PROBLEMS
1.You buy 100 kg of cucumbers that contain 99% water. .A few days later they are found to be 98% water.ls it true that the cucumbers now only weigh 50 kg? 2. The fern Pteris vittata. has been shown (Nature, 409, 579 (2001)) to effectively extract arsenic from soils. The study showed that in normal soil, which contains 6 ppm of arsenic, in two weeks the fern reduced the soil concentration to 5 ppm while accumulating 755 ppm of arsenic. In this experiment, what was the ratio of the soil mass to the plant mass? The initial arsenic in the fern was 5 ppm. 3. 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 drier, and the resulting product contains 25% water, how much water is evaporated per ton of sludge sent to the drier. 4. The figure shown is a sketch of an artificial kidney, a medical device used to remove waste metabolites from your blood in cases of kidney malfunction. The dialyzing fluid passes across a hollow membrane, and the waste products diffuse from the blood into the dialyzing fluid. If the blood entering the unit flows at the rate of 220 mL/min, and the blood exiting the unit flows at the rate of 215 mL/min, how much water and urea (the main waste product) pass into the dialysate if the entering concentration of urea is 2.30 mg/mL and the exit concentration of urea is 1.70 mg/L? If the dialyzing fluid flows into the unit at the rate of 100 mL/min, what is the concentration of the urea in the dialysate?
4a. [Computational]
The figure shown is a sketch of an artificial kidney, a medical device used to remove waste metabolites from your blood in cases of kidney malfunction. The dialyzing fluid passes across a hollow membrane, and the waste products diffuse from the blood into the dialyzing fluid. If the blood entering the unit flows at the rate of {Bin} mL/min, and the blood exiting the unit flows at the rate of {Bout} mL/min, how many mg of urea (the main waste product) pass into the dialysate if the entering concentration of urea is {Xin} mg/mL and the exit concentration of urea is {Xout} mg/L? Ans. {Bin}*{Xin}-{Bout}*{Xout} 4b. [Computational]
The figure shown is a sketch of an artificial kidney, a medical device used to remove waste metabolites from your blood in cases of kidney malfunction. The dialyzing fluid passes across a hollow membrane, and the waste products diffuse from the blood into the dialyzing fluid. The blood entering the unit flows at the rate of {Bin} mL/min, and the blood exiting the unit flows at the rate of {Bout} mL/min. The entering concentration of urea is {Xin} mg/mL and the exit concentration of urea is {Xout} mg/L.
If the dialyzing fluid flows into the unit at the rate of {Din} mL/min, what is the concentration of the urea in the dialysate (in mg/L)? Ans. 1000*({Bin}*{Xin}-{Bout}*{Xout})/({Din}+({Bin}-{Bout}))
5. A multiple stage evaporator concentrates a weak NaOH solution from 3% to 18 %, and processes 2 tons of solution per day. How much product is made per day? How much water is evaporated per day? 6. 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 3000 pounds of an adhesive solution containing 13% polymer by weight. On hand is 500 pounds 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. 7. A lacquer plant must deliver 1000 lb of an 8% nitrocellulose solution. They stock a 5.5% solution. How much dry nitrocellulose must be dissolved in the solution to fill the order? 8. A gas containing 80% CH4 and 20% He is sent through a quartz diffusion tube (see Figure) to recover the helium. Twenty percent by weight of the original gas is recovered, and its composition is 50% He. Calculate the composition of the waste gas if 100 kg moles of gas are processed per minute.
8calculated. A gas containing {x}% CH4 and {=(100-{x})}% He by weight is sent through a quartz diffusion tube (see Figure) to recover the helium. {P} % by weight of the original gas is recovered, and its composition is {y}% He by weight. Calculate the percentage of Helium (by weight) in the waste gas if 100 kg moles of gas are processed per minute.
9. In many fermentations, the maximum amount of cell mass must be obtained. However, the amount of mass that can be made is ultimately limited by the cell volume. Cells occupy a finite volume and have a rigid shape so that they cannot be packed beyond a certain limit. There will always be some water remaining in the interstices between the adjacent cells, which represent the void volume that at best can be as low as 40% of the fermenter volume. Calculate the maximum cell mass on a dry basis per Liter of the fermenter that can be obtained if the wet cell density is 1.1 g/cm 3. Note that cells themselves consist of about 75% water and 25% solids, and cell mass is reported as dry weight in the fermentation industry. 10. A polymer blend is to be formed-from the three compounds whose composition approximate formulas are listed in the table. Determine the percentages of pound A, B, and C to be introduced into the mixture to achieve the desired composition.
Compound ( % ) Composition A B C Desired mixture (CH4)x 25 35 55 30 (C2H6)x 35 20 40 30 (C3H8)x 40 45 5 40 Total 100 100 100 100 How would you decide to blend compounds A, B, C, and D [(CH4)x = 10% , (C2H6)x= 30%,(C3H8)x = 60%] to achieve the desired mixture? 11. Your boss asks you to calculate the flow through a natural-gas pipeline. Since it is 20 in. in diameter, it is impossible to run the gas through any kind of meter or measuring device. You decide to add 100 lb of CO2 per minute to the gas through a small 1/2-in. piece of pipe, collect samples of the gas downstream, and analyze them for CO2. Several consecutive samples after 1hr are
time % CO2 1hr, 0 min 2.0 10min 2.2 20min 1.9 30 min 2.1 40min 2.0 (a) Calculate the flow of gas in pounds per minute at the point of injection. (b) Unfortunately for you, the gas upstream of the point of injection of CO 2 already contained 1.0 percent CO2. How much was your original flow estimate in error (in percent)? Note: In part (a) the natural gas is all methane, CH4.
12. 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 72.3 kg/min for 12 min. Five miles downstream from the injection point, the steady-state ammonia concentration is found to be 0.382 weight percent. The gas upstream from the point of ammonia injection contains no measurable ammonia. How many kilograms of natural gas are flowing through the pipelines per hour? 13. Water pollution in the Hudson River has claimed considerable recent attention, especially pollution from sewage outlets and industrial wastes. To determine accurately bow 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 after it mixes. On one test of the proposal you add ten pounds of NaBr per hour for 24 hours 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 60.3 lb/ft3 and river water density is 62.4 lb/ft 3. What is the flow rate of the sewage in lb/min? 14. A new process for separating a mixture of incompatible polymers, such as polyethylene terephthalate (PET) and polyvinyl chloride (PVC), promises to expand the recycling and reuse of plastic waste. The first commercial plant, at Celanese's recycling facility in Spartanburg, S.C., has been operating since February at a PET capacity of 15 million lb/yr. Operating cost: 0.5¢/lb. Targeted to replace the conventional sorting of individual PET bottles from PVC containers upstream of the recycling step, this process first chops the mixed waste with rotary-blade cutter to 0.5-in. chips. The materials are then suspended in water, and air is forced through to create a bubble-like froth that preferentially entraps the PVC because of its different surface-tension characteristics. A food-grade surfactant is also added to enhance the separation. The froth is skimmed away along with the PVC, leaving behind the PET material. For a feed with 2% PVC, the process has recovered almost pure PET with an acceptable PVC contamination level of 10 ppm. How many lb of PVC are recovered per year from the above cited process?
15. If 100 g of Na2SO4 is dissolved in 200 g of H2O and the solution is cooled until 100 g of Na2SO4 · 10H2O crystallizes out, find · (a) The composition of the remaining solution (mother liquor). (b) The grams of crystals recovered per 100 g of initial solution. 16. A chemist attempts to prepare some very pure crystals of borax (sodium tetraborate, Na 2B4O7 · 10H2O) by dissolving 100 g of Na 2B4O7 in 200 g of boiling water. He then carefully cools the solution slowly until some Na2B4O7· 10H2O recovered in the crystals recovered in the crystals per 100 g of total initial solution (Na2B4O7 plus H2O), if the residual solution at 55oC after the crystal are removed contains 12.4% Na2B4O7. 17. 1000 kg of FeCl 3·6H2O are added to a mixture of crystals of FeCl 3·H2O to produce a mixture of FeCl3·2.5H2O crystals. How much FeCl 3·H2O must be added to produce the most FeCl 3·2.5H2O? 18. The solubility of barium nitrate at 100 oC is 34 g/100 g of H 2O and at 0oC is 5.0 g/100 g of H 2O. If you start with 100 g of Ba (NO 3)2 and make a saturated solution is cooled to 0 oC, how much Ba (NO 3)2 is precipitated out of solution? The precipitated crystal carry along with them on their surface 4 g of H 2O per 100 g of crystals. 19. A water solution contains 60% Na 2S2O2 together with 1% soluble impurity. Upon cooling to 10 oC, Na2S2O2 · 5H2O crystallizes out. The solubility of this hydrate is 1.4Ib Na 2S2O2· 5H2O/lb crystal free water. The crystals removed carry as adhering solution 0.06 lb solution/lb crystals. When dried to remove the remaining water (but not the water of hydration), the final dry Na 2S2O2 · 5H2O crystals 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 100 lb of the original solution, calculate: (a) The amount of water added before cooling. (b) The percentage recovery of the Na 2S2O2 in the dried hydrated crystals. 20. Paper pulp is sold on the basis that contains 12 percent moisture; if the moisture exceeds this value, the purchaser can deduct any charges for the excess moisture and also deduct for the freight costs of the excess moisture. A shipment of pulp became wet and was received with a moisture of 22 percent. If the original price for the pulp was $40/ton of air-dry pulp and if the freight is $1.00/100lb shipped, what price should be paid per ton of pulp delivered? 21. A laundry can purchase soap containing 30% water for a price of $0.30/kg fob the soap manufacturing plant ( i.e., at the soap plant before shipping costs which are owed by the purchaser of the soap). It can also purchase a different grade of soap that contains only 5% water. The freight rate between the soap plant and the laundry is $6.05/100 kg. What is the maximum price the laundry should pay for the 5% soap?
22. A manufacturer of briquets has a contract to make briquets for barbecuing that are guaranteed to not contain over 10% moisture or 10% ash. The basic material they use has the analysis: moisture 12.4%, volatile material 16.6%, carbon 57.5%, and ash 13.5%. To meet the specifications ( at their limits) they plan to mix with the base material a certain amount of petroleum coke that has the analysis: volatile material 8.2%, carbon 88.7%, and moisture 3.1%. How much petroleum coke must be added per 100 lb of the base material? 23. 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 46.0 C5 0.6 Total 100.0 The flow rate is 5804 kg mol/day, If the overhead and bottoms streams leaving the process have the following compositions, what are the flow rates of the overhead and bottoms streams in kg mol/day? Component C3 i-C4 n- C4 C5 Total
Overhead 3.4 95.7 0.9 ___ 100.00
Mole % bottoms ___ 1.11 97.6 1.3 100.00
24. The organic fraction in the wastewater is measured in terms of the biological oxygen demand (BOD) material, namely the amount of dissolved oxygen required to biodegrade the organic contents. If the dissolved oxygen (DO) concentration in a body of water drops too low, the fish in the stream or lake may die. The Environmental Protection Agency has set the minimum summer levels for lakes at 5 mg/L of DO. (a) If a stream is flowing at 0.3 m 3/s and has an initial BOD of 5 mg/L before reaching the discharge point of a sewage treatment plant, and the plant discharges 3.785 ML/day of wastewater, with a concentration of 0.15 g/L of BOD; what will be the BOD concentration immediately below the discharge point of the plant? (b) The plant reports a discharge of 15.8 ML/day having a BOD of 72.09 mg/L. If the EPA measures the flow of the stream before the discharge point at 530 ML/day with 3 mg/L of BOD, and measures the downstream concentration of 5 mg/L of BOD, is the report correct?
25. Suppose that 100 L/min are drawn from a fermentation tank and passed through an extraction tank in which the fermentation product (in the aqueous phase) is mixed with an organic solvent, and then the aqueous phase is separated from the organic phase. The concentration of the desired enzyme ( 3-
hydroxybutyrate dehydrogenase )in the aqueous feed to the extraction tank is 10.2 g/L. The pure organic extraction solvent runs into the extraction tank at the rate of 9.5 L/min. If the ratio of the enzyme in the exit product stream (the organic phase) from the extraction tank to the concentration of the enzyme in the exit waste stream ( the aqueous phase )from the tank is D= 18.5( g/L organic)/(g/L aqueous), what is the fraction recovery of the enzyme and the amount recovered per min? Assume negligible miscibility between the aqueous and organic liquids in each other, and ignore any change in density on removal or addition of the enzyme to either stream.
26. Consider the following process for recovering NH 3 from a gas stream composed of N 2 and NH3 ( see figure below).
Flowing upward through the process is the gas stream, which can contain NH 3 and N2 but not solvent S, and flowing downward through the device is a liquid stream which contain NH 3 and liquid S but not N2. The weigh fraction of NH3 in the gas stream A leaving the process is related to the weight fraction of NH3 in the liquid stream B leaving the process by the following empirical relationship: NH3 = 2NH3. Given the data shown the figure above, calculate the flow rates and compositions of streams A and B. 27. MTBE (methyl tertiary butyl ether) is added to gasoline to increase the oxygen content of the gasoline. MTBE is soluble in water to some extent, and becomes a contaminant when the gasoline gets into surface or underground water. The gasoline used by boats has an MTBE content of 10%. The boats operate in a well-mixed flood control pond having the dimensions 3 km long, 1 km wide, and 3 m deep on the average. Suppose that each of the 25 boats on the pond spill 0.5 L of gasoline during 12 hours of daylight. The flow of water (that contains no MTBE) into the pond is 10 m 3/ hr, but no water leaves because the water level is well below the spillway of the pond. By how much will the concentration of MTBE increase in the pond after the end of 12 hours of boating? Data: The specific gravity of gasoline is 0.72.
27calculated. MTBE (methyl tertiary butyl ether) is added to gasoline to increase the oxygen content of the gasoline. MTBE is soluble in water to some extent, and becomes a contaminant when the gasoline gets into surface or underground water. The gasoline used by boats has an MTBE content of
{=100*{percent}}%. The boats operate in a well-mixed flood control pond having the dimensions {={L}/1000} km long, {={W}/1000} km wide, and {D} m deep on the average. Suppose that each of the {n} boats on the pond spill {V} L of gasoline during 12 hours of daylight. The flow of water (that contains
no MTBE) into the pond is {Q} m3/ hr, but no water leaves because the water level is well below the spillway of the pond. By how much will the concentration of MTBE increase in the pond after the end of 12 hours of boating? Data: The specific gravity of gasoline is 0.72.
Ans. {Percent}*{V}*{0.72}/(1000*({L}*{W}*{D}+12*{Q}))
