If 1000 Kgh of This Fuel is to Be Burned With 300 Excess Air
The following problems can be found in the book: Elementary Principles of Chemical Processes, Third Edition, by Richard M.Felder and Ronald W.Rousseau published by John Wiley & Sons, Inc.
These are only some sample problems and it is adviseable that you buy the textbook.
1. Water enters a 2.00m ³ tank at a rate of 6.00kg/s and is withdrawn at a rate of 3kg/s. The tank is initially half full.
a) Is the process continuous, batch or semi batch? Is it transient or steady state? b) Write a mass balance process. Identify the term of the general balance equation present and state the reason for omitting any terms. c) How long will it take to overflow?
2. Eggs are sorted into two sizes (large and extra large) at the Cheerful Chicken Dairy. Unfortunately business has not been good lately, and since the Cheerful Chicken Dairy's 40-year-old-egg-sorting machine finally gave up the ghost there have been no funds available to replace it. Instead, Old Fred, one of the firm's sharper-eyed employees, has been equipped with a "Large" rubber stamp in his right hand and an "X-Large" stamp in his left hand and assigned to stamp each egg with the appropriated label as it goes by on the conveyor belt. Down the line another employee puts the eggs into either of the two hoppers, each egg according to its stamp. The system works reasonably well, all things considered, except that Old Fred has a heavy hand and on average breaks 30% of the 120 eggs that pass him each minute. At the same time, a check of the "X-Large" stream reveals a flow rate of 70 eggs/minute, of which 25 eggs/minute are broken.
a) Draw and label a flowchart for this process. b) Write and solve balances about the egg sorter on total eggs and broken eggs. c) How many "large" eggs leave the plant each minute, and what fraction of them are broken? d) Is Old Fred right- or left-handed?
3. One thousand kilograms per hour of a mixture containing equal parts by mass of methanol and water is distilled. Product stream leave the top and the bottom of the distillation column. The flow rate of the bottom stream is measured and found to be 673kg/h, and the overhead stream is analyzed and found to contain 90.0wt% methanol.
a) Draw and label a flowchart of the process and do the degree-of-freedom analysis. b) Calculate the mass and the mole fractions of methanol and the molar flow rates of methanol and water in the bottom product stream. 4.Two aqueous sulphuric acid solutions containing 20.0 wt% H2SO4 (SG = 1.139) and 60.0 wt% H2SO4 (SG = 1.498) are mixed to form a 4.00 a) Calculate the mass fraction of sulphuric acid in the product solution. b) Taking 100kg of the 20% feed solution as a basis, draw and label a flowchart of this process, labelling both masses and volumes, and do the degree-of-freedom analysis. Calculate the feed ratio (litres 20% solution/litre 60% solution) c) What feed rate of the 60% solution (L/h) would be required to produce 1250kg/h of the product.
molar solution (SG =1.213)
5. Wet air containing 4.0 mole% water vapour is passed through a column of calcium chloride pellets. The pellets absorb 97.0% of the water and none of the other constituents of the air. The column packing was initially dry and had a mass of 3.40kg. Following 5.0 hours of operation, the pellets are reweighed and found to have a mass of 3.54kg.
a) Calculate the molar flow rate (mol/h) of the feed gas and the mole fraction of water vapour in the produc gas.
b) The mole fraction of water in the product gas is monitored and found to have the value calculated in part (a) for the first 10 hours of operation, but then it begins to increase. What is the most likely cause of the increase? If the process continues to run, what will the mole fraction of water in the process eventually be?
6.The indicator dilution method is a technique used to determine flow rates of fluids in channels for which devices like rotameters and orifice meters cannot be used (e.g., rivers, blood vessels, and large-diameter pipelines). A stream of an easily measured substance (the tracer) is injected into the channel at a known rate and the tracer concentration is measured at a point far enough downstream of the injection point for the tracer to be completely mixed with the flowing fluid. The larger the flow rate of the fluid, the lower the tracer concentration at the measurement point. A gas stream that contains 1.50 mole% CO 2 flows through a pipeline. Twenty (20.0) kilograms of CO2 per minute is injected into the line. A sample of gas is drawn from a point in the line 150 meters downstream of the injection point and found to contain 2.3mole% CO2.
a) Estimate the gas flow rate (kmol/min) upstream of the injection stream. b) Eighteen seconds elapses from the instant the additional CO 2 is first injected to the time the CO 2 concentration at the measurement point begin to rise. Assuming that the tractor travel at the average velocity of the gas in the pipeline (i.e. neglecting diffusion of CO 2 ), estimate the average velocity (m/s). If the molar gas density is 0.123kmol/m 3 , what is the pipe diameter?
7.Following is a labelled flowchart for a steady-state two-unit process, with boundaries shown to donate subsystems about which balances can be taken. State the maximum number of balances that can be written for each subsystem and the order in which you would write balances to determine the unknown process variables.
8. Fresh orange juice contains 12.0 wt% solid and the water, and concentrated orange juice contain 42.0 wt% solids. Initially a single evaporation process was used for the concentration, but volatile constituents of the juice escaped with the water, leaving the concentrate with a flat taste. The current process overcomes this problem by bypassing the evaporator with a fraction of the fresh juice. The juice that enters the evaporator is concentrated to 58 wt% solids, and the evaporator product stream is mixed with the bypassed fresh juice to achieve the desire final concentration.
a) Draw and label a flowchart of this process, neglecting the vaporization of everything in the juice but water. First prove that the subsystem containing the point where the bypass stream split's off from the evaporator feed has one degree of freedom. Then perform the degree-of-freedom analysis for the overall system, the evaporator, and the bypass- evaporator product mixing point, and write in order the equations you would solve to determine all unknown stream variables , but don't do any calculations.
b) Calculate the amount of product (42% concentrate) produced per 100kg fresh juice fed to the process and the fraction of the feed that bypass the evaporator. c) Most of the volatile ingredients that provide that taste of the concentrated are contained in the fresh juice that bypasses the evaporator. You could get more of these ingredients in the final product by evaporator to (say) 90% solids instead of 58%; you could then bypass a greater fraction of the fresh juice and thereby obtain an even better tasting product. Suggest possible drawbacks to this proposal.
9. In the production of a bean oil, beans containing 13.0 wt% oil and 87.0 wt% solids are grounded and fed to a stirred tank (the extractor) along with a recycled stream of liquid n -hexane. The feed ratio is 3kg hexane/kg beans. The grounded beans are suspended in the liquid, and essentially all of the oil in the beans is extracted into the hexane. The extractor effluent passes to a filter. The filter cake contains 75.0 wt% bean solids and the balance bean oil and hexane, the latter two in the same ratio in which they emerge from the extractor. The filter cake is discarded and the liquid filtrate is fed to a heated evaporator in which the hexane is vaporized and the oil remains a liquid. The oil is stored in drums and shipped. The hexane vapour is subsequently cooled and condensed, and the liquid hexane condensate is recycled to the extractor.
a) Draw and label a flowchart of the process, do the degree-of-freedom analysis, and write in an efficient order the equation you would solve to determine all unknown stream variables. b) Calculate the yield of bean oil product (kg oil/kg beans fed), the required fresh hexane feed (kg/C6H14 /kg beans fed), and the recycle to fresh feed ratio (kg hexane recycled/kg fresh feed).
10. Ammonia is burned to form nitric oxide in the following reaction:
4NH3 + 5O2 → 4NO + 6H2O
a) Calculate the ratio (lb-mole o2 react/lb-mole NO formed). 11.Titanium dioxide (TiO2) is used extensively as a white pigment. It is produced from an ore that contains ilmenite (FeTiO 3 ) and ferric oxide (Fe
b) If ammonia is fed to a continuous reactor at a rate of 100.0 kmol NH3/h, what oxygen feed rate (kmol/h) would correspond to% excess O2?
c) If 50.0kg of ammonia and 100.0kg of oxygen are fed to a batch reactor, determine the limiting reactant, the percentage by which the other reactant is in excess, and the extent of reaction (mol) and mass of NO produced (kg) if the reaction proceeds to complet ion.
Suppose an ore containing 24.3% Ti by mass is digested with an 80% H2SO4 solution, supplied in 50% excess of the amount needed to convert all the ilmenite to titanyl sulphate and all the ferric oxide to ferric sulphate [Fe(SO4)3]. Further suppose that 89% of the ilmenite actually decomposes. Calculate the masses (kg) of ore and 80% sulphuric acid solution that must be fed to produce 1000kg of pure TiO2.
12.Methanol is formed from carbon monoxide and hydrogen in the gas-phase reaction
CO + 2H 2 D CH3OH The mole fractions of the reactive species at equilibrium satisfy the reaction
(A) (B) (C)
Where P is the total pressure (atm), K e the reaction equilibrium constant (atm -2 ), and T the temperature (K). The equilibrium constant K e equals 10.5 at 373K, and 2.316 X 10 -4 at 573K. A semilog plot of K e (logarithmic scale) versus 1/ T (rectangular scale) is approximately linear between T = 300 K and T = 600 K 13.
a) Derive a formula for K e (T), and use to show that K e (450K) = 0.0548 atm -2 .
b) Write expressions for n A , n B and n C (gram-moles of each species), and y A, y B, and y C, in terms of n A0, n B0, n C0 and x e where x e (mol) is the value of the extent of reaction at equilibrium.
c) Suppose you begin with equimolar quantities of CO and H2 and no CH3OH, and the reaction proceeds to equilibrium at 423K and 2.00atm. Calculate the molar composition of the product ( y A , y B , and y C ) and the fractional conversion of CO.
6 HF + SiO2(aq) → H2SiF6(s) + 2 H2O(l)
The hydrogen fluoride exiting from the reactor is subsequently dissolved in enough water to produce 60.0wt% hydrofluoric acid. Calculate the quantity of fluorite ore needed to produce a metric ton of aqueous hydrofluoric acid. (Note some of the data given is not needed to solve the problem.)
A single-pass conversion of 60.0% is achieved in the reactor. The methanol in the reactor product is separated from the formaldehyde and hydrogen in a multiple-unit process. The production rate of formaldehyde is 900.0 kg/h. a) Calculate the required feed rate of methanol to the process (kmol/h) if there is no recycle. 15. Methanol is synthesized from carbon monoxide and hydrogen in a catalytic reactor. The fresh feed to the process contains 32.0 mole% CO, 64.0% H
14.A catalytic reactor is used to produce formaldehyde from methanol from the reaction CH3OH → CHOH + H2
b) Suppose the recovered methanol is recycled to the reactor and the single-pass conversion remains 60%. Without doing any calculations, prove that you have enough information to determine the required fresh feed rate of methano l (kmol/h) and the rates (kmol/h) at which methanol enters and leaves the reactor.
a) For a basis of 100 mol fresh feed/h, calculate the production rate of methanol (mol/h), the molar flow rate and composition of the purge gas, and the overall and single-pass conversions.
b) Briefly explain in your own words the reason for including (i) the rececly stream and (ii) the purge stream in the design.
16. A gas contains 80.0 wt% propane, 15.0 wt% n-butane, and the balance water.
a) Calculate the molar composition of this gas on both a wet and a dry basis and the ratio (mol H 2 O/ mol dry gas).
b) If 100 kg/h of this fuel is to be burned with 30% excess air, what is the required air feed rate (kmol/h)? How would the answer change if the combustion were only 75% complete.
17. Butane is burned with air. No carbon m onoxide is present in the combustion products.
a) Use a degree of freedom analysis to prove that if the percentage excess air and the percentage conversion of butane are specified the molar composition of the product gas can be determined. b) Calculate the molar composition of the product gas for each of the following three cases:
i) theoretical air supplied, 100% conversion of butane;
ii) 20% excess air, 100% conversion of butane; and
iii) 20% excess air, 90% conversion of butane.
18. A gas containing methane, ethane, and carbon dioxide is analyzed with a gas chromatograph (GC) and flame ionization detector (FID): the GC separates the components of the gas, and the FID registers signals proportional to the amount of each hydrocarbon (but not CO 2 ) in its sample chamber.
T he area under each peak is proportional to the number of carbon atoms in the sample, so that 1 mol of ethane would yield a peak with twice the area of a peak corresponding to 1 mol of methane. This fuel is being burned with air in a continuous combustion chamber. The molar feed ratio of air to fuel was supposed to be 7:1, but you suspect the air flow meter is not functioning properly. To check it, you take a 0.50-mol sample of the product gas and pas it through the condenser, which condenses essentially all of the water in the sample. The condensate (which can be assumed to be pure water) is weighed and found to have a mass of 1.134g. The dry gas leaving the condenser is analyzed and found to contain no hydrocarbons, no CO, and 11,9% CO 2 . a) Calculate the molar composition (component mole fractions) of the fuel gas and the desired percent excess air. b) Calculate the actual molar feed ratio of air to fuel and the actual percent excess air. 19. The composition of coal is determined by a proximate analysis. The coal is first finely ground and air dried. Samples of the dried coal are then subjected to several operations, with the sample weights being recorded before and after each operation. Moisture content is determined as the weight loss when a sample is held at 105°C in an oxygen-free atmosphere for roughly 2 h, added to the weight loss in the initial drying step. Volatile matter (primarily organic tars) is determined by holding a sample at 925°C in an oxygen-free atmosphere for 7 min and subtracting the moisture loss from the total weight loss. Ash (or mineral matter – oxides and sulphates of silicon, aluminium, iron, calcium, sulphur, and trace minerals) is the residue that remains after a sample has been heated to 800°C in an oxygen-containing atmosphere until all the organic matter has been burned away. Fixed carbon is what is present in coal besides moisture, volatile matter,and ash. a) Use the following proximate analysis data to determine the percentages by mass of moisture, fixed carbon, volatile matter, and ash in coal: 
Air-dried at 25°C for 12 h: 1.207g (before) --> 1.147g (after)
The remaining tests are performed on air-dried samples.
Kept at 105°C for 2 h in the presence of N 2 : 1.234g (before) --> 1.204g (after)
Kept at 925°C for 7 min in the presence of N 2 : 1.347g (before) --> 0.811g (after)
Kept at 800°C for 1 h in the presence of O 2 : 1.175g (before) --> 0.111g (after)
b) If the mass ratio of C to H in the volatile matter is 6:1, calculate the gram-moles of air theoretically required to burn 1 metric ton of this coal.
20. Fuel oils contain primarily organic compounds and sulphur. The molar composition of the organic fraction of a fuel oil may be represented by the formula C p H q O r ; the mass fraction of sulphur in the fuel is xs (kg S/kg fuel); and the percentage excess air, Pxs, is defined in terms of the theoretical air required to burn only the carbon and hydrogen in the fuel. a) For a certain high-sulphur No.6 fuel oil, p = 0.71, q = 1.1, r = 0.003, and xs = 0.02. Calculate the composition of the stack gas on a dry basis if this fuel is burn
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