Solved: The feed to an ammonia synthesis reactor contains

Perform the following estimations without using a calculator. (a) Estimate the mass of water (kg) in an Olympic-size swimming pool. (b) A drinking glass is being filled from a pitcher. Estimate the mass flow rate of the water (g/s). (c) Twelve male heavyweight boxers coincidentally get on the same elevator in Great Britain. Posted on the elevator wall is a sign that gives the maximum safe combined weight of the passengers, Wmax, in stones. (A stone is a unit of mass equal to 14 lbm. It is commonly used in England as a measure of body weight, which, like the numerical equivalence between the lbm and lbf, is only valid at or near sea level.) If you were one of the boxers, estimate the lowest value of Wmax for which you would feel comfortable remaining on the elevator. (d) The Trans-Alaska Pipeline has an outside diameter of 4 ft and extends 800 miles from the North Slope of Alaska to the northernmost ice-free port in Valdez, Alaska. How many barrels of oil are required to fill the pipeline? (e) Estimate the volume of your body (cm3 ) in two different ways. (Show your work.) (f) A solid block is dropped into water and very slowly sinks to the bottom. Estimate its specific gravity

Calculate densities in lbm/ft3 of the following substances: (a) a liquid with density of 995 kg/m3. Use (i) conversion factors from the table on the inside front cover and (ii) Equation 3.1-2. (b) a solid with a specific gravity of 5.7. What did you assume to come up with your answer?

The specific gravity of gasoline is approximately 0.70. (a) Estimate the mass (kg) of 50.0 liters of gasoline. (b) The mass flow rate of gasoline exiting a refinery tank is 1150 kg/min. Estimate the volumetric flow rate in liters/s. (c) Estimate the average mass flow rate lbm/min delivered by a gasoline pump. (d) Gasoline and kerosene specific gravity 0:82 are blended to obtain a mixture with a specific gravity of 0.78. Calculate the volumetric ratio (volume of gasoline/volume of kerosene) of the two compounds in the mixture, assuming Vblend Vgasoline Vkerosene.

In September 2014 the average price of gasoline in France was 1.54 euro/liter, and the exchange rate was $1.29 per euro (). How much would you have paid, in dollars, for 50.0 kg of gasoline in France, assuming gasoline has a specific gravity of 0.71? What would the same quantity of gasoline have cost in the United States at the prevailing average price of $3.81/gal?

Liquid benzene and liquid n-hexane are blended to form a stream flowing at a rate of 1700 lbm/h. An on-line densitometer(an instrument used to determine density) indicates that the stream has a density of 0.810 g/mL. Using specific gravities from Table B.1, estimate the mass and volumetric feed rates of the Interactive Tutorial #1 Questions with Immediate Feedback 68 CHAPTER 3 Processes and Process Variables WEBC03 06/04/2015 20:23:44 Page 69 two hydrocarbons to the mixing vessel (in U.S. customary units). State at least two assumptions required to obtain the estimate from the recommended data.

You purchase six oranges that weigh a total of 2 lbf and 13 ounces. After cutting them open and squeezing all the juice your strength allows into a large measuring cup, you weigh the remaining pulp and orange peels. They weigh 1 lbf and 12 ounces and the total volume of the juice is 1.75 cups. What is the specific gravity of orange juice? State any assumptions you make

A small family home in Tucson, Arizona, has a rooftop area of 1967 square feet, and it is possible to capture rain falling on about 56% of the roof. A typical annual rainfall is about 14 inches. If the family wanted to install a tank to capture the rain for an entire year, without using any of it, what would be the required volume of the tank in m3 and in gallons? How much would the water weigh when the tank was full (in N and in lbf)?

At 25C, an aqueous solution containing 35.0 wt% H2SO4 has a specific gravity of 1.2563. A quantity of the 35% solution is needed that contains 195.5 kg of H2SO4. (a) Calculate the required volume (L) of the solution using the given specific gravity. (b) Estimate the percentage error that would have resulted if pure-component specific gravities of H2SO4 SG 1:8255 and water had been used for the calculation instead of the given specific gravity of the mixture.

Hot mix asphalt (HMA) is commonly used in the construction of roadways in the United States at a rate estimated to be 500,000,000 tons/year. A typical upper layer (there may be as many as 5 layers of different thicknesses and compositions) of a high-volume highway is composed of crushed stone (also known as crushed aggregate) and asphalt binder and is approximately 1.25 inches thick. The stone, which has a specific gravity of about 2.7, is mixed with asphalt binder (SG = 1.03) to form the HMA with a composition of approximately 95 wt% aggregate and 5% asphalt. What is the volume ft3 of asphalt binder and weight (tons) of HMA required for the top layer of a 15-mile segment of interstate highway with 5 lanes, each of which has a width of 12 ft?

A rectangular block of solid carbon (graphite) floats at the interface of two immiscible liquids. The bottom liquid is a relatively heavy lubricating oil, and the top liquid is water. Of the total block volume, 54.2% is immersed in the oil and the balance is in the water. In a separate experiment, an empty flask is weighed, 35:3 cm3 of the lubricating oil is poured into the flask, and the flask is reweighed. If the scale reading was 124.8 g in the first weighing, what would it be in the second weighing? (Suggestion: Recall Archimedes principle, and do a force balance on the block.)

A rectangular block floats in pure water with 0.5 inch above the surface and 1.5 inches below the surface. When placed in an aqueous solution, the block of material floats with 1 inch below the surface. Estimate the specific gravities of the block and the solution. (Suggestion: Call the horizontal crosssectional area of the block A. A should cancel in your calculations.)

An object of density \(\rho_{\mathrm{a}}\), volume \(V_a\), and weight \(W_a\) is thrown from a rowboat floating on the surface of a small pond and sinks to the bottom. The weight of the rowboat without the jettisoned object is \(W_b\). Before the object was thrown out, the depth of the pond was \(h_{\mathrm{p} 1}\), and the bottom of the boat was a distance \(h_{\mathrm{b} 1}\) above the pond bottom. After the object sinks, the values of these quantities are \(h_{\mathrm{p} 2} \text { and } h_{\mathrm{b} 2}\). The area of the pond is \(A_p\); that of the boat is \(A_{\mathrm{b}} \cdot A_{\mathrm{b}}\) may be assumed constant, so that the volume of water displaced by the boat is \(A_{\mathrm{b}}\left(h_{\mathrm{p}}-h_{\mathrm{b}}\right)\). (a) Derive an expression for the change in the pond depth \(\left(h_{\mathrm{p} 2}-h_{\mathrm{p} 1}\right)\). Does the liquid level of the pond rise or fall, or is it indeterminate? (b) Derive an expression for the change in the height of the bottom of the boat above the bottom of the pond \(\left(h_{\mathrm{b} 2}-h_{\mathrm{b} 1}\right)\). Does the boat rise or fall relative to the pond bottom, or is it indeterminate?

Since the 1960s, the Free Expression Tunnel at North Carolina State University has been the Universitys way to combat graffiti on campus. The tunnel is painted almost daily by various student groups to advertise club meetings, praise athletic accomplishments, and declare undying love. You and your engineering classmates decide to decorate the tunnel with chemical process flowcharts and key Adapted from a problem contributed by Paul Blowers of the University of Arizona. Problems 69 WEBC03 06/04/2015 20:23:44 Page 70 equations found in your favorite text, so you purchase a can of spray paint. The label indicates that the can holds nine fluid ounces, which should cover an area of approximately 25 ft2. (a) You measure the tunnel and find that it is roughly 8 feet wide, 12 feet high, and 148 feet long. Based on the stated coverage, how many cans of spray paint would it take to apply one coat to the walls and ceiling of the tunnel? (b) Having just heard a lecture on process safety in your engineering class, you want to take appropriate safety precautions while painting the tunnel. One useful source for this type of information is the Safety Data Sheet (SDS), a document used in industry to provide workers and emergency personnel with procedures for safely handling or working with a specified chemical. Other sources of information about hazardous substances can be found in handbooks,5 and some countries, including the United States, have laws that require employers to provide their employees with Safety Data Sheets.6 Besides composition information, the SDS contains information such as physical properties (melting point, boiling point, flash point, etc.), other threats to health and safety, recommended protective equipment, and recommended procedures for storage, disposal, first aid, and spill handling. The SDS can typically be found online for most common substances. Search the web for spray paint SDS and find a representative SDS for a typical spray paint product. Based on the document you find, what are the top three hazards that you might encounter during your tunnel painting project? Suggest one safety precaution for each listed hazard.

Limestone (calcium carbonate) particles are stored in 50-L bags. The void fraction of the particulate matter is 0.30 (liter of void space per liter of total volume) and the specific gravity of solid calcium carbonate is 2.93. (a) Estimate the bulk density of the bag contents (kg CaCO3/liter of total volume). (b) Estimate the weight (W) of the filled bags. State what you are neglecting in your estimate. (c) The contents of three bags are fed to a ball mill, a device something like a rotating clothes dryer containing steel balls. The tumbling action of the balls crushes the limestone particles and turns them into a powder. (See pp. 21-64 of Perrys Chemical Engineers Handbook, 8th ed.) The limestone coming out of the mill is put back into 50-L bags. Would the limestone (i) just fill three bags, (ii) fall short of filling three bags, or (iii) fill more than three bags? Briefly explain your answer.

A useful measure of an individual’s physical condition is the fraction of his or her body that consists of fat. This problem describes a simple technique for estimating this fraction by weighing the individual twice, once in air and once submerged in water. (a) A man has body mass \(m_b\) = 122:5 kg. If he stands on a scale calibrated to read in newtons, what would the reading be? If he then stands on a scale while he is totally submerged in water at \(30^{\circ} \mathrm{C}\) (specific gravity = 0:996) and the scale reads 44.0 N, what is the volume of his body (liters)? (Hint: Recall from Archimedes’ principle that the weight of a submerged object equals the weight in air minus the buoyant force on the object, which in turn equals the weight of water displaced by the object. Neglect the buoyant force of air.) What is his body density, \(\rho_{\mathrm{b}}(\mathrm{kg} / \mathrm{L})\)? (b) Suppose the body is divided into fat and nonfat components, and that \(x_f\) (kilograms of fat/kilogram of total body mass) is the fraction of the total body mass that is fat: \(x_{\mathrm{f}}=\frac{m_{\mathrm{f}}}{m_{\mathrm{b}}}\) Prove that \(x_{\mathrm{f}}=\frac{\frac{1}{\rho_{\mathrm{b}}}-\frac{1}{\rho_{\mathrm{nf}}}}{\frac{1}{\rho_{\mathrm{f}}}-\frac{1}{\rho_{\mathrm{nf}}}}\) where \(\rho_{\mathrm{b}}, \rho_{\mathrm{f}}, \text { and } \rho_{\mathrm{nf}}\) are the average densities of the whole body, the fat component, and the nonfat component, respectively. [Suggestion: Start by labeling the masses \(\left(m_{\mathrm{f}} \text { and } m_{\mathrm{b}}\right)\) and volumes \((V_f and V_b)\) of the fat component of the body and the whole body, and then write expressions for the three densities in terms of these quantities. Then eliminate volumes algebraically and obtain an expression for \(m_f/m_b\) in terms of the densities.\(^7\) ] (c) If the average specific gravity of body fat is 0.9 and that of nonfat tissue is 1.1, what fraction of the man’s body in Part (a) consists of fat? (d) The body volume calculated in Part (a) includes volumes occupied by gas in the digestive tract, sinuses, and lungs. The sum of the first two volumes is roughly 100 mL and the volume of the lungs is roughly 1.2 liters. The mass of the gas is negligible. Use this information to improve your estimate of \(x_f\).

In April 2010, the worst oil spill ever recorded occurred when an explosion and fire on the Deepwater Horizon offshore oil-drilling rig left 11 workers dead and began releasing oil into the Gulf of Mexico. One of the attempts to contain the spill involved pumping drilling mud into the well to balance the pressure of escaping oil against a column of fluid (the mud) having a density significantly higher than those of seawater and oil. In the following problems, you may assume that seawater has a specific gravity of 1.03 and that the subsea wellhead was 5053 ft below the surface of the Gulf. (a) Estimate the gauge pressure (psig) in the Gulf at a depth of 5053 ft. (b) Measurements indicate that the pressure inside the wellhead is 4400 psig. Suppose a pipe between the surface of the Gulf and the wellhead is filled with drilling mud and balances that pressure. Estimate the specific gravity of the drilling mud. (c) The drilling mud is a stable slurry of seawater and barite SG 4:37. What is the mass fraction of barite in the slurry? (d) What would you expect to happen if the barite weight fraction were significantly less than that estimated in Part (c)? Explain your reasoning.

Aqueous solutions of the amino acid L-isoleucine (Ile) are prepared by putting 100.0 grams of pure water into each of six flasks and adding different precisely weighed quantities of Ile to each flask. The densities of the solutions at 50:0  0:05C are then measured with a precision densitometer, with the following results: r (g Ile/100 g H2O) 0.0000 0.8821 1.7683 2.6412 3.4093 4.2064 (g solution/cm3 ) 0.98803 0.98984 0.99148 0.99297 0.99439 0.99580 (a) Plot a calibration curve showing the mass ratio, r, as a function of solution density, , and fit a straight line to the data to obtain an equation of the form r a b. (b) The volumetric flow rate of an aqueous Ile solution at a temperature of 50C is 150 L/h. The density of a sample of the stream is measured at 50C and found to be 0:9940 g/cm3. Use the calibration equation to estimate the mass flow rate of Ile in the stream (kg Ile/h). (c) It has just been discovered that the thermocouple used to measure the stream temperature was poorly calibrated and the temperature was actually 47C.Wouldthe Ile mass flow rate calculated in Part (b) be too high or too low? State any assumption you make and briefly explain your reasoning.

The following data have been obtained for the effect of solvent composition on the solubility of a serine, an amino acid, at 10.0C: Volume % Methanol 0 10 20 30 40 60 80 100 Solubility (g/100 mL solvent) 22.72 18.98 11.58 6.415 4.205 1.805 0.85 0.65 Solution Density (g/mL) 1.00 0.98 0.97 0.95 0.94 0.91 0.88 0.79 The data were obtained by mixing known volumes of methanol and water to obtain the desired solvent compositions, and then slowly adding measured amounts of serine to each mixture until no more would go into solution. The temperature was held constant at 10.0C. SAFETY 7 If you cant work out the proof, take the given formula as valid and proceed to the next part. ENVIRONMENTAL BIOENGINEERING BIOENGINEERING Problems 71 WEBC03 06/04/2015 20:23:45 Page 72 (a) Derive an expression for solvent composition expressed as mass fraction of methanol, x, as a function of volume fraction of methanol, f . (b) Prepare a table of solubility of serine (g serine/g solution) versus mass fraction of methanol

Before a rotameter can be used to measure an unknown flow rate, a calibration curve of flow rate versus rotameter reading must be prepared. A calibration technique for liquids is illustrated below. A flow rate is set by adjusting the pump speed; the rotameter reading is recorded, and the effluent from the rotameter is collected in a graduated cylinder for a timed interval. The procedure is carried out twice for each of several pump settings. ROTAMETER GRADUATED CYLINDER STOPWATCH VARIABLESPEED PUMP Rotameter Collection Volume Reading Time (min) Collected (cm3 ) 2 1 297 2 1 301 4 1 454 4 1 448 6 0.5 300 6 0.5 298 8 0.5 371 8 0.5 377 10 0.5 440 10 0.5 453 (a) Assuming the liquid is water at 25C, draw a calibration curve of mass flow rate, m_ (kg/min), versus rotameter reading, R, and use it to estimate the mass flow rate of a water stream for which the rotameter reading is 5.3. (b) The mean difference between duplicates, Di , provides an estimate of the standard deviation of a single measurement, which was given the symbol sx in Eq. 2.5-4: sx  ffiffiffi p 2 Di 0:8862Di Moreover, confidence limits on measured values can be estimated to a good approximation using the mean difference between duplicates. For example, if a single measurement of Y yields a value Ymeasured, then there is a 95% probability that the true value of Y falls within the 95% confidence limits Ymeasured 1:74Di and Ymeasured 1:74Di. 8 For a measured flow rate of 610 g/min, estimate the 95% confidence limits on the true flow rate.

How many of the following are found in 15.0 kmol of xylene (C8H10)? (a) kg C8H10; (b) mol C8H10; (c) lb-mole C8H10; (d) mol (g-atom) C; (e) mol H; (f) g C; (g) g H; (h) molecules of C8H10.

Liquid toluene is flowing through a pipe at a rate of \(175 \mathrm{~m}^{3} / \mathrm{h}\). (a) What is the mass flow rate of this stream in kg/min? (b) What is the molar flow rate in mol/s? (c) In fact, the answer to Part (a) is only an approximation that is almost certain to be slightly in error. What did you have to assume to obtain the answer?

A mixture of methanol and propyl acetate contains 25.0 wt% methanol. (a) Using a single dimensional equation, determine the g-moles of methanol in 200.0 kg of the mixture. (b) The flow rate of propyl acetate in the mixture is to be 100.0 lb-mole/h. What must the mixture flow rate be in \(\mathrm{lb}_{\mathrm{m}} / \mathrm{h}\)?

The feed to an ammonia synthesis reactor contains 25 mole% nitrogen and the balance hydrogen. The flow rate of the stream is 3000 kg/h. Calculate the rate of flow of nitrogen into the reactor in kg/h. (Suggestion: First calculate the average molecular weight of the mixture.)

As described in Problem 3.16, a drilling mud is a slurry pumped into oil wells being drilled. The mud has several functions: It floats rock cuttings to the top of the well where they can easily be removed; lubricates and cools the drill bit; and keeps loose solids and water from leaking into the borehole. A drilling mud is prepared by blending barite SG 4:37 with seawater SG 1:03. The seawater has a dissolved salt content of approximately 3.5 wt%. You have been asked to determine the specific gravity of the mud and the wt% barite. You collect a sample of the mud from a blending tank on an oil platform and make the following observations: (i) The mud appears homogeneous, even after standing for 2 days; (ii) the tare mass of the calibrated vessel into which you pour the sample of mud is 118 g; (iii) the volume of the collected sample is 100 mL, and the mass of the collection vessel and sample is 323 g; and (iv) the mass of the vessel and residue remaining after completely evaporating water from the sample is 254 g. (a) Estimate the specific gravity of the mud and the wt% barite. (b) What is the practical importance of Observation (i)?

A mixture is 10.0 mole% methyl alcohol, 75.0 mole% methyl acetate (C3H6O2), and 15.0 mole% acetic acid. Calculate the mass fractions of each compound. What is the average molecular weight of the mixture? What would be the mass (kg) of a sample containing 25.0 kmol of methyl acetate?

Certain solid substances, known as hydrated compounds, have well-defined molecular ratios of water to some other species. For example, calcium sulfate dihydrate (commonly known as gypsum, CaSO4
2H2O), has 2 moles of water per mole of calcium sulfate; alternatively, it may be said that 1 mole of gypsum consists of 1 mole of calcium sulfate and 2 moles of water. The water in such substances is called water of hydration. (More information about hydrated salts is given in Chapter 6.) In order to eliminate the discharge of sulfuric acid into the environment, a process has been developed in which the acid is reacted with aragonite (CaCO3) to produce calcium sulfate. The calcium sulfate then comes out of solution in a crystallizer to form a slurry (a suspension of solid particles in a liquid) of solid gypsum particles suspended in an aqueous CaSO4 solution. The slurry flows from the crystallizer to a filter in which the particles are collected as a filter cake. The filter cake, which is 95.0 wt% solid gypsum and the remainder CaSO4 solution, is fed to a dryer in which all water (including the water of hydration in the crystals) is driven off to yield anhydrous (water-free) CaSO4 as product. A flowchart and relevant process data are given below. Solids content of slurry leaving crystallizer: 0.35 kg CaSO4
2H2O/L slurry CaSO4 content of slurry liquid: 0.209 g CaSO4/100 g H2O Specific gravities: CaSO4
2H2O(s), 2.32; liquid solutions, 1.05 Slurry Filter cake Filtrate Water vapor CaSO4(s) CaSO4(aq) CRYSTALLIZER FILTER DRYER (a) Briefly explain in your own words the functions of the three units (crystallizer, filter, and dryer). (b) Take a basis of one liter of solution leaving the crystallizer and calculate the mass (kg) and volume (L) of solid gypsum, the mass of CaSO4 in the gypsum, and the mass of CaSO4 in the liquid solution. (c) Calculate the percentage recovery of CaSO4that is, the percentage of the total CaSO4 (precipitated plus dissolved) leaving the crystallizer recovered as solid anhydrous CaSO4. (d) List five potential negative consequences of discharging H2SO4 into the river passing the plant.

In the manufacture of pharmaceuticals, most active pharmaceutical ingredients (APIs) are made in solution andthen recovered by separation. Acetaminophen, a pain-killing drug commercially marketed as Tylenol, is synthesized in an aqueous solution and subsequently crystallized. The slurry of crystals is sent to a centrifuge from which two effluent streams emerge: (1) a wet cake containing 90.0 wt% solid acetaminophen MW 151 g/mol and 10.0 wt% water (plus some acetaminophen and other dissolved substances, which we will neglect), and (2) a highly dilute aqueous solution of acetaminophen that is discharged from the process. ENVIRONMENTAL Equipment Encyclopedia crystallizer, filter, dryer www.wiley.com/college/felder Adapted from Stephanie Farrell, Mariano J. Savelski, and C. Stewart Slater (2010), Integrating Pharmaceutical Concepts into Introductory Chemical Engineering CoursesPart I, http://pharmahub.org/resources/360. BIOENGINEERING Problems 73 WEBC03 06/04/2015 20:23:45 Page 74 The wet cake is fed to a dryer where the water is completely evaporated, leaving the residual acetaminophen solids bone dry. If the evaporated water were condensed, its volumetric flow rate would be 50.0 L/h. Following is a flowchart of the process, which runs 24 h/day, 320 days/yr. A denotes acetaminophen. CENTRIFUGE A(s) in A(aq) A(aq) to waste disposal DRYER 50.0 L H2O(l)/h Wet cake 90.0 wt% A(s) 10.0 wt% H2O(l) mA(tonne A(s)/yr) (a) Calculate the yearly production rate of solid acetaminophen (tonne/yr), using as few dimensional equations as possible. (b) A proposal has been made to subject the liquid solution leaving the centrifuge to further processing to recover more of the dissolved acetaminophen instead of disposing of the solution. On what would the decision depend?

Things were going smoothly at the Breaux Bridge Drug Co. pilot plant during the midnight to 8 a.m. shift until Therèse Lagniappe, the reactor operator, let the run instruction sheet get too close to the Coleman stove that was being used to heat water to prepare Lagniappe’s bihourly cup of Community Coffee. What followed ended in a total loss of the run sheet, the coffee, and a substantial portion of the novel Lagniappe was writing. Remembering the less than enthusiastic reaction she got the last time she telephoned her supervisor in the middle of the night, Lagniappe decided to rely on her memory of the required flow-rate settings. The two liquids being fed to a stirred-tank reactor were circulostoic acid (CSA: MW = 75, SG = 0:90) and flubitol (FB: MW = 90, SG = 0:75). The product from the system was a popular over-the-counter drug that simultaneously cures high blood pressure and clumsiness. The molar ratio of the two feed streams had to be between 1.05 and 1.10 mol CSA/mol FB to keep the contents of the reactor from forming a solid plug. At the time of the accident, the flow rate of CSA was 45.8 L/min. Lagniappe set the flow of flubitol to the value she thought had been in the run sheet: 55.2 L/min.Was she right? If not, how would she have been likely to learn of her mistake? (Note: The reactor was stainless steel, so she could not see the contents.)

A mixture of methanol (methyl alcohol) and water contains 60.0% water by mass. (a) Assuming volume additivity of the components, estimate the specific gravity of the mixture at 20C. What volume (in liters) of this mixture is required to provide 150 mol of methanol? (b) Repeat Part (a) with the additional information that the specific gravity of the mixture at 20C is 0.9345 (making it unnecessary to assume volume additivity). What percentage error results from the volume-additivity assumption?

Coal being used in a power plant at a rate of 8000 lbm/min has the following composition: Component Weight % (dry basis) Ash 7.2 Sulfur 3.5 Hydrogen 5.0 Carbon 75.2 Nitrogen 1.6 Oxygen 7.5 In addition, there are 4.58 lbm H2O per lbm of coal. Determine the molar flow rate of each element in the coal (including water) other than ash.

Drop-on-demand (DoD) technology is an emerging form of drug delivery in which a reservoir is filled with a solution of an active pharmaceutical ingredient (API) dissolved in a volatile liquid, and a device Equipment Encyclopedia centrifuge www.wiley.com/college/felder BIOENGINEERING Adapted from Stephanie Farrell, Mariano J. Savelski, and C. Stewart Slater (2010), Integrating Pharmaceutical Concepts into Introductory Chemical Engineering CoursesPart I, http://pharmahub.org/resources/360. 74 CHAPTER 3 Processes and Process Variables WEBC03 06/04/2015 20:23:45 Page 75 sprays nanometer-scale drops of the solution onto an edible substrate, such as a small strip the size of a stick of chewing gum. The liquid evaporates very rapidly, causing the API to crystallize on the substrate. The exact dose required by a patient can be administered based on the known concentration of the API in the reservoir and the volume of solution deposited on the substrate, enabling greater dosage accuracy than can be provided by administering fractions of tablets. (a) A DoD device is charged with a 1.20 molar solution of ibuprofen (the API) in n-hexane. The molecular weight of ibuprofen is 206.3 g/mol. If a prescribed dosage is 5.0 mg ibuprofen/kg patient weight, how many milliliters of solution should be sprayed for a 245-pound man and a 65-pound child? How many drops are in each dose, assuming that each drop is a sphere with a radius of 1 nm? (b) The DoD device is to be automated, so that the operator enters a patients body weight into a computer that determines the required solution volume and causes that volume to be sprayed on the substrate. Derive a formula for the volume, Vdose (mL), in terms of the following variables: Ms (mol API/L) = molarity of reservoir solution SGs = specific gravity of reservoir solution MWAPI (g/mol) = molecular weight of API D (mg API/kg body weight) = prescribed dosage Wp (lbf) = patients weight Check your formula by verifying your solution to Part (a). (c) Calculate the surface-to-volume ratio of a sphere of radius r. Then calculate the total drop surface area of 1 mL (= 1 cm3 ) of the solution if it were sprayed as drops of (i) radius 1 nm and (ii) 1 mm. Speculate on the likely reason for spraying nanoscale drops instead of much larger drops.

A mixture of methane and air is capable of being ignited only if the mole percent of methane is between 5% and 15%. A mixture containing 9.0 mole% methane in air flowing at a rate of 7:00 102 kg/h is to be diluted with pure air to reduce the methane concentration to the lower flammability limit. Calculate the required flow rate of air in mol/h and the percent by mass of oxygen in the product gas. (Note: Air may be taken to consist of 21 mole% O2 and 79% N2 and to have an average molecular weight of 29.0.)

In the manufacture of paper, logs are cut into small chips, which are stirred into an alkaline solution that dissolves several of the chemical constituents of wood but not cellulose. The slurry of undissolved chips in solution is further processed to recover most of the original solution constituents and dried wood pulp. In one such process, wood chips with a specific gravity of 0.64 containing 45 wt% water and 47 wt% (dry basis) cellulose are treated to produce 1400 tons/day of dry wood pulp containing 85 wt% cellulose. Estimate the feed rate of logs (logs/min), assuming that the logs have an average diameter of 8 inches and an average length of 7 feet.

A liquid mixture is prepared by combining N different liquids with densities 1; 2; ... ; N. The volume of component i added to the mixture is Vi, and the mass fraction of this component in the mixture is xi. The components are completely miscible. The following two formulas provide estimates of the density of the liquid mixture, , if the volume of the mixture equals the sum of the pure-component volumes.9 Only one of the formulas is correct, however. i XN i1 xii ii 1 XN i1 xi i Determine whether (i) or (ii) is the correct formula (show your proof), and then use the correct formula to estimate the density (g/cm3 ) of a liquid mixture containing 60.0 wt% acetone, 25.0 wt% acetic acid, and 15.0 wt% carbon tetrachloride.

A gaseous mixture of CO, \(CO_2\), \(CH_4\), and \(N_2\) is analyzed with a gas chromatograph (see Problem 3.36). The output appears on a computer monitor, as shown here. For each of the three species, the area under the peak is approximately proportional to the number of moles of the indicated substance in the sample. From other information, it is known that the molar ratio of methane (\(CH_4\)) to nitrogen is 0.200. (a) What are the mole fractions of the four species in the gas? (b) What is the average molecular weight of the gas?

A gas chromatograph (GC) is a device used to separate, identify, and quantify components of gas mixtures. It consists of a column of solid particles that adsorb the gas components to different extents. A sample of a mixture is injected into a steadily flowing carrier gas and passed through the column, and a detector at the outlet measures a variable (such as electrical conductivity) proportional to the concentration of each species in the gas emerging from the column. The greater the extent to which a species is adsorbed on the solid particles, the more slowly it is released and so the longer it takes to emerge from the column. The detector signal is often mapped as a series of peaks on a recorder, such as the plot in Problem 3.35. Each peak corresponds to a specific component, and the area under the peak is proportional to the amount of that component in the sample [nimol kiAi, where Ai is the area of the peak corresponding to the ith species]. The proportionality constants ki are determined in separate calibration experiments in which known amounts of the components are injected into the GC sample port and the corresponding peak areas are measured. Prepare a spreadsheet to calculate the composition of a mixture from a set of peak areas obtained from a chromatograph. The spreadsheet should appear as follows: Sample Species MW k Peak Area Mole Fraction Mass Fraction 1 CH4 16.04 0.150 3.6 C2H6 30.07 0.287 2.8 C3H8 0.467 2.4 0.353 C4H10 0.583 1.7 2 CH4 16.04 0.150 7.8 C2H6 2.4 . . . . . . . . . . . . . . . . . . . . . You may use additional columns to store intermediate quantities in the calculation of the mass and mole fractions. In the actual spreadsheet, replace the dashes () with numbers. Test your program on data for five mixtures of methane, ethane, propane, and n-butane. The k values for these species are those given in the above table, and the measured peaks are given below. For example, the area of the methane peak for the first mixture is 3.6, the area of the ethane peak for the same mixture is 2.8, and so on. Sample A1 A2 A3 A4 1 3.6 2.8 2.4 1.7 2 7.8 2.4 5.6 0.4 3 3.4 4.5 2.6 0.8 4 4.8 2.5 1.3 0.2 5 6.4 7.9 4.8 2.3

Concerns regarding emissions of CO2 into the atmosphere have increased substantially since an article on combustion of forests and grasslands was published in 1990.10 Data in the table below show global emissions of carbon-containing compounds released to the atmosphere from biomass combustion and from all combustion sources in 1990. Compound Metric Tons C, All Sources Metric Tons C, % from Biomass CO2 8700 40 CO 1100 26 CH4 380 10 The numbers in the middle column reflect annual quantities of carbon released to the atmosphere in the indicated compounds; for example, 8700 metric tons of carbon 8:7 106 kg C was released in carbon dioxide. (a) Determine the combined annual release (in metric tons) of all three species resulting from biomass combustion and the average molecular weight of the combined gases. (b) Find a reference on atmospheric pollution and list the environmental hazards associated with CO and CO2 release. What other elements might be released in environmentally hazardous forms if biomass is burned? (c) From recent data, estimate the percentage change in total CO2 emissions since 1990.

A 5.00-wt% aqueous sulfuric acid solution 1:03 g/ml flows through a 45-m long pipe with a 6.0 cm diameter at a rate of 82 L/min. (a) What is the molarity of sulfuric acid in the solution? (b) How long (in seconds) would it take to fill a 55-gallon drum, and how much sulfuric acid lbm would the drum contain? (You should arrive at your answers with two dimensional equations.) (c) The mean velocity of a fluid in a pipe equals the volumetric flow rate divided by the cross-sectional area normal to the direction of flow. Use this information to estimate how long (in seconds) it takes the solution to flow from the pipe inlet to the outlet.

You notice that the water in your friends swimming pool is cloudy and that the pool walls are discolored at the water line. A quick analysis reveals that the pH of the water is 8.0 when it should be 7.2. The pool is 5 m wide, 12 m long, and has an average depth of 2 m. What volume (mL) of 5.00 wt% sulfuric acid SG 1:03 should be added to return the pool to the desired pH?

A gas stream contains 18.0 mole% hexane and the remainder nitrogen. The stream flows to a condenser, where its temperature is reduced and some of the hexane is liquefied. The hexane mole fraction in the gas stream leaving the condenser is 0.0500. Liquid hexane condensate is recovered at a rate of 1.50 L/min. N2 C6H14(v) (5.00 mole%) N2 C6H14(v) (18.0 mole%) Liquid condensate 1.50 L C6H14 (l)/min CONDENSER (a) What is the flow rate of the gas stream leaving the condenser in mol/min? (Hint: First calculate the molar flow rate of the condensate and note that the rates at which C6H14 and N2 enter the unit must equal the total rates at which they leave in the two exit streams.) (b) What percentage of the hexane entering the condenser is recovered as a liquid? (c) Suggest a change you could make in the process operating conditions to increase the percentage recovery of hexane. What would be the downside?

The little-known rare earth element nauseum (atomic weight = 172) has the interesting property of being completely insoluble in everything but 25-year-old single-malt Scotch. This curious fact was discovered in the laboratory of Professor Ludwig von Schlimazel, the eminent German chemist whose invention of the bathtub ring won him the Nobel Prize. Having unsuccessfully tried to dissolve nauseum in 7642 different solvents over a 10-year period, Schlimazel finally came to the 30 mL of The Macsporran that was the only remaining liquid in his laboratory. Always willing to suffer personal loss the name of science, Schlimazel calculated the amount of nauseum needed to make up a 0.03 molar solution, put the Macsporran bottle on the desk of his faithful technician Edgar P. Settera, weighed out the calculated amount of nauseum and put it next to the bottle, and then wrote the message that has become part of history: “Ed Settera. Add nauseum!” How many grams of nauseum did he weigh out? (Neglect the change in liquid volume resulting from the nauseum addition.)

The half-life t1/2 of a radioactive species is the time it takes for half of the species to emit radiation and decay (turn into a different species). If a quantity N0 of the species is present at time t 0, the amount present at a later time t is given by the expression N N0 1 2
t=t1=2 Each decay event involves the emission of radiation. A unit of the intensity of radioactivity is a curie (Ci), defined as 3:7 1010 decay events per second. A 300,000-gallon tank has been storing aqueous radioactive waste since 1945. The waste contains the radioactive isotope cesium-137 137Cs, which has a half-life of 30.1 years and a specific radioactivity of 86.58 Ci/g. The isotope undergoes beta decay to radioactive barium-137, which in turn emits gamma rays and decays to stable (nonradioactive) barium with a half-life of 2.5 minutes. The concentration of 137Cs in 2013 was 2:50 103 g/L. (a) What fraction of the 137Cs would have to decay for the level of cesium-related radioactivity of the contents to be 1:00 103 Ci/L? What total mass of cesium (kg) would that loss represent? In what year would that level be reached? (b) What was the concentration of 137Cs in the tank (g/L) when the waste was first stored? (c) Explain why the radioactive cesium in the tank poses a significant environmental threat while the radioactive barium does not. 3.

The reaction A ! B is carried out in a laboratory reactor. According to a published article the concentration of A should vary with time as follows: CA CA0 exp kt where CA0 is the initial concentration of A in the reactor and k is a constant. (a) If CA and CA0 are in lb-moles/ft3 and t is in minutes, what are the units of k? (b) The following data are taken for CAt: t(min) CA(lb-mole/ft3 ) 0.5 1.02 1.0 0.84 1.5 0.69 2.0 0.56 3.0 0.38 5.0 0.17 10.0 0.02 Verify the proposed rate law graphically (first determine what plot should yield a straight line), and calculate CA0 and k. (c) Convert the formula with the calculated constants included to an expression for the molarity of A in the reaction mixture in terms of t (seconds). Calculate the molarity at t 265 s.

Perform the following pressure conversions, assuming when necessary that atmospheric pressure is 1 atm. Unless otherwise stated, the given pressures are absolute.(a) 2600 mm Hg to psi (b) 275 ft H2O to kPa (c) 3.00 atm to N/cm2 (d) 280 cm Hg to dyne/m2 (e) 20 cm Hg of vacuum to atm (absolute) (f) 25.0 psig to mm Hg (gauge) (g) 25.0 psig to mm Hg (absolute) (h) 325 mm Hg to mm Hg gauge (i) 45.0 psi to cm of carbon tetrachloride

A storage tank containing oil (SG = 0:92) is 10.0 meters high and 16.0 meters in diameter. The tank is closed, but the amount of oil it contains can be determined from the gauge pressure at the bottom. (a) A pressure gauge connected to the bottom of the tank was calibrated with the top of the tank open to the atmosphere. The calibration curve is a plot of height of oil, h(m), versus \(P_{\text {gauge }}\)(kPa). Sketch the expected shape of this plot. What height of oil would lead to a gauge reading of 68 kPa? What would be the mass (kg) of oil in the tank corresponding to this height? (b) An operator observes that the pressure gauge reading is 68 kPa and notes the corresponding liquid height from the calibration curve. What he did not know was that the absolute pressure above the liquid surface in the tank was 115 kPa when he read the gauge. What is the actual height of the oil? (Assume atmospheric pressure is 101 kPa.)

A rectangular block of height L and horizontal cross-sectional area A floats at the interface between two immiscible liquids, as shown below. L h0 h1 h2 Fluid 1 1(g/cm3 ) Fluid 2 2(g/cm3) Block b(g/cm3 ) (a) Derive a formula for the block density, b, in terms of the fluid densities 1 and 2, the heights h0, h1, and h2, and the cross-sectional area A. (It is not necessary that all of these variables appear in the final result.) (b) Force balances on the block can be calculated in two ways: (i) in terms of the weight of the block and the hydrostatic forces on the upper and lower block surfaces; and (ii) in terms of the weight of the block and the buoyant force on the block as expressed by Archimedes principle. Prove that these two approaches are equivalent.

In the movie, Willy Wonka and the Chocolate Factory, Augustus Gloop leans over the chocolate river to get a drink and falls in. He is sucked through the pipe leading to the fudge room where he is saved by the Oompa Loompa workers. Unfortunately, real-life accidents do not always have such happy endings, even when they involve chocolate. In a tragic 2009 accident, a worker suffered fatal injuries after falling into a cylindrical mixing vat that had an 8-ft diameter and was 8 ft tall. At the time of the accident, the vat was full of molten chocolate. (a) What was the total weight \((lb_f)\) of chocolate in the vat? The specific gravity of chocolate is approximately 1.24. (b) Determine the pressure (psig) at the bottom of the tank. (c) Speculate on whether a person would float or sink in the vat and list two possible causes of the worker’s death.

The viewing window in a diving suit has an area of roughly 65 \(\mathrm{cm}^{2}\). (a) If an attempt were made to maintain the pressure on the inside of the suit at 1 atm, what force \(\left(\mathrm{N} \text { and } \mathrm{lb}_{\mathrm{f}}\right)\) would the window have to withstand if the diver descended to a depth of 150 m. Take the specific gravity of the water to be 1.05. (b) Repeat the calculation of Part (a) for the deepest Guiness-verified SCUBA dive.

The great Boston molasses flood occurred on January 15, 1919. In it, 2.3 million gallons of crude molasses flowed from a 30-foot-high storage tank that ruptured, killing 21 people and injuring 150. The estimated specific gravity of crude molasses is 1.4. What were the mass of molasses in the tank in lbm and the pressure at the bottom of the tank in lbf/in2? Give at least two possible causes of the tragedy.

The chemical reactor shown below has a cover that is held in place by a series of bolts. The cover is made of stainless steel SG 8:0, is 3 inches thick, has a diameter of 24 inches, and covers and seals an opening 20 inches in diameter. During turnaround, when the reactor is taken out of service for cleaning and repair, the cover was removed by an operator who thought the reactor had been depressurized using a standard venting procedure. However, the pressure gauge had been damaged in an earlier process upset (the reactor pressure had exceeded the upper limit of the gauge), and instead of being depressurized completely, the vessel was under a gauge pressure of 30 psi. BOURDON GAUGE 3 in. 20 in. 24 in. BOLTS COVER REACTOR (a) What force lbf were the bolts exerting on the cover before they were removed? (Hint: Dont forget that a pressure is exerted on the top of the cover by the atmosphere.) What happened when the last bolt was removed by the operator? Justify your prediction by estimating the initial acceleration of the cover upon removal of the last bolt. (b) Propose an alteration in the turnaround procedure to prevent recurrence of an incident of this kind.

In the movie The Drowning Pool, private detective Lew Harper (played by Paul Newman) is trapped by the bad guy in a room containing a swimming pool. The room may be considered rectangular, 5 meters wide by 15 meters long, with an open skylight window 10 meters above the floor. There is a single entry to the room, reached by a stairway: a locked 2-m high by 1-m wide door, whose bottom is 1 meter above the floor. Harper knows that his enemy will return in eight hours and decides he can escape by filling the room with water and floating up to the skylight. He plugs the drain with his clothes, turns on the water valves, and puts his plan into action. Assume that water enters the room at about 10 times the rate at which it enters an average bathtub and that the door can withstand a maximum force of 4500 newtons. Estimate (i) whether the door will break before the room fills and (ii) whether Harper has time to escape if the door holds. State any assumptions you make.

A housing development is served by a water tower with the water level maintained between 20 and 30 meters above the ground, depending on demand and water availability. Responding to a residents complaint about the low flow rate of water at his kitchen sink, a representative of the developer measured the water pressure at the tap above the kitchen sink and at the junction between the water main (a pipe connected to the bottom of the water tower) and the feed pipe to the house. The junction is 5 m below the level of the kitchen tap. All water valves in the house were turned off. (a) If the water level in the tower was 25 m above tap level, what should be the gauge pressures (kPa) at the tap and junction? SAFETY Equipment Encyclopedia reactors www.wiley.com/college/felder SAFETY 80 CHAPTER 3 Processes and Process Variables WEBC03 06/04/2015 20:23:47 Page 81 (b) Suppose the pressure measurement at the tap was lower than your estimate in Part (a), but the measurement at the junction was as predicted. State a possible explanation. (c) If pressure measurements corresponded to the predictions in Part (a), what else could be responsible for the low water flow to the sink?

Two mercury manometers, one open-end and the other sealed-end, are attached to an air duct. The reading on the open-end manometer is 25 mm and that on the sealed-end manometer is 800 mm. Determine the absolute pressure in the duct, the gauge pressure in the duct, and the atmospheric pressure, all in mm Hg.

A student goes to the laboratory supply room and obtains five feet of clear plastic tubing with an outer diameter of 1/2 inch and a wall thickness of 1/16 inch. She bends the tube into a U shape with the open ends pointing up and uses a funnel to pour 75 mL of water into the tube. By blowing air into one end of the tube, she generates a 6-inch difference in the water levels on each side. (a) What was the pressure (atm) she exerted with her lungs on the water in the tube? State all assumptions you make. (b) If the fluid had been ethanol instead of water, what would the difference in the liquid levels have been?

Three different liquids are used in the manometer shown here. P1 P2 h1 h2 A B C (a) Derive an expression for P1 P2 in terms of A, B, C, h1, and h2. (b) Suppose fluid A is methanol, B is water, and C is a manometer fluid with a specific gravity of 1.37; pressure P2 121:0 kPa; h1 30:0 cm; and h2 24:0 cm. Calculate P1 (kPa).

The level of toluene (a flammable hydrocarbon) in a storage tank may fluctuate between 10 and 400 cm from the top of the tank. Since it is impossible to see inside the tank, an open-end manometer with water or mercury as the manometer fluid is to be used to determine the toluene level. One leg of the manometer is attached to the tank 500 cm from the top. A nitrogen blanket at atmospheric pressure is maintained over the tank contents. Toluene 10 cm < h < 400 cm To atmosphere N2 500 cm R Manometer fluid (H2O or Hg) (a) When the toluene level in the tank is 150 cm below the top h 150 cm, the manometer fluid level in the open arm is at the height of the point where the manometer connects to the tank. What manometer reading, R (cm), would be observed if the manometer fluid is (i) mercury, (ii) water? Which manometer fluid would you use, and why? Equipment Encyclopedia manometer www.wiley.com/college/felder Equipment Encyclopedia manometer www.wiley.com/college/felder Problems 81 WEBC03 06/04/2015 20:23:47 Page 82 (b) Briefly describe how the system would work if the manometer were simply filled with toluene. Give several advantages of using the fluid you chose in Part (a) over using toluene. (c) What is the purpose of the nitrogen blanket?

The liquid level in a tank is determined by measuring the pressure at the bottom of the tank. A calibration curve is prepared by filling the tank to several known levels, reading the bottom pressure from a Bourdon gauge, and drawing a plot of level (m) vs. pressure (Pa). (a) Would you expect the calibration curve to be a straight line? Explain your answer. (b) The calibration experiment was done using a liquid with a specific gravity of 0.900, but the tank is used to store a liquid with specific gravity of 0.800. Will the liquid level determined from the calibration curve be too high, too low, or correct? Explain. (c) If the actual liquid level is 8.0 meters, what value will be read from the calibration curve? If the tank has a height of 10.0 m, what value will be read from the curve when the tank overflows?

A fluid of unknown density is used in two manometersone sealed-end, the other across an orifice in a water pipeline. The readings shown here are obtained on a day when barometric pressure is 756 mm Hg. Patm P = 0 7.23 m 26 cm (a) (b) H2O What is the pressure drop (mm Hg) from point a to point b?

An open-end mercury manometer is connected to a low-pressure pipeline that supplies a gas to a laboratory. Because paint was spilled on the arm connected to the line during a laboratory renovation, it is impossible to see the level of the manometer fluid in this arm. During a period when the gas supply is connected to the line but there is no gas flow, a Bourdon gauge connected to the line downstream from the manometer gives a reading of 7.5 psig. The level of mercury in the open arm is 900 mm above the lowest part of the manometer. Paint PIPE BOURDON GAUGE h = 900 mm (a) When the gas is not flowing, the pressure is the same everywhere in the pipe. How high above the bottom of the manometer would the mercury be in the arm connected to the pipe? (b) When gas is flowing, the mercury level in the visible arm drops by 25 mm. What is the gas pressure (psig) at this moment?

An inclined manometer is a useful device for measuring small pressure differences. h 1 2 L Equipment Encyclopedia manometer www.wiley.com/college/felder Equipment Encyclopedia manometer www.wiley.com/college/felder Equipment Encyclopedia manometer www.wiley.com/college/felder 82 CHAPTER 3 Processes and Process Variables WEBC03 06/04/2015 20:23:47 Page 83 The formula given in Section 3.4 for the pressure difference in terms of the liquid-level difference h remains valid, but while h would be small and difficult to read for a small pressure drop if the manometer were vertical, L can be made quite large for the same pressure drop by making the angle of the inclination, , small. (a) Derive a formula for h in terms of L and . (b) Suppose the manometer fluid is water, the process fluid is a gas, the inclination of the manometer is 15, and a reading L 8:7 cm is obtained. What is the pressure difference between points 1 and 2 ? (c) The formula you derived in Part (a) would not work if the process fluid were a liquid instead of a gas. Give one definite reason and another possible reason.

An open-end mercury manometer is to be used to measure the pressure in an apparatus containing a vapor that reacts with mercury. A 10-cm layer of silicon oil SG 0:92 is placed on top of the mercury in the arm attached to the apparatus. Atmospheric pressure is 765 mm Hg. (a) If the level of mercury in the open end is 365 mm below the mercury level in the other arm, what is the pressure (mm Hg) in the apparatus? (b) When the instrumentation specialist was deciding on a liquid to put in the manometer, she listed several properties the fluid should have and eventually selected silicon oil. What might the listed properties have been?

An orifice meter (see Figure 3.2-1) is to be calibrated for the measurement of the flow rate of a stream of liquid acetone. The differential manometer fluid has a specific gravity of 1.10. h VALVE The calibration is accomplished by connecting the orifice meter in series with a rotameter that has previously been calibrated for acetone, adjusting a valve to set the flow rate, and recording the flow rate (determined from the rotameter reading and the rotameter calibration curve) and the differential manometer reading, h. The procedure is repeated for several valve settings to generate an orifice meter calibration curve of flow rate versus h. The following data are taken. Manometer Reading h(mm) Flow Rate V_(mL/s) 0 0 5 62 10 87 15 107 20 123 25 138 30 151 (a) For each of the given readings, calculate the pressure drop across the orifice, P(mm Hg). (b) The flow rate through an orifice should be related to the pressure drop across the orifice by the formula V_ KP n Verify graphically that the given orifice calibration data are correlated by this relationship, and determine the values of K and n that best fit the data. (c) Suppose the orifice meter is mounted in a process line containing acetone and a reading h 23 mm is obtained. Determine the volumetric, mass, and molar flow rates of acetone in the line.

Convert the temperatures in Parts (a) and (b) and temperature intervals in Parts (c) and (d): (a) T 85F to R, C, K (b) T 10C to K, F, R Equipment Encyclopedia manometer www.wiley.com/college/felder Equipment Encyclopedia orifice meter www.wiley.com/college/felder Problems 83 WEBC03 06/04/2015 20:23:47 Page 84 (c) T 85C to K, F, R (d) T 150R to F, C, K

A temperature scale that never quite caught on was formulated by the Austrian chemist Johann Sebastian Farblunget. The reference points on this scale were \(0^{\circ} \mathrm{FB}\), the temperature below which Farblunget’s postnasal drip began to bother him, and \(1000^{\circ} \mathrm{FB}\), the boiling point of beer. Conversions between \({ }^{\circ} \mathrm{C} \text { and }{ }^{\circ} \mathrm{FB}\) can be accomplished with the expression \(T\left({ }^{\circ} \mathrm{C}\right)=0.0940 T\left({ }^{\circ} \mathrm{FB}\right)+4.00\) Louis Louis, Farblunget’s French nephew, attempted to follow in his uncle’s footsteps by formulating his own temperature scale. He defined the degree Louie using as reference conditions the optimum serving temperature of marinated snails \(\left(100^{\circ} \mathrm{L} \text { corresponding to } 15^{\circ} \mathrm{C}\right)\) and the temperature at which the elastic in his briefs began to relax \(\left(100^{\circ} \mathrm{L} \text { corresponding to } 43^{\circ} \mathrm{C}\right)\). (a) At what temperature in \({ }^{\circ} \mathrm{F}\) does beer boil? (b) What is the temperature interval of 10.0 Farblunget degrees equivalent to in \({ }^{\circ} \mathrm{C}, \mathrm{K},{ }^{\circ} \mathrm{F} \text {, and }{ }^{\circ} \mathrm{R} \text { ? }\) (c) Derive equations for \(T\left({ }^{\circ} \mathrm{C}\right)\) in terms of \(T\left({ }^{\circ} \mathrm{L}\right)\) (see Example 3.5-1) and \(T\left({ }^{\circ} \mathrm{L}\right)\) in terms of \(T\left({ }^{\circ} \mathrm{FB}\right)\). (d) What is the boiling point of ethane at 1 atm (Table B.1) in \({ }^{\circ} \mathrm{F}, \mathrm{K},{ }^{\circ} \mathrm{R},{ }^{\circ} \mathrm{FB} \text {, and }{ }^{\circ} \mathrm{L} \text { ? }\) (e) What is a temperature interval of 50.0 Louie degrees equivalent to in Celsius degrees, Kelvin degrees, Fahrenheit degrees, Rankine degrees, and Farblunget degrees?

A thermocouple is a temperature-measurement device that consists of two dissimilar metal wires joined at one end. An oversimplified diagram follows. V(mV) Metal 1 Metal 2 POTENTIOMETER A voltage generated at the metal junction is read on a potentiometer or millivoltmeter. When certain metals are used, the voltage varies linearly with the temperature at the junction of the two metals: VmV aTC b An iron-constantan thermocouple (constantan is an alloy of copper and nickel) is calibrated by inserting its junction in boiling water and measuring a voltage V 5:27 mV, and then inserting the junction in silver chloride at its melting point and measuring V 24:88 mV. (a) Derivethelinear equation forVmVinterms ofTC. Then convertitto an equation forT interms ofV. (b) If the thermocouple is mounted in a chemical reactor and the voltage is observed to go from 10.0 mV to 13.6 mV in 20 s, what is the average value of the rate of change of temperature, dT/dt, during the measurement period? (c) State the principal benefits and disadvantages of thermocouples.

A thermostat control with dial markings from 0 to 100 is used to regulate the temperature of an oil bath. A calibration plot on logarithmic coordinates of the temperature, TF, versus the dial setting, R, is a straight line that passes through the points R1 20:0; T1 110:0F and R2 40:0; T2 250:0F. (a) Derive an equation for TF in terms of R. (b) Estimate the thermostat setting needed to obtain a temperature of 320F. (c) Suppose you set the thermostat to the value ofRcalculated in Part (b), and the reading of a thermocouple mounted in the bath equilibrates at 295F instead of 320F. Suggest several possible explanations.

As will be discussed in detail in Chapter 5, the ideal-gas equation of state relates absolute pressure, P(atm); gas volume, V(liters); number of moles of gas, nmol; and absolute temperature, T(K): PV 0:08206nT (a) Convert the equation to one relating Ppsig, Vft3, nlb-mole, and TF. (b) A 30.0 mole% CO and 70.0 mole% N2 gas mixture is stored in a cylinder with a volume of 3.5 ft3 at a temperature of 85F. The reading on a Bourdon gauge attached to the cylinder is 500 psi. Calculate the total amount of gas (lb-mole) and the mass of CO lbm in the tank. Equipment Encyclopedia thermocouple www.wiley.com/college/felder 84 CHAPTER 3 Processes and Process Variables WEBC03 06/04/2015 20:23:48 Page 85 (c) Approximately to what temperature (F) would the cylinder have to be heated to increase the gas pressure to 3000 psig, the rated safety limit of the cylinder? (The estimate would only be approximate because the ideal gas equation of state would not be accurate at pressures this high.)

Streams of methane and air (79 mole% N2, the balance O2) are combined at the inlet of a combustion furnace preheater. The pressures of each stream are measured with open-end mercury manometers, the temperatures are measured with resistance thermometers, and the volumetric flow rates are measured with orifice meters. PREHEATER Measurement point 3 Measurement point 1 Measurement point 2 CH4 Air Data: Flowmeter 1: V1 947 m3/h Flowmeter 2: V2 195 m3/min Manometer 1: h1 232 mm Manometer 2: h2 156 mm Manometer 3: h3 74 mm Resistance thermometer 1: r1 26:159 ohms Resistance thermometer 2: r2 26:157 ohms Resistance thermometer 3: r3 44:789 ohms Atmospheric pressure: A sealed-end mercury manometer reads h 29:76 inches The resistance thermometers were calibrated by measuring their resistances at the freezing and boiling points of water, with the following results: T 0C: r 23:624 ohms T 100C: r 33:028 ohms A straight-line relationship between T and r may be assumed. The relationship between the total molar flow rate of a gas and its volumetric flow rate is, to a good approximation, given by a form of the ideal gas equation of state: n_ kmol s
12:186PatmV_m3/s TK where P is the absolute pressure of the gas. (a) Derive the resistance thermometer calibration formula for TC in terms of rohm. (b) Convert the given gas law expression to an expression for n_kmol/min in terms of Pmm Hg, TC, and V_m3/min. (c) Calculate the temperatures and pressures at points 1, 2, and 3. (d) Calculate the molar flow rate of the combined gas stream. (e) Calculate the reading of flowmeter 3 in m3/min. (f) Calculate the total mass flow rate and the mass fraction of the methane at point 3.

You are part of a team working on the development of a process in which a mineral species (labeled A for proprietary reasons) undergoes a reaction to form a new pigment to be used in house paints. In a series of experiments in a large well-mixed stirred tank reactor, you fill a tank with a known quantity of an inert liquid, bring the liquid up to a specified temperature, add a known quantity of A, and measure the concentration of A in the tank as a function of time. The reaction gives off heat as it progresses, but cooling water circulating in a jacket around the reactor keeps the temperature of the reacting mixture constant. The following data are recorded. A research article indicates that concentration of A should vary with time according to the following expression: \(C_{\mathrm{A}}(t)=\frac{1}{\frac{1}{C_{\mathrm{A} 0}}+k t}\) (1) where \(C_{\mathrm{A} 0}(\mathrm{~mol} / \mathrm{L})\) is the initial concentration of A in the reactor \(\left[C_{\mathrm{A}}(t=0)\right]\) and k is called the reaction rate constant. Despite being called a constant, k is a strong function of the absolute temperature in the reactor: \(k(T)=k_{0} \exp \left(-\frac{E_{\mathrm{a}}}{R T(\mathrm{~K})}\right)\) (2) In this equation (known as the Arrhenius equation after the Swedish chemist who proposed it), \(k_0\) is a constant, \(E_a\)(J/mol) is the reaction activation energy, and \(R=8.314 \mathrm{~J} /(\mathrm{mol} \cdot \mathrm{K})\) is the universal gas constant. Your task will be to verify that the expressions for \(C_A\)(t) and k(T) fit the data, and if they do, to determine the parameters \(C_A0\) and k at each temperature and then the constants \(k_0\) and \(E_a\). (a) What are the units of k, \(k_0\), and \(E_a\) if \(C_A\) is in mol/L and t is in min? (b) Transform Equation 1 into an equation of the form y=at+b, so that if Equation 1 is valid, a plot of y vs. t would be a straight line. How would you determine \(C_A0\) and k from the slope and intercept of the line? (c) Create an Excel spreadsheet with the structure shown as Rows 1–10 in the figure at the end of this problem statement, and fill in the data table in Columns A–I. Then create the four scatterplots shown in Rows 15–21. In the “Trendline” options of each plot, check the boxes for “Display equation on chart” and “Display R-squared value on chart” but not the one for “Set intercept.” \(R^2\) is the coefficient of determination (it has several other names as well), and provides a measure of how well a straight line fits a set of data: the closer it is to 1, the better the fit. What can you conclude about Equation 1 from the four plots? (d) From the four trendline equations, calculate the values of k and \(C_A0\) for each of the four experimental temperatures and fill in Columns B–I in Rows 12 and 13 of the spreadsheet. (e) Enough A was initially added to the tank to make the initial concentration \(C_A0\)=0:25 mol/L, yet you calculated four different values of \(C_A0\) in Part (d). How do you explain this result? (f) Next, transform Equation 2 so that a straight-line plot (y=ax+b) would enable you to calculate the parameters \(k_0\) and \(E_a\). Below the four charts of Part (c), insert the information shown in Rows 23–27, Columns A–D, filling in the k values from the results of Part (d). Create the appropriate plot, show the trendline equation and \(R^2\) value, use the equation to determine \(k_0\) and \(E_a\), and fill in Columns A and B in Rows 29–31. What can you conclude about the temperature dependence of the reaction rate constant? (g) In running this set of experiments, it is essential that the reactor temperature be carefully controlled and the reactor contents be very well mixed. Speculate on the probable reasons for both requirements. (h) Finally, create and fill in Rows 1–3 and 12 of Columns J and K. Use Equation 2 to calculate k at \(120^{\circ} \mathrm{C}\) and \(160^{\circ} \mathrm{C}\) and insert them in Cells J13 and K13, respectively. Then fill in Rows 5–10 of Columns J and K using Equation 1 and assuming an initial concentration \(C_A0\)=0:25 mol/L. In which of the two sets of estimated concentrations would you have more confidence? Explain your answer.