1.14% H2, 6.03% O2, and 82.95% N2 with a dew point of 53.46˚C. The stack gases leave at
300˚C, 765mmHg with a volume ratio of 2.049m3 wet stack gas/m3 wet air. Calculate:
a. % excess (25.01)
b. Formula of the hydrocarbon (C2H6)
c. Volume % analysis of the fuel (74.32% C2H6, 25.68% N2)
CASE III
1. The burning of pure butane with excess air gives a stack gas which analyzes 11.55% CO 2
on a dry basis. Assuming complete combustion, calculate:
a. % excess (19.98)
b. Complete Orsat analysis of the stack gas (3.75% O2, 84.7% N2)
2. Producer gas analyzing 25.3% CO, 13.2% H2, 0.4% CH4, 5.4% CO2, 0.5% O2, and 55.2% N2
is burned in excess air at 25˚C, 745torr, and 60% RH. Partial Orsat analysis of the stack
gas shows 16.13% CO2, 1.79% CO, and 0.72% H2. Calculate:
a. % excess (11.04)
3. A pure saturated hydrocarbon is burned in excess air. Air is supplied at a rate of
284.14m3/kmol of the hydrocarbon. Air enters at 30˚C, 1atm, and saturated with water
vapor. Partial Orsat analysis of the stack gas shows 8.68% CO 2 and 1.3% CO. Calculate:
a. Formula of the hydrocarbon (CH4)
b. Complete Orsat analysis of the stack gas (11.29%O2, 78.73% N2)
c. % excess air (14.92%)
4. A fuel containing methane, ethane, and 2% hydrogen sulfide is burned in a furnace to
produce a stack gas having a partial Orsat analysis of 7.5% CO 2, 3% CO, and 0.15% SO2.
Assuming complete conversion of hydrogen to water, calculate:
a. % of methane and ethane in the feed (56% methane, 42% ethane)
b. Complete Orsat analysis of the stack gas (7.5% CO 2, 3% CO, 0.15% SO2, 84.92%
N2, 4.43% O2)
c. % excess (14.89%)
COMBUSTION OF LIQUID FUELS
CASE I
1. Gasoline with an octane number of 85 is burned in an experimental engine in 30%
excess air. The product gas has a molal ratio of CO 2 to CO of 5:2 and H 2 to CO of 1:1.
What is the expected Orsat analysis? Density of iso-octane is 0.6918 and for heptane is
0.684 g/mL. (7.37% CO2, 2.95% CO, 2.95% H2, 7.79% O2, 78.94% N2)
2. Crude petroleum oil is generally considered to be formed from animal and vegetable
debris accumulating in sea basins or estuaries and decomposed by anaerobic bacteria
resulting in a black viscous product. A typical elemental analysis shows 80% C, 13% H, 1%
N, 3% O, and 3% S. During combustion, air supplied is less than the theoretical so that all
of the O2 is used up. 70% of the C burns to CO 2, the rest to CO. The molal ratio of CO to
H2 in the exhaust gas is 1:2. Assume that the sulfur in the fuel burns to SO 2 and the
nitrogen combines with the nitrogen from air. Calculate:
a. Orsat analysis of the exhaust gas (12.56% CO2, 5.38% CO)
b. % of the theoretical air which is supplied for combustion (70.7%)
c. Equivalence ratio (1.4)
3. An alcogas mixture made up of 85% gasoline and 15% ethanol is used as fuel for an
engine in the presence of 17.05m3 air/kg alcogas supplied essentially dry at 30˚C and
740mmHg. 80% of the C burns to CO2, the rest to CO. Molal ratio of H2 to CO is 1:2.
Assume that gasoline has the same composition as a mixture of iso-octane and heptane
with an octane number of 95. Use a density of 0.6918g/mL for iso-octane and
0.684g/mL for heptane. Calculate:
a. % excess (36.06%)
b. Orsat analysis of the exhaust gas (8.18% CO2, 2.05% CO, 1.02% H2)
4. A ternary blend of gasoline (90% octane number), alcohol (75% ethanol, 25% methanol),
and benzole (75% benzene, 15% toluene, and 10% xylene) is burned completely in 35%
excess O2. Analysis of the blend shows 70% gasoline, 15% benzole, and 15% alcohol.
Calculate the complete analysis of the exhaust gas. (9.79% CO2, 5.14% O2, 74.63% N2,
10.43% H2O)
CASE II
1. A boiler uses high grade distillate fuel oil. Analysis of the stack gases at 375˚C and
765torr shows 9% CO2, 1.21% CO, 0.37% H2, 7.05% O2, and 82.37% N2. Assuming that the
fuel oil consists only of hydrocarbons, calculate:
a. % excess (40.04%)
b. Weight composition of the fuel oil (84.95% C, 15.05% H)
c. AFR (20.85)
2. Cetane numbers are used to indicate the quality of diesel fuel oils for compression
ignition engines. It is defined as the % by volume of cetane (C 16H34) in a mixture of
cetane and methylnaphthalene (C11H10) mixture that has the same performance as the
fuel. If the test study on the combustion of the mixture gave a product gas analyzing
7.14% CO2, 4.28% CO, 8.24% O2, and 80.34% N2, what is the cetane number of the
diesel? Density of cetane is 0.7751 and methylnaphthalene is 1.025 g/mL. (44.59)
3. Biodiesel from a palm oil has an approximate formula of CxHyOz. Excess air is supplied at
30˚C 100kPa and 85% RH. The exhaust gas leaves at 250˚C and 750mmHg with a
complete analysis of 12.08% CO2, 0.25% CO, 0.55% H2, 2.12% O2, 71.17% N2, and the rest
is water. Find:
a. Formula of the biodiesel (C19H34O2)
b. Equivalence Ratio (0.91)
4. Cetane number is defined as the volumetric percentage of cetane in a liquid mixture
with methylnaphthalene. Cetane has a specific gravity of 0.77 while methylnaphthalene
is approximately as dense as water. If a mixture of the two produces a stack gas
containing 10% CO2, 2.5% CO, 1% H2, and 4.5% O2 when burned in excess air, calculate:
a. % excess (14.44)
b. The weight composition of the liquid fuel (97.75% cetane, 2.25%
methylnaphthalene)
c. The cetane number (98.26)
CASE III
1. A low grade fuel oil containing approximately 81% C, 8% H, 3% O, 4% N, and 4% S is
burned in an industrial burner producing a stack gas with a partial Orsat analysis that
shows 11.22% CO2 and 1.46% CO. The molal ratio of H2 to CO in the combustion gas is
1:5. Calculate:
a. Complete Orsat analysis (5.84% O2, 80.96% N2)
b. % excess (30.04)
c. Equivalence ratio (0.77)
d. Cubic meters of air (30˚C, 760mmHg) per kg oil (13.53)
2. A German fuel blend called Reichkrafskoff is made up of 50% motor benzole (75%
benzene, 15% toluene, 10% xylene), 25% tetralin (C 10H12), and 25% industrial alcohol
(80% ethanol, 20% methanol). Afer combustion in excess air, a stack gas containing
9.13% CO2 and 1.83% CO is obtained. Calculate:
a. % excess (50.04%)
3. Biodiesel made from jatropha was found to have an analysis of 14.2% palmitic acid,
C16H32O2, 6.9% stearic acid, C18H36O2, 43.1% oleic acid, C18H34O2, and 35.8% linoleic acid,
C18H32O2. This fuel is burned in excess air at 32˚C and 98kPa with 75% RH. Partial Orsat
analysis of the exhaust gas shows 11.63% CO 2, 0.61% CO, and 0.91% H 2. The exhaust
gases leave at 300˚C and 740mmHg. Find:
a. Complete Orsat analysis (5.19% O2, 81.66% N2)
b. % excess (25.65%)
c. AFR (15.9)
4. A sample of oil containing 70% benzene, 20% toluene, and 10% mixed xylene is burned
to produce a stack gas. Partial Orsat analysis of the stack shows 10% carbon dioxide
assuming complete combustion. Calculate:
a. Complete Orsat analysis of the stack gas (10% CO2, 81.08% N2, 8.92% O2)
b. % excess (70.61)
c. Dew point of the stack gas if it exits the burner at 5mmHg gauge and dry air is
used (33.3˚C)
COMBUSTION OF SOLID FUELS (TYPE 1)

1. A coal-fired boiler uses a high volatile-A bituminous coal with an ultimate analysis of
75.2% C, 5.19% H, 8.72% O, 1.5% N, 7.8% ash, and 1.6% S. 60% excess air is supplied.
Assume CO to CO2 ratio of 0.175. The flue gas leaves at 300˚C and 740torr. Calculate:
a. Calorific value of coal (31.47 MJ/kg)
b. AFR (16.15)
c. Cubic meter air supplied per 100kg coal (1401.98)
d. Complete analysis of the flue gas if air is supplied at 28˚C, 100kPa, and essentially
dry (9.19% CO2, 1.61% CO, 0.09% SO2, 8.4% O2, 4.47% H2O, 76.24% N2)
2. An industrial plant uses a high grade semi-anthracite coal analyzing 90.04% C, 0.79% S,
and 1.2% N on an ash and moisture free basis. If this coal were burned in excess air
saturated with water at 30˚C and 105kPa, a flue gas with the following Orsat analysis
results: 10.83% CO2, 1.08% CO, 0.22% H2, 8.17% O2, and the remainder is N2 and SO2.
Calculate:
a. Ultimate analysis of the coal (4.67% H, 3.3% O)
b. % excess (55.16%)
3. A boiler is fired with coal containing 72.63% C, 14% ash, 1.6% N, and 1.2% S burnt under
conditions that the elimination of combustibles from the residue is complete. The air
enters the furnace at 25˚C, 760mmHg, with 80% RH. The flue gas goes to the stack at
280˚C and 110kPa. The average flue gas Orsat analysis is 8.41% CO 2, 2.52% CO, 0.76% H2,
and 9.86% O2. Assume that all the sulfur and nitrogen in the coal burns to SO 2 and N2
respectively. Calculate the following:
a. % excess (65.3%)
b. Ultimate analysis of the coal (4.3% H, 6.27% O)
c. Cubic meter flue gas per kg coal (24.46)
d. Cubic meter air per kg coal (13.77)
4. A certain coal is pulverized and burnt in a burner. Analysis of coal showed 70% C, 10.7%
ash and 1.2% N. The residue is substantially free of combustible. A sample of the flue gas
collected and analyzed in an Orsat apparatus over mercury contains 8.3% CO 2, 3.32% CO,
0.32% SO2, 3.32% H2, and 9.53% O2. Air supplied is at 30˚C, 1atm, and saturated with
water. Calculate:
a. Complete ultimate analysis of coal (4.69% H, 8.27% O, 5.14% S)
b. % excess (45.15%)
c. Cubic meter flue gas (250˚C, 1atm) per kg coal (22.73)
5. A burner uses Pittsburgh coal analyzing 14.1% ash, 2.1% N and 4.3% S. Excess air is
supplied dry at 22˚C and 1atm. The stack gases at 285˚C and 765mmHg analyzes 9.65%
CO2, 1.16% CO, 0.24% SO2, 0.58% H2, and 9.16% O2. Calculate:
a. Complete ultimate analysis (72.63% C, 4.11% H, 2.76% O)
b. Equivalence Ratio (0.61)
c. Cubic meters air per kg coal (13.57)
d. Cubic meter stack gas per kg coal (26.26)
6. Anthracite, the highest rank coal, is a hard, glossy, black coal used primarily for
residential and commercial space heating. In a combustion operation, the anthracite
used showed 92.8% C and 1.3% ash. If this coal is burned in dry air at 28˚C, 1atm,
combustion gases with the following Orsat analysis result: 14.15% CO 2, 5.77% O2, 79.97%
N2, 0.03% SO2, and 0.08% NO. The combustion gases leave at 600˚C and 800mmHg.
Calculate:
a. Ultimate analysis of the anthracite coal (2.99% H, 1.78% O, 0.61% N, 0.52% S)
b. Calorific value of the anthracite coal (35.4)
c. % excess (37.27%)
d. AFR (15.96)
e. Complete analysis of combustion gases (13.77% CO 2, 5.62% O2, 2.66% H2O,
0.03% SO2, 0.08% NO, 77.84% N2)
7. On an “as received” basis, the proximate analysis of a representative coal from the
Semirara Plant is 32% VCM, 53% FC, 10% ash, 1.2% N, and 6.2% S. Its calorific value is
23.78MJ/kg. On the assumption that this coal is burnt with 150% excess air so that the
molal ratio of CO2 to CO is 5:1, calculate:
a. Cubic meter dry air at 25˚C and 750mmHg per kg coal (16.65)
b. Complete analysis of the flue gas (5.76% CO 2, 1.15% CO, 0.28% SO2, 12.75% O2,
76.41% N2, 3.66% H2O)
c. Cubic meter flue gas at 240˚C and 770mmHg per kg coal (28.88)
8. A medium volatile bituminous coal has an “as received” analysis of 27.13% VCM, 62.52%
FC, 7.11% ash, 0.95% S, and 1.28% N. Its calorific value is 32.3 MJ/kg. This coal is
supplied in excess air supplied at 30˚C, 756torr, and 80% RH. Partial Orsat analysis of the
stack gas shows 9.78% CO2 and 2.45% CO. Calculate:
a. % excess (49.24)
b. Complete Orsat analysis of the stack gas (0.06% SO2, 8.18% O2, 79.53% N2)
c. Cubic meter air per kg coal (13.89)
d. Cubic meter stack gas (270˚C, 768mmHg) per kg coal (25.45)
9. A high volatile B bituminous coal analyzing 22% VCM, 64% FC, 4% M, 1.4% N, and 1.6% S
has a calorific value or 32.5MJ/kg. It is burned in excess air supplied essentially dry at
28˚C and 1atm. The stack gas leaves at 250˚C, 740mmHg, and contains 8.37% CO 2, 4.19%
CO, and 2.51% H2. Calculate:
a. % excess (38.91%)
b. Complete Orsat analysis of the stack gas (8.99% O2, 75.845% N2, 0.095% SO2)
c. Cubic meter stack gas per cubic meter air (1.89)
10. A low volatile bituminous coal has the following analysis on an “as received” basis:
10.76% M, 68.12% FC, 13.63% VCM, 0.44% N, 0.65% S, and 7.49% ash. The calorific
value of this coal was analyzed to be 30.45 MJ/kg. The coal was burned in a burner with
excess air at 50˚C, 750mmHg, and 15% RH. Partial dry analysis of the stack gas shows
8.05% CO2, and 3.87% CO. The stack gas leaves the burner at 300˚C and 760mmHg.
Calculate:
a. Complete Orsat analysis of the stack gas (0.04% SO2, 9.34% O2, 78.7% N2)
b. % excess (54.87)
c. Cubic meter wet air per 100 kg coal (1147.32)
COMBUSTION OF UNCOKED COAL

1. A furnace burns coal analyzing coal containing 4.1% M, 24% VCM, 63% FC, 1.2% N, 1.8%
S, and 8.9% ash. Its calorific value is 32MJ/kg. Determine the % VCM, C, and calorific
value lost in the residue if it analyzes 4.8% VCM, 12.6% FC, and 82.6% ash. (2.155%)
2. A furnace is fired with coal with the following proximate analysis: 5% M, 60% FC, 25%
VCM, and 10% ash. Its calorific value is 31.33 MJ/kg. Calculate the % VCM, C, and CV lost
in the residue if the residue analyzes 14.4% FC, 6% VCM, and 79.6% ash. (3.02)
3. A boiler is fired with coal analyzing 13.8% VCM, 8.6% ash, 3% M, 1.2% S, negligible N,
and a calorific value of 32.95 MJ/kg. The dry residue removed analyzes 5% VCM, 27% FC,
and 68% ash. 60% excess air is supplied at 32˚C, 758mmHg, and 85% RH. 90% of the
carbon gasified burns to CO2, the rest to CO. The molal ratio of H2 to CO is 2:9. Calculate:
a. % C lost in the residue (4.58)
b. Cubic meter air per kg coal (15.43)
c. Orsat analysis of the stack gas (9.93% CO 2, 1.1% CO, 0.25% H2, 0.06% SO2, 9.2%
O2, 79.46% N2)
d. Cubic meter stack gas (400˚C and 765mmHg) per kg coal (34.59)
4. A high volatile A bituminous coal analyzing 73.77% C, 5.23% H, 10% O, 1.4% N, 8.1% ash,
3.9% M, and 1.5% S is burned in a furnace together with 45% excess air supplied
saturated with water vapor at 25˚C and 1atm. Analysis of the wetted residue shows 16%
VCM, 23.55% FC, 32.48% ash, and 27.97% H 2O. The stack gases leave at 300˚C and
745torrs with a CO to CO2 ratio of 0.12. Calculate:
a. % C and CV lost in the residue (11.21)
b. Orsat analysis of the stack gas (9.93% CO 2, 1.19% CO, 0.08% SO2, 8.83% O2,
79.97% N2)
c. Cubic meter stack gas per kg coal (25.39)
5. A sample of coal was found to contain 1% N, 10% ash, and 5.8% S. Analysis of the
residue showed uncoked coal with 20.71% VCM lost in the residue. Orsat analysis of the
stack gas shows 8.93% CO2, 1.56% CO, 0.34% SO2, 9.87% O2, and 79.3% N2. Assume that
N in the coal is gasified to N2. Calculate:
a. Complete ultimate analysis of coal (67.11% C, 3.95% H, 12.14% O)
b. Complete analysis of the residue if it contains 37.93% ash (54.26% FC, 7.81%
VCM)
c. % excess (39.51)
6. Coal fired in a furnace analyzes 34% VCM, 48% FC, 7.7% ash, 1.2% N, 1.57% S. The
residue contains 6.2% VCM, 8.75% FC, 35% ash, and 50.05% H 2O. Air is supplied at 35˚C,
765mmHg, and 85% RH. The stack gases leave at 250˚C and 766 mmHg with an Orsat
analysis of 9.3% CO2, 2.3% CO, 2.3% H2, 0.1% SO2, 9.5% O2, and 76.5% N2. Calculate:
a. % C lost in the residue (4.01)
b. CV of coal (28.36)
c. Ultimate analysis of coal (68.29% C, 6.22% H, 15.02% O)
d. % excess (44.29)
7. A medium volatile bituminous coal with the following analysis was fired in a furnace in
the presence of excess air: 10.76% VCM, 80.31% C, 0.87% N, 0.71% S, and 8.18% ash.
The analysis of the refuse shows 4.57% VCM, 32.29% FC, and 63.14% ash. About 5.5% of
the carbon fired to the furnace is lost in the refuse. Analysis of the stack gas showed
13.35% CO2 and 1.85% CO. Find:
a. GCV of the coal (32.22 MJ/kg)
c. % excess (16.33)
8. An uncoked coal contains 55.3% VCM, 35.3% FC, 3.3% moisture, and 7.1% ash. Further
analysis found that it elementally contains 2.5% N and 1.5% S. Its calorific value was
found to be 32.3 MJ/kg. The refuse analyzes 65% ash, and 90% of the carbon gasified
burns to CO2 while the balance CO. The exiting stack gas was also found to contain a
CO/H2 ratio of 9/2. If air is supplied 23% in excess and saturated with water vapor at
100kPa and 25˚C, calculate:
a. % VCM and FC in the refuse (21.36% VCM, 13.64% FC)
b. Modified analysis of the coal (81.24% C, 3.26% net H, 1.1% CW)
c. Complete analysis of the stack gas (12.24% CO 2, 1.36% CO, 6.54% H2O, 0.3% H2,
5.019% O2, 0.09% SO2, 74.27% N2)
COMBUSTION OF COKED COAL

value lost in the residue if it analyzes 24% FC and 76% ash. (no VCM lost, 3.61% C lost,
2.97% CV lost)
in the residue if the residue analyzes 19.6% C and 80.4% ash. (no VCM lost, 3.19% C lost,
2.63% CV lost)
3. The analysis of a coal indicates 75% C, 17% H, 2% S, and the balance noncombustible
ash. The coal is burned at a rate of 5000kg/hr, and the feed rate of air to the furnace is
50kmol/min. All of the ash and 6% of the carbon in the fuel leave the furnace as a
molten slag. The remainder of the carbon leaves in the stack gas as CO and CO 2. The
hydrogen in the coal is oxidized to water, and the sulfur emerges as SO 2. The selectivity
of CO2 to CO production is 10:1. Calculate:
a. % excess (19.29%)
b. Complete analysis of the stack gas (8.28% CO 2, 0.83% CO, 13.17% H2O, 0.1% SO2,
4.15% O2, 73.47% N2)
4. Dry coke composed of 4% ash, 90% carbon, and 6% hydrogen is burned in a furnace with
dry air. The solid refuse lef afer combustion contains 10% carbon and 90% ash. The
Orsat analysis of the flue gas gives 13.9% CO 2, 0.8% CO, 4.3% O2, and 81% N2. Calculate
the percent of excess air. (21.46)
5. Coal fired in a furnace analyzes 57.1% C, 8% ash, 1.4% N, and 0.77% S. The residue
contains 24.5% C and 75.5% ash. Orsat analysis of the stack gas shows 11.21% CO 2,
1.57% CO, 7.45% O2, and 79.77% N2. Calculate:
a. Complete analysis of the coal (5.86% H, 26.87% O)
b. % excess (39.37)
6. A high semi-anthracite coal has a complete analysis of 85.86% C, 4.44% H, 2.7% O, 1.2%
N, 5% ash, and 0.8% S. Analysis of the residue shows 58% C and 42% ash. Air is supplied
dry at 30˚C and 750mmHg. Partial Orsat analysis of the stack gas (400˚C, 755mmHg)
shows 8.05% CO2, 2.42% CO, and 2.9% H2. Assume that the S and N gasified burns to SO2
and NO respectively. Calculate:
a. % excess (54.3)
b. Complete Orsat analysis of the stack gas (10.66% O 2, 75.79% N2, 0.04% SO2,
0.14% NO)
c. Cubic meter stack gas per cubic meter air (2.31)
7. A local utility burns coal having the following ultimate analysis: 83.05% C, 4.45% H,
3.36% O, 1.08% N, 0.7% S, and 7.36% ash. Partial Orsat analysis of the stack gas afer
complete combustion showed 15.4% CO2. Moisture in the fuel is 3.9%, and the air has an
average humidity of 0.0048 kg water per kg dry air. The refuse showed 14% C, with the
remainder being ash. Calculate:
a. Orsat analysis of the stack gas (3.73% O2, 80.82% N2)
b. % excess (6.11)
8. A furnace is fired with coal with the following analysis: 36.3% VCM, 49.6% FC, 10.7% ash,
3.4% M, 1.2% N, and 5.1% S. Its calorific value is 29.5 MJ/kg. Analysis of the wetted
residue shows 12% C, 65% ash, and 23% H 2O. Dry air is supplied at 27˚C and 1atm. The
stack gases leave at 350˚C, 745 mmHg and with a partial Orsat analysis of 8.71% CO 2,
1.74% CO, and 0.35% H2. Calculate:
a. Complete Orsat analysis of the stack gas (0.29% SO2, 9.5% O2, 79.41% N2)
b. % excess (65.24)
c. Cubic meter stack gas per kg coal (29.54)
COMBUSTION OF COMBINATION OF COKED AND UNCOKED COAL
value lost in the residue if it analyzes 7.5% VCM, 29.2% FC, and 63.3% ash. (4.39% VCM
lost, 6.11% C lost, 5.81% CV lost)
in the residue if the residue analyzes 25% FC, 4% VCM, and 71% ash (2.25% VCM lost,
5.09% C lost, 4.59% CV lost)
3. The following data were obtained during coal combustion:
Coal: 13.8% VCM, 74.6% FC, 8.6% ash, 3% M, 1.2% S
CV = 32.9582 MJ/kg, Residue: 4% VCM, 40% FC, 56% ash
Air: 25˚C, 740torr, 80% RH, 50% excess
Stack gas: 300˚C, 755torrs, H2/CO ratio = 1:4, CO/CO2 ratio = 1:10
Calculate:
a. Cubic meter air per kg coal (14.28)
b. Orsat analysis of the stack gas (10.34% CO2, 1.03% CO, 0.26% H2, 0.07% SO2,
8.75% O2, 79.55% N2)
4. Coal fired in a furnace analyzes 30% VCM, 51% FC, 14% ash, 5% M, 1.6% N and 1.2% S
with a GCV of 30.1 MJ/kg. Residue analysis shows 30% FC, 15% VCM, 40% ash and 15%
H2O. Air supplied is 50% excess and is saturated at 25˚C and 740mmHg. Molar ratio of
CO2 to CO is 5:1 and H2 to CO is 1:1. The stack gas leaves at 300˚C and 765mmHg.
Calculate:
a. Orsat analysis of the stack gas (7.92% CO 2, 1.58% CO, 1.58% H2, 0.06% SO2,
11.13% O2, 77.72% N2)
b. Cubic meter stack gas per cubic meter air (1.92)
5. The analysis of a coal fired in a boiler showed 57.04% total C, 30.5% VCM, 1.2% N, 9.7%
ash, and 6.3% S. Analysis of the wetted residue showed 13.8% FC, 21.5% VCM, 47.8%
ash, and 16.9% H2O. Air is at 28˚C, 756mmHg, and 76% RH. Orsat analysis of the stack
gas shows 7.92% CO2, 2.38% CO, 0.39% SO2, 1.19% H2, 10.65% O2, and 77.47% N2.
Calculate:
a. % VCM and C lost in the residue (14.3% VCM lost, 6.26% C lost)
b. Calorific value of the coal (22.82 MJ/kg)
c. Ultimate analysis of the coal (4.68% H, 21.08% O)
d. % excess O2 (62.91)
6. A furnace burns coal analyzing 78.35% C, 27% VCM, 2.1% N, 7.1% ash, and 0.5% S.
Analysis of the residue shows 6% VCM, 32% FC, and 62% ash. Air supplied is at 30˚C,
735torr, with 90% RH. The stack gases at 250˚C and 745torr has a partial Orsat analysis
of 9.79% CO2 and 1.47% CO. Assuming that 5.2% of the C fired is lost in the residue,
calculate:
a. Complete ultimate analysis of the coal (4.87% H, 7.08% O)
b. % excess (54.48)
c. Complete Orsat analysis of the stack gas (8.87% O2, 79.84% N2)
d. Cubic meter stack gas per kg coal (26.1)
7. Coal fired in a furnace analyzes 16.6% VCM, 16% ash, 61.4% FC, 6% M, 1.2% N and 1.8%
S with a calorific value of 26.75 MJ/kg. Analysis of the residue shows 44% ash, 8% VCM,
34% FC, and 14% H2O. Partial Orsat analysis of the stack gas shows 10.77% CO 2, 1.62%
CO, and 0.81% H2. Air supplied is at 27˚C, 765torr, and 80% RH. Calculate:
a. % C and % VCM lost in the residue (19.92, 17.52)
b. % excess (19.2)
c. Cubic meter air per kg coal (9.03)
d. Orsat analysis of the stack gas (8.02% O2)
8. A solid fuel whose calorific value is approximately 30 MJ/kg contains 60% VCM, 30% FC,
2% moisture, 8% ash, 1.3% N, and no S. Analysis of the refuse is 75% ash and the
balance equal masses of VCM and FC. This fuel is completely burned in 25% excess air
supplied at 1.03atm, 303K, and 93% RH. Calculate:
a. % VCM, FC, and C lost (2.22% VCM lost, 4.44% FC lost, 3.05% C lost)
b. Complete analysis of the stack gas (14.71% CO2, 6.77% H2O, 2.17% O2, 76.35% N2)
COMBUSTION OF RAW SULFUR

1. Raw sulfur analyzing 95% S and 5% inert is burned with 65% excess air (S to SO 2). Air is
supplied at 30˚C, 740mmHg, and 60% RH. Analysis of the cinder shows 10% S and 90%
inert. 88% of the S gasified burns to SO2, the rest to SO3. Calculate:
a. % excess with respect to SO3 (10)
b. Cubic meter air per kg raw S (6.12)
c. Complete analysis of the burner gas (10.93% SO 2, 7.45% O2, 1.49% SO3, 77.54%
N2, 2.59% H2O)
2. Raw sulfur which is 75% pure is burned in excess air supplied at a rate of 4.713 m 3/kg of
raw sulfur at 25˚C, 745mmHg, and 80% RH. If 87% of the sulfur charged burns to SO 2 and
the rest to SO3, calculate:
a. % excess with respect to SO2 (64.89%)
b. % excess with respect to SO3 (9.93%)
c. Complete analysis of the burner gas (10.89% SO 2, 7.31% O2, 77.62% N2, 1.63%
SO3, 2.56% H2O)
3. Raw sulfur analyzing 88% S and 12% inert when burned produces a gas with an Orsat
analysis of 9.79% SO2, 9.16% O2, and 81.05% N2. Dry air is supplied at 25˚C and
745mmHg. The burner gas leaves at 250˚C and 760mmHg. Calculate:
a. % excess air with respect to SO2 (87.02)
b. % excess air with respect to SO3 (24.68)
c. Cubic meter burner gas per cubic meter air (1.706)
4. The burner gas from a sulfur burner analyzes 9.2% SO 2, 7.13% O2, and 83.67% N2. The
raw sulfur charged contains 82% pure sulfur and analysis of the cinder shows 20%
unburned sulfur. Calculate:
a. % excess with respect to SO2 (59.96)
b. % excess with respect to SO3 (6.64)
c. Cubic meter of saturated air (28˚C, 750torr) per kg raw S (5.08)
d. Cubic meter of burner gas (300˚C, 730torr) per kg raw S (9.75)
5. Raw sulfur containing 83% S and 17% inert is burned in saturated air supplied 20% in
excess with respect to the conversion to sulfur trioxide at atmospheric pressure and
20˚C. The cinder analyzes 80% inert, with the balance sulfur trioxide and 40% of the
water from the air. If 80% of the sulfur is converted to sulfur dioxide, calculate:
a. % excess with respect to SO2 (80)
b. Complete analysis of the cinder (2.27% SO3, 17.73% H2O)
c. Complete analysis of the stack gas (9.31% SO 2, 2.26% SO3, 1.41% H2O, 8.24% O2,
78.78% N2)
6. The burning of raw sulfur containing 90.5% sulfur is aided with the combustion of a
liquid mixture of equal masses of benzene and toluene supplied at 2kg per kg of raw
sulfur. 85% saturated air is supplied at 298K, 101kPa, and 23% in excess with respect to
the conversion to sulfur dioxide. 90% of the C is converted to CO 2, the balance CO. 90%
of the S is converted to sulfur dioxide, and the rest sulfur trioxide. The stack gases leave
at 110kPa and 1000K. Assuming that the conversion of H to water is complete, and that
only the inert exit in the cinder, calculate:
b. Complete analysis of the stack gas (9.95% CO 2, 1.11% CO, 8.46% H2O, 1.84% SO2,
0.2% SO3, 4.14% O2, 74.3% N2)
c. Volumetric ratio between stack gas and air (3.19)
COMBUSTION OF PYRITE ORES

1. Dry pyrite fines containing 82% FeS 2 and 18% gangue are burned in a Herreshoff Burner.
The cinder produced contains 3.06% SO 3 and no unburned FeS2. Orsat analysis of the
burner gas showed 8.15% SO2, 8.46% O2, and 83.39% N2. Calculate:
a. % of the FeS2 charged converted to SO2 (85.93%)
c. Complete analysis of the burner gas (8.06% SO2, 8.37% O2, 1.12% SO3, 82.45% N2)
2. Pyrite analyzing 78% FeS2 and 22% gangue is burned at a rate of 1000kg/hr. Analysis of
the cinder shows 7.22% S as unburned FeS 2 and SO3 absorbed by the Fe2O3 and 27.9%
gangue. Air supplied is 70% in excess based on conversion of FeS 2 to SO2. The ratio of SO2
to SO3 in the burner gas is 3.48:1. Calculate:
b. % of the FeS2 charged lost in the cinder (12.03%)
c. Complete analysis of the burner gas (6.28% SO2, 9.58% O2, 82.34% N2, 1.8% SO3)
3. Pyrite fines containing FeS2 and gangue are charged to a burner. An analysis of the cinder
shows 11.11% FeS2, 66.63% Fe2O3, 2.67% SO3, and 19.6% gangue. Air is supplied 17.33%
in excess (FeS2 to SO3) at 25˚C, 740mmHg, and 80% RH. If 8% of the SO 3 formed is
absorbed in the cinder, calculate:
a. Analysis of the pyrites (85% FeS2, 15% gangue)
b. % of the FeS2 charged lost in the cinder (10)
c. % excess with respect to SO2 (60)
d. Orsat analysis of the burner gas (6.88% SO2, 8.67% O2, 84.45% N2)
e. Cubic meter of burner gas at 350˚C and 750mmHg per kg pyrite (7.55)
4. In the burning of pyrite containing 92% FeS 2 and 8% gangue, 13% of the FeS 2 charged is
lost in the cinder. A partial analysis of the cinder also shows 5.31% SO 3. The Orsat
analysis of the burner gas shows 6.75% SO 2, 6.88% O2, and 86.37% N2. Air supplied is at
23˚C, 743mmHg, and 88% RH. Calculate:
a. % excess with respect to SO2 (40%)
c. Complete analysis of cinder (10.33% gangue, 68.91% Fe2O3, 15.45% FeS2)
d. Cubic meter air per kg pyrite (3.58)
e. Cubic meter burner gas (250˚C, 750mmHg) per kg pyrite (5.93)
5. Pyrite fines containing 87% FeS 2 is burned with 25% excess dry air (SO 3) for a 70% yield
of SO2 and a fractional conversion of 0.15 for SO3. The cinder analyzes 15% gangue, with
the balance Fe2O3, unburnt FeS2, and SO3. Calculate:
b. Analysis of the cinder (15.06% FeS2, 56.88% Fe2O3, 13.06% SO3)
c. Complete analysis of the stack gas (6.56% SO2, 0.49% SO3, 10.31% O2, 82.64% N2)
6. A mixture of pyrite and pure sulfur is burned with excess air to produce a stack gas
containing 4.25% SO2, 8.95% O2, and 86.8% N2 on a dry basis. The pyrite contains 90%
FeS2 and 10% gangue. The pure sulfur contributes to 6% of the total S content of the
mixture. 6% of the total S is lost in the cinder, 40% of which is in the form of SO 3, and
60% is in the form of unburnt FeS2. Calculate:
a. Complete analysis of the cinder (13.48% gangue, 4.13% SO 3, 4.64% FeS2, 77.75%
Fe2O3)
b. Kg cinder per kg feed (0.72)
c. % S converted to SO3 (49.71)
PRODUCTION OF OLEUM AND SULFURIC ACID

1. Raw sulfur, 96% pure, is burned in dry excess air producing a gas with an Orsat analysis
of 18% SO2, 0.5% O2, and 81.5% N2. The burner gases are fed to a catalytic converter
together with 20% excess secondary air resulting in the oxidation of 60% of the SO 2 to
SO3. The gases from the converter enter an absorber to produce the acid. Assuming no
further oxidation of the SO2 taking place in the absorber, calculate:
a. Complete analysis of the burner gas (17.63% SO 2, 0.49% O2, 2.06% SO3, 79.82%
N2)
b. Complete analysis of the converter gas (4.95% SO 2, 3.65% O2, 8.89% SO3, 82.51%
N2)
c. Weight of an 85% concentrated H2SO4 solution per kg raw S charged if the
absorbing acid is 40% H2SO4 (2.82)
d. Weight of a 5% oleum formed per kg raw S charged if the absorbing acid is a 90%
H2SO4 solution (4.5)
2. Raw sulfur containing 83% pure S is burned together with 80% excess air (SO 2). An
analysis of the cinder shows 20% unburned sulfur and 80% inert. 90% of the sulfur
gasified burns to SO2 and the rest to SO3. Air is supplied saturated at 30˚C and
750mmHg. The gases from the burner enter a converter where catalytic oxidation of SO 2
to SO3 takes place. A partial Orsat analysis of the converter gas shows 1.37% SO 2. The
gases from the converter enter an absorber where afer absorption in acid solution
forms a waste gas with a partial Orsat analysis of 0.55% SO 2. Calculate per 100kg raw
sulfur:
a. Complete analysis of the burner gas (9.59% SO 2, 9.03% O2, 76.06% N2, 1.07% SO3,
4.25% H2O)
b. % of the SO2 entering the converter that is converted to SO3 (88.29)
c. Complete analysis of the converter gas (1.17% SO 2, 9.96% SO3, 4.44% H2O, 5.01%
O2, 79.42% N2)
d. Complete Orsat analysis of the waste gas (5.5% O2, 93.95% N2)
e. Weight of a 60% dilute H2SO4 solution needed to produce an 87% H2SO4 solution
(248.04)
f. If the absorbing acid is 94% H2SO4, what weight of 14% oleum is formed?
(587.59)
3. Raw sulfur analyzing 85.3% S is burned in 20% excess air (SO 3) supplied at 300K, 101kPa,
and saturated with water vapor. 2% of the SO 3 exits in the cinder along with the inert,
where the inert measure 90% by weight. The stack gases then enter a converter where a
fractional conversion of 0.73 is achieved. The converter gas then enters a gas absorber
where 56% of the remaining SO2 undergoes further conversion to SO 3 and hence gets
involved in the sulfuric acid production. Calculate:
a. Complete analysis of the burner gas (7.11% SO 2, 4.32% SO3, 7.01% O2, 3.57% H2O,
77.99% N2)
b. Complete analysis of the converter gas (1.97% SO 2, 9.76% SO3, 3.66% H2O, 4.53%
O2, 80.07% N2)
c. Weight of pure absorbing water needed to produce a 30% dilute acid solution,
and the weight of the produced acid (604.29kg water, 800.27 kg solution)
d. Weight of a 60% dilute acid required to produce a 90% concentrated solution,
and the weight of the produced solution (212.32 kg 60% solution, 408.3 kg 90%
solution)
e. Weight of a 95% concentrated solution needed to produce 20% oleum, and the
weight of the oleum produced (371.34 kg solution, 567.32 kg oleum)
4. The roasting of pyrites analyzing 85% FeS2 and 15% gangue utilizes 40% excess air (SO2)
supplied at a rate of 357m3/hr at 23˚C, 743mmHg, and 88% RH. A partial analysis of the
cinder showed 25.92% FeS2 and 17.83% gangue. Only 65% of the FeS 2 gasified is
converted to SO2 and the rest to SO3. Calculate the following per kg pyrite used:
a. Complete analysis of the cinder (50.08% Fe2O3, 6.17% SO3)
b. Complete analysis of the burner gas (5.4% SO2, 8.64% O2, 80.95% N2, 2.4% SO3,
2.61% H2O)
c. Weight of 15% oleum formed from 85% H 2SO4 if all of the SO2 reacts in the
converter (1.61)
5. 1000 kg/hr pyrites analyzing 81% FeS 2 and 19% gangue is burned in excess air to
produce a burner gas with an Orsat analysis of 5.84% SO 2, 9.72% O2, and 84.44% N2.
Analysis of the cinder shows 8.29% unburned FeS 2 and 3.81% SO3. The gases from the
burner enter a catalytic converter where SO 2 is oxidized to SO3. Partial Orsat analysis of
the converter gas shows 1.87% SO2. No additional secondary air is supplied in the
converter. The converter gases are then sent to an absorber where contact with acid
takes place. The waste gas from the absorber analyzes 0.95% SO 2, 7.82% O2, and 91.23%
N2. Calculate:
a. Complete analysis of the burner gas (5.71% SO2, 2.21% SO3, 9.51% O2, 82.57% N2)
b. % conversion of SO2 to SO3 in the converter (69.94%)
c. Complete analysis of the converter gas (1.75% SO 2, 6.33% SO3, 7.66% O2, 84.26%
N2)
d. Weight of a 60% H2SO4 needed to produce a concentrated 90% H 2SO4 solution
per hour (818.73)
e. Weight of an 88% H2SO4 acid needed to produce 12% oleum per hour (1017.95)
6. Pyrite containing 80% FeS2 and 20% gangue is burned in excess air to produce a gas with
a complete analysis of 7.78% SO2, 1.39% O2, 82.06% N2, 4.92% SO3, and 3.85% H2O.
Analysis of the cinder shows total sulfur content of 6.46% due to the presence of
unburned FeS2 and SO3 absorbed by Fe2O3. Air supplied is at 27˚C, 745mmHg, and
saturated with water vapor. The burner gases then enter a converter together with 30%
excess secondary air (supplied at the same conditions as the primary air) based on the
conversion of all SO2 to SO3. 75% of the SO2 actually burns to SO3. The converter gases
enter an absorber and are absorbed in acid solution. The waste gases formed has a
partial Orsat analysis of 0.7% SO2. Calculate per kg of pyrite:
b. Complete analysis of the converter gas (1.72% SO 2, 83.49% N2, 9.52% SO3, 3.74%
H2O, 1.53% O2)
c. Kg of an 80% H2SO4 solution formed from a 40% acid charged (1.74)
d. Kg of a 75% H2SO4 solution needed to produce 10% oleum (0.63)
LIME PRODUCTION
1. The burning of limestone containing 65% CaCO 3, 25% MgCO3, and 10% inert using a gas
mixture made up of 75% ethane and 25% propane produces a burner gas containing
22.07% CO2, 0.9% CO, 3.02% O2, and 74% N2. Calculate:
a. LFR (5.43)
b. % excess (15.03%)
2. A rotary kiln is charged with 4 metric tons/hr of limestone containing 54% CaCO 3, 38%
MgCO3, 3% SiO2, 1.2% Fe2O3 and 3.8% H2O. 125kg of fuel oil containing 86% C, 10.5% H,
2.4% O, 1% N, and 0.1% S is charged per metric ton of limestone. The lime product
leaves the bottom and contains 2.3% CO2. Air supplied is at 25˚C, 755mmHg, and
saturated with water. Partial Orsat analysis of the kiln gas shows 20.61% CO 2 and 1.18%
CO. Calculate:
a. Kg of lime formed per hour (2151.07)
b. % excess (35.44)
c. Complete Orsat analysis of the kiln gas (5.633% O2, 0.005% SO2, 72.572% N2)
3. A fuel gas made up of a mixture of methane and ethane is burned in excess air and the
heat given off is used to calcine completely a stone containing 95% CaCO 3 and 5% inert.
Complete analysis of the kiln gas shows 21.42% CO 2, 5.54% O2, 62.54% N2, and 10.5%
H2O. Calculate:
a. Analysis of the fuel gas (74.94% CH4, 25.06% C2H6)
b. LFR (10.49)
4. A kiln used to calcine a limestone analyzing 52% CaCO 3, 30% MgCO3, 5% Al2O3, 4% inert,
6% SiO2, and 3% moisture. Coal is burned to supply the heat of calcination. Analysis of
coal shows 13.8% VCM, 8.6% ash, 3% moisture, and negligible N and S with a calorific
value of 32.95 MJ/kg. Analysis of the kiln gas shows 18.57% CO 2, 1% CO, 0.22% H2, 8.39%
O2, and 71.82% N2. Calculate:
a. Kg limestone per kg coal (7.49)
b. LFR (4.38)
5. Limestone analyzing 70% CaCO3, 20% MgCO3, and the balance inert is burned with a
liquid fuel containing 80% C and the balance equal amounts of H and S, and excess air
supplied at 300K, 1atm, and 95% RH. Some of the S in the fuel is converted to SO 3, while
the rest to SO2, with the former adhering to the lime, and the latter joining the stack
gases whose partial Orsat analysis contains 13% CO2 and 0.51% SO2. The exiting lime
contains 2% CO2, and 1% SO3. Calculate:
a. % S converted to SO3 (2.85)
b. LFR (0.71)
c. % excess (6.86)
6. A limestone partially analyzes 45% CO 2 and 5% inert. It is burned with uncoked coal with
a GCV of 32 MJ/kg analyzing 60% VCM, 30% FC, 3% moisture, and 7% ash with negligible
N and S. The weight of limestone is 1.5 times the weight of the coal supplied. 35% excess
dry air is supplied at 300K and 1atm. Upon heating to 1800K, 3% of the VCM is lost, 90%
of the gasified C is converted to CO2, with the balance CO, and hydrogen combustion is
complete. The losses from the coal are mixed with the non-volatile mater of the
limestone to produce impure lime. Calculate:
a. % CaCO3 and % MgCO3 in the limestone (56.82% CaCO3, 38.18% MgCO3)
b. LFR (0.92)
c. Orsat analysis of the stack gas (15.3% CO2, 1.36% CO, 6.44% O2, 76.9% N2)
7. Limestone is calcined in a vertical kiln fired with blast furnace gas. Analysis of the stone
shows 52% CaO, 2.1% MgO, 1.2% H 2O, 1.22% Al2O3, 0.33% SiO2, and 43.15% CO2. The
blast furnace gas contains 27% CO, 12% CO 2, 2% H2, 5% CH4, and 54% N2. The gas leaving
the kiln contains 35.8% CO2, 1% O2, and 63.2% N2. Calculate:
a. % excess (10.02)
b. LFR expressed in kg lime per mole fuel (24.89)
8. A calcination plant is manufacturing 10 metric tons of lime per day consisting of 83%
CaO, 5% CaCO3, and 12% inert. The fuel used is coal gas analyzing 5.9% CO, 53.2% H 2,
29.6% CH4, 4.1% CO2, 0.7% O2 and 6.5% N2 entering at 25˚C, 740mmHg with 80% RH.
Orsat analysis of the kiln gas shows 10.63% CO 2, 0.66% CO, 0.66% H2, 6.75% O2, and
81.3% N2. Calculate:
a. Kg of limestone charged per day (16521.43)
b. Cubic meter coal gas per day (14870.38)
c. % excess (40.01)
9. A plant is burning limestone analyzing 47% CaCO 3, 45% MgCO3, and 8% inert. The kiln is
fired with producer gas containing 25.3% CO, 13.2% H 2, 0.4% CH4, 5.4% CO2, 0.5% O2,
and 55.2% N2. The wet kiln gas is sampled and the average analysis is found to be
21.97% CO2, 3.54% CO, and 5.28% H2. If the LFR is 20 kg of lime / kmol of producer gas,
calculate:
a. % excess (43.18%)
b. Complete Orsat analysis of the kiln gas (7.75% O2, 61.46% N2)
10. A plant produces lime analyzing 53% CaO, 35% MgO, and 12% inert. Water gas analyzing
38.3% CO, 52.8% H2, 0.4% CH4, 5.5% CO2, 0.1% O2, and 2.9% N2 is used as fuel. Analysis
of the kiln gas shows 15.71% CO 2, 3.31% CO, 6.61% H2, 9.81% O2, and 64.56% N2.
Calculate:
a. Weight of limestone per mole water gas (28.13)
b. % excess air (38.77)
CEMENT PRODUCTION
1. Portland cement is manufactured by the dry process in a rotary kiln using 1000kg/hr of a
raw mix made up of 83% limestone and 17% clay by weight. Analysis of the raw
materials is shown:
Component Limestone % Clay %
CaO 54 8
Fe2O3 0.4 3.8
Al2O3 0.7 16.5
SiO2 3 51.7
MgO 0.7 2.1
Loss on ignition 41.2 17.9
In the kiln, coal is added to supply heat of combustion. Coal contains 68% C, 4.1% H,
1.7% O, 2.2% S, and 24% ash (21.77% Al 2O3, 49.72% SiO2, 7.81% CaO, 17.03% Fe2O3, and
3.67% MnO). Air supplied is 10% in excess at 27˚C, 100kPa, and 80% RH. Complete
combustion of coal takes place with all carbon converted to CO 2 and hydrogen to water.
All sulfur is further converted to SO3 and together with the ash goes into the clinker.
Partial Orsat analysis of the stack gas shows 22.7% CO 2. The clinker is cooled and gypsum
(essentially pure CaSO4) amounting to 2% its weight is added. The final mixture is
crushed to the desired fineness to produce the Portland cement. Calculate:
a. Analysis of raw mix (46.18% CaO, 0.98% Fe 2O3, 3.39% Al2O3, 11.28% SiO2, 0.94%
MgO, 37.24% Loss on ignition)
b. Amount of coal required per hour (316.93)
c. Orsat analysis of the kiln gas (2.01% O2, 75.29% N2)
d. Volumetric flow rate (m3/hr) of fresh air (2849.71)
e. Volumetric flow rate (m3/hr) of the stack gas measured at 540˚C and 740mmHg
(8634.13)
f. Analysis of the clinker (64.86% CaO, 3.15% Fe 2O3, 7% Al2O3, 20.88% SiO2, 1.3%
MgO, 0.39% MnO, 2.42% SO3)
g. Chemical constitution of the clinker expressed as 4CaO.Al 2O3.Fe2O3, 3CaO.Al2O3,
2CaO.SiO2, and 3CaO.SiO2 (9.58% C4AF, 13.2% C3A, 19.19% C2S, 53.92% C3S)
h. The amount of Portland cement per hour (735.62)
i. Silica modulus (2.06)
j. Alumina-Iron ratio (2.22)
k. Lime saturation factor (95.7)
l. Hydraulic modulus of cement (2.09)
2. Portland cement is manufactured by the dry process conforming to the following
specifications:
LSF=92
AR = 2
Magnesia, MgO, should not exceed 1.5% and sulfur as SO 3 is 2.2% by weight
Silica content of 24% by weight is acceptable
The above cement is manufactured in a rotary kiln using limestone and clay as raw
materials mixed in 75:25 proportion by weight. Analysis of raw materials is as follows:
CaO 54.55 7.13
Fe2O3 0.4 1.88
Al2O3 0.8 0.56
SiO2 1.72 61.09
MgO 0.85 2.16
Loss on ignition 41.68 27.18
In the kiln, coal is added to supply heat of combustion. Coal contains 67.2% C, 4% H,
1.7% S, 2.2% O, 2.6% H2O, and 22.3% ash. Its gross calorific value is 25.62 MJ/kg on a dry
ash-free basis. Air supplied is 10% in excess at 27˚C, 100kPa, and 75% RH. The clinker is
cooled and gypsum (essentially pure CaSO4) amounting to 3% its mass is added. The final
mixture is crushed to the desired fineness to produce 1000kg/hr of Portland cement.
Calculate:
a. The composition of the clinker (4.03% Al2O3, 66.26% CaO, 2.01% Fe2O3)
b. Hydraulic modulus of cement (2.21)
c. Lime-silica ratio (2.82)
d. Silica modulus (3.97)
e. Chemical constitution of the clinker expressed as 4CaO.Al 2O3.Fe2O3, 3CaO.Al2O3,
2CaO.SiO2, and 3CaO.SiO2 (6.11% C4AF, 7.27% C3A, 25.43% C2S, 57.49% C3S)
f. Analysis of the raw mix (42.7% CaO, 0.77% Fe 2O3, 0.74% Al2O3, 16.56% SiO2,
1.18% MgO, 38.06% CO2)
g. Analysis of the ash (62.89% CaO, 16.22% Al2O3, 5.41% Fe2O3, 15.48% SiO2)
h. The amount of limestone, clay, and coal required per hour (925.62 kg limestone,
308.54 kg clay, 829.38 kg coal)
i. % of the total sulfur of coal going into the stack gas (60.6)
j. The volumetric flowrate (m3/hr) of fresh air (7335.81)
k. Orsat analysis of the stack gas (19.79% CO2, 0.06% SO2, 1.85% O2, 78.3% N2)
3. Portland cement is made by the dry process by burning a raw mixture containing 80:20
limestone and clay supplied at 1000kg/hr in a rotary kiln along with coal and excess air.
Analysis of the raw mix is as follows:
CaO 55 6
Fe2O3 0.4 3
Al2O3 0.8 18
SiO2 2 56
MgO 0.8 2
Loss on ignition 41 15
Coal with a calorific value of 30 MJ/kg containing 55% VCM, 30% FC, 3% M, and 12% ash
with negligible N and 4.3% S is used. Mass ratio between raw mix and coal is 5:2. Air is
supplied 30% in excess at 298K, 1atm, and 95% RH. Analysis of the ash is as follows: 22%
Al2O3, 50% SiO2, 7% CaO, 18% Fe2O3, and 3% MnO. 60% of the S is converted to SO 2 and
exits in the kiln at 1000K and 110kPa, while the remainder is converted to SO 3 and
adheres to the clinker. The clinker is then cooled and gypsum amounting to 2% its weight
is added. The final mixture is then finely crushed to form Portland cement. Assuming
complete combustion of the coal, and that there are no combustibles in the clinker,
calculate:
a. Analysis of the raw mix (45.2% CaO, 0.92% Fe 2O3, 4.24% Al2O3, 12.8% SiO2, 1.04%
MgO, 35.8% LOI)
b. Orsat analysis of the stack gas (18.6% CO2, 0.18% SO2, 4.64% O2, 76.59% N2)
c. Volumetric ratio between kiln gas an air (3.27)
d. Analysis of the clinker (64.39% CaO, 2.52% Fe 2O3, 7.49% Al2O3, 21.49% SiO2,
1.47% MgO, 0.2% MnO, 2.43%SO3)
e. Constitution of the clinker (7.66% C4AF, 15.57% C3A, 27.67% C2S, 44.99% C3S)
f. Amount of Portland cement produced per hour (721.34)
g. Lime saturation factor (92.85)
h. Alumina ratio (2.97)
i. Silica modulus (2.15)
j. Hydraulic modulus (2.04)
4. 1000kg of Portland cement is produced per hour. The gypsum weighs 2% of the clinker’s
weight, and the clinker alone analyzes 2.4% SO3, 0.2% MnO, 1.4% MgO, and 2.4% Fe2O3.
It has an alumina ratio of 2.9 and a silica modulus of 2.33. This cement is produced by
the burning of raw mixtures of limestone and clay containing 35.6% ignition losses via
the dry process along with a solid fuel containing 65.5% C, 4.1% H, 1.9% O, 4.2% S, and
balance ashes, and dry air is supplied 25% in excess. The ash is the only source of MnO,
and all the S is converted to SO 3 and adheres in the clinker. The ash analyzes 7.8% CaO,
17.1% Fe2O3, 21.7% Al2O3, 49.8% SiO2, and 3.6% MnO. Assuming complete combustion of
the coal, calculate:
a. Analysis of the clinker (64.83% CaO, 6.96% Al2O3, 21.81% SiO2)
b. Hydraulic modulus (2.08)
c. Lime saturation factor (93.05)
d. Constitution of the clinker (7.29% C4AF, 14.37% C3A, 26.23% C2S, 48.07% C3S)
e. Kg of coal required (224.14)
f. Kg of raw mix required (1401.24)
g. Analysis of the raw mix (45.06% CaO, 1.01% Fe 2O3, 4.03% Al2O3, 13.32% SiO2,
0.98% MgO, 35.6% LOI)
h. Orsat analysis of the stack gas (24.51% CO2, 3.67% O2, 71.83% N2)

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MOLARITY, MOLALITY, CONCENTRATION

1. How many mg/L are equivalent to 1.2% solution of a substance in water?

GAUGE AND ABSOLUTE PRESSURE

MASS AND MOLAR COMPOSITIONS

MATERIAL BALANCE WITHOUT REACTION (MULTIPLE UNITS)

MATERIAL BALANCE WITH REACTION (SINGLE UNIT)

MATERIAL BALANCE WITH REACTION (MULTIPLE UNITS)

COMBUSTION OF SOLID FUELS (TYPE 1)

COMBUSTION OF UNCOKED COAL

COMBUSTION OF COKED COAL

COMBUSTION OF RAW SULFUR

COMBUSTION OF PYRITE ORES

PRODUCTION OF OLEUM AND SULFURIC ACID

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