A hygrometer is used to measure the moisture content of

Ten mL of pure liquid water in a cylinder with a movable piston is heated at a constant pressure of 1 atm from an initial temperature of 80C. The temperature of the system is monitored, and the following behavior is observed: @ 80 Time (a) What is happening in steps AB, BC, and CD? What is the temperature corresponding to the horizontal portion of the curve? (b) Estimate the volume occupied by the water at points Band C. (Assume the vapor follows the ideal gas equation of state.)

A quantity of liquid chloroform is placed in an open, transparent, three-liter flask and boiled long enough to purge all air from the vapor space. The flask is then sealed and allowed to equilibrate at 30C, at which temperature chloroform has a vapor pressure of 243 mm Hg. Visual inspection shows 10 mL of liquid chloroform present. (a) What is the pressure in the flask at equilibrium? Explain your reasoning. (b) What is the total mass (grams) of chloroform in the flask? What fraction is in the vapor phase at equilibrium?

Ethyl acetate has a vapor pressure of 118.3 mm Hg at 29SC and a normal boiling point of 77.0C. Estimate the vapor pressure at 45C using (a) the Antoine equation and constants from Table B.4; (b) the Clausius-Clapeyron equation and the two given data points; and (c) linear interpolation between the two given points. Taking the first estimate to be correct, calculate the percentage error associated with the second and third estimates.

The vapor pressure of ethylene glycol at several temperatures is given below: TCOC) I 79.7 105.8 120.0 141.8 178.5 197.3 p'(mm Hg) I 5.0 20.0 40.0 100.0 400.0 760.0 Use a semilog plot based on the Clausius-Clapeyron equation to derive an equation for p'(mm Hg) as a function of T (QC). From the plot, estimate the heat of vaporization of ethylene glycol in kllmo\. (Remember to use absolute temperatures in the Clausius-Clapeyron equation.)

You are given vapor pressure data in the form of [T (QC), p' (mm Hg)] pairs. Construct a spreadsheet or write a computer program to perform the following tasks: (a) ReadinTl,p~,T2,p;, ... ,TN'p~, (b) Fit the Clausius-Clapeyron equation to the data using the method of least squares (Appendix A.1) or a fitting routine embedded in the spreadsheet. In completing this task you should find the values of a and b in the formula y = ax + b, ,...here y = In p' and x = 1/(T + 273.2). Print out the values of a and b. Test your program by fitting the data for ethylene glycol given in Problem 6.4. Then use your formula to estimate the vapor pressures of this substance at soec, 80Q C, and nOeC, and the boiling points at 760 mm Hg and 2000 mm Hg. In which of the last two values would you have the least confidence? Explain your reasoning

The apparatus shown here is used to measure the vapor pressure of ethylene diamine. The system is loaded with pure ethylene diamine and the bath is adjusted to each of several known temperatures. The following readings are taken on a day when the atmospheric pressure is 758.9 mm Hg: Merwry Level T(QC) Right Arm (mm) Left Arm (mm) 42.7 138 862 58.9 160 840 68.3 182 818 77.9 213 787 88.6 262 738 98.3 323 677 105.8 383 617

Estimate the vapor pressure of acetone (mm Hg) at \(50^{\circ} \mathrm{C}\) (a) from data in Perry's Chemical Engineers' Handbook and the Clausius-Clapeyron equation, (b) from the Cox chart (Figure 6.1-4), and (c) from the Antoine equation using parameters from Table B.4.

The vapor pressure of an organic solvent is 50 mm Hg at 25C and 200 mm Hg at 45C. The solvent is the only species in a closed flask at 35C and is present in both liquid and vapor states. The volume of gas above the liquid is 150 mL. Estimate the amount of the solvent (mol) contained in the gas phase.

Liquid methyl ethyl ketone (MEK) is introduced into a vessel containing air. The system temperature is increased to 55C, and the vessel contents reach equilibrium with some MEK remaining in the liquid state. The equilibrium pressure is 1200 mm Hg. (a) Use the Gibbs phase rule to determine how many degrees of freedom exist for the system at equilibrium. State the meaning of your result in your own words. (b) Mixtures of MEK vapor and air that contain between 1.8 mole% MEK and 11.5 mole% MEK can ignite and burn explosively if exposed to a flame or spark. Determine whether or not the given vessel constitutes an explosion hazard.

When a flammable liquid (such as gasoline or charcoal lighter fluid) ignites, it is not the liquid itself that burns: what actually happens is that the liquid vaporizes and the resulting air-vapor mixture burns. If the temperature is such that the percentage of the vapor in the mixture is below a certain level (the lower flammable limit), the liquid will not ignite if exposed to a spark or other ignition source. A match may burn in the mixture, but the flame will not spread. (a) The flash point of a liquid is the lowest temperature at which the liquid vaporizes sufficiently to form an ignitable mixture with air. For example, the flash point of octane at 1 atm is BOC (55F), which means that dropping a match into an open container of octane is likely to start a fire on a warm summer day but not on a cold winter day. (Please do not try it!) Suppose you are keeping two solvents in your laboratory-one with a flash point of 15C and the other with a flash point of 75C. How do these solvents differ from the standpoint of safety? How might you treat them differently? (b) The lower flammable limit (LFL) of methanol in air is 6.0 mole%. Calculate the temperature at which the equilibrium percentage of methanol vapor in a saturated methanol-air mixture would equal the LFL. (This temperature is a rough estimate of the flash point.) (c) Suppose an open container of methanol is kept at a temperature below the temperature calculated in part (b). Why would it still be unsafe to expose the container to a flame?

A gas mixture contains 10.0 mole% H20(v) and 90.0 mole% N2 The gas temperature and absolute pressure at the start of each of the three parts of this problem are 50C and 500 mm Hg. Ideal gas Student behavior may be assumed in every part of this problem. Workbook (a) If some of the gas mixture is put in a cylinder and slowly cooled at constant pressure, at what temperature would the first drop of liquid form? (b) If a 30.0-liter flask is filled with some of the gas mixture and sealed and the water vapor in the flask is completely condensed, what volume (cm3) would be occupied by the liquid water? (c) If the gas mixture is stored in a rigid-walled cylinder and a low-pressure weather front moves in and the barometric (atmospheric) pressure drops, which of the following would change: (i) the gas density, (ii) the absolute pressure of the gas, (iii) the partial pressure of water in the gas, (iv) the gauge pressure of the gas, (v) the mole fraction of water in the gas, (vi) the dew-point temperature of the mixture?

Pure chlorobenzene is contained in a flask attached to an open-end mercury manometer. When the flask contents are at 58.3C, the height of the mercury in the arm of the manometer connected to the flask is 747 mm and that in the arm open to the atmosphere is 52 mm. At llOC, the mercury level is 577 mm in the arm connected to the flask and 222 mm in the other arm. Atmospheric pressure is 755 mmHg. (a) Extrapolate the data using the Clausius-Clapeyron equation to estimate the vapor pressure of chlorobenzene at 130e. Problems 283 (b) Air saturated with chlorobenzene at l30C and 101.3 kPa is cooled to 58.3C at constant pressure. Estimate the percentage of the chlorobenzene originally in the vapor that condenses. (See Example 6.3-2.) (c) Summarize the assumptions you made in doing the calculation of part (b)

The latest weather report includes the following statement: "The temperature is 78F, barometric pressure is 29.9 inches, and the relative humidity is 87%." From this information, estimate the mole fraction of water in the air and the dew point (OF), molal humidity, absolute humidity, and percentage humidity of the air.

It has been suggested that Atlanta-Fulton County Stadium earned the nickname "The Launching Pad" because baseballs carried farther than normal in the region's hot, humid atmosphere. With this suggestion in mind, examine the effect of temperature and humidity on the buoyant force exerted on a baseball by calculating the density (giL) of air at the following conditions and a pressure of 1 atm: Condition Temperature CF) I 70 II 70 III 90 Relative Humidity 50% 80% 80% Explain why your results make sense. Then argue for or against the suggestion in the first sentence.

Air at 50% relative humidity is cooled isobarically at 1 atm absolute from 90C to 25e. (a) Estimate the dew point and degrees of superheat of the air at 90e. (b) How much water condenses (mol) per cubic meter of feed gas? (See Example 6.3-2.) (c) Suppose a sample of the 90C air is put in a closed variable-volume chamber containing a mirror and the pressure is raised at constant temperature until a mist forms on the mirror. At what pressure (atm) would the mist form? (Assume ideal gas behavior.)

In a device to produce potable water, humid air at 90F, 29.7 in Hg, and 95% relative humidity is cooled to 40F at constant pressure. What volumetric flow rate of air into the cooler (ft3/min) is required to provide 10.0 gal/min of condensed water

Air containing 20.0 mole% water vapor at an initial pressure of 1 atm absolute is cooled in a I-liter sealed vessel from 200C to 15e. (a) What is the pressure in the vessel at the end of the process? (Hint: The partial pressure of air in the system can be determined from the expression Pair = najrRT/ V and P = Pair + PH20. You may neglect the volume of the liquid water condensed, but you must show that condensation occurs.) (b) What is the mole fraction of water in the gas phase at the end of the process? (c) How much water (grams) condenses?

Air at 90°C and 1.00 atm (absolute) contains 10.0 mole% water. A continuous stream of this air enters a compressor-condenser, in which the temperature is lowered to 15.6°C and the pressure is raised to 3.00 atm. The air leaving the condenser is then heated isobarically to 100°C. Calculate the fraction of water that is condensed from the air, the relative humidity of the air at 100°C, and the ratio \(\mathrm{m}^{3}\) outlet air at 100°C/\(\mathrm{m}^{3}\) feed air at 90°C.

Dry air is bubbled through 25.0 liters of water at a rate of 15.0 liters (STP)/min. The air leaving the liquid is saturated with water at 25C and 1.5 atm. How long will it take for all of the water to vaporize?

A storage tank for liquid n-octane has a diameter of 30 ft and a height of 20 ft. During a typical 24-h period the level of liquid octane falls from 18 ft to 8 ft, after which fresh octane is pumped into the tank to return the level to 18 ft. As the level in the tank falls, nitrogen is fed into the free space to maintain the pressure at 16 psia; when the tank is being refilled, the pressurt; is maintained at 16 psia by discharging gas from the vapor space to the environment. The nitrogen in the tank may be considered saturated with octane vapor at all times. The average tank temperature is 90F. (a) What is the daily rate, in gallons and Ibm, at which octane is used? (b) What is the variation in absolute pressure at the bottom of the tank in inches of mercury? (c) How much octane is lost to the environment during a 24-h period? (d) Why is nitrogen used in the vapor space of the tank when air would be cheaper?

A lOOO-galion tank currently contains 100.0 gallons of liquid toluene and a gas saturated with toluene vapor at 85F and 1 atm. (a) What quantity of toluene (Ibm) will enter the atmosphere when the tank is filled and the gas displaced? (b) Suppose that 90% of the displaced toluene is to be recovered by compressing the displaced gas to a total pressure of 5 atm and then cooling it isobarically to a temperature T CF). Calculate T.

A gas mixture containing 85.0 mole% N z and the balance n-hexane flows through a pipe at a rate of 100.0 m3/h. The pressure is 2.00 atm absolute and the temperature is 100e. (a) What is the molar flow rate of the gas in kmol/h? (b) Is the gas saturated? If not, to what temperature (0C) would it have to be cooled at constant pressure in order to begin condensing hexane? (c) To what temperature CC) would the gas have to be cooled at constant pressure in order to condense 80% of the hexane?

Solids soaked with liquid hexane are dried by being contacted with nitrogen at an elevated temperature. The gas stream leaving the dryer is at 80C 1 atm absolute, and 50% relative saturation. (a) One of several possibilities for recovering the hexane from the gas is to send the stream to a cooling condenser. The gas stream leaving the condenser would contain 5.00 mole% hexane, and hexane condensate would be recovered at a rate of 1.50 kmol/min. The condenser would be operated at a pressure of 1 atm absolute. N h h T N 80C 1 t 2 Ig 2, am C6H14 (Sr = 50%) CONDENSER N2 DRYER (l atm) C6H14 (v)(5 mole"lo) Wet solids Dry solids 1.5 kmoi C6Hl4(lllmin Calculate the temperature to which the gas must be cooled and the required flow rate of fresh nitrogen to the dryer in standard cubic meters per minute (SCMM). (b) In an alternative arrangement, the gas leaving the dryer would be compressed to 10.0 atm and the temperature would simultaneously be increased so that the relative saturation remains at 50%. The gas then would be cooled at constant pressure to produce a stream containing 5.00 mole% hexane. Calculate the final gas temperature and the ratio of volumetric flow rates of the gas streams leaving and entering the condenser. State any assumptions you make. (c) What would you need to know to determine which of processes (a) and (b) is more costeffective?

A 20,000-liter storage tank was taken out of service to repair and reattach a feed line damaged in a collision with a tanker. The tank was drained and then opened several days later for a welder to enter Student and perform the required work. No one realized, however, that 15 liters of liquid nonane (CyHzo) Workbook remained in a collection sump at the bottom of the tank after the draining had been completed. (a) Nonane has a lower explosion limit of 0.80 mole% and an upper explosion limit of 2.9 mole%7 (i.e., nonane-air mixtures at 1 atm can explode when exposed to a spark or flame if the nonane mole fraction is between the two given values). Assume any liquid nonane that evaporates spreads uniformly throughout the tank. Is it possible for the average gas-phase composition in the tank to be within the explosion limits at any time? Even when the average composition falls outside those limits, why is an explosion still a possibility? (Hint: Think about that assumption.) (b) Nonane has a vapor pressure of 5.00 mm Hg at 25.8C and 40.0 mm Hg at 66.0C. Use the Clausius-Clapeyron equation (6.1-3) to derive an expression for p*(T). Then calculate the temperature at which the system would have to equilibrate in order for the gas in the tank to be at the lower explosion limit. (c) Fortunately, a safety inspector examined the system before the welder began work and immediately canceled the work order. The welder was cited and fined for violating established safety procedures. One requirement was for the tank to be purged thoroughly with steam after being drained. What is the purpose of this requirement? (Why purge, and why with steam rather than air?) What other precautions should be taken to be sure that the welder is in no danger?

An adult takes roughly 12 breaths each minute, inhaling approximately 500 mL with each breath. Oxygen and carbon dioxide are exchanged in the lungs. The amount of nitrogen exhaled equals the amount inhaled, and the mole fraction of nitrogen in the exhaled air is 0.75. The exhaled air is saturated with water vapor at body temperature, 37C. Estimate the increase in the rate of water loss (g1day) when a person breathing air at 23C and a relative humidity of 50% enters an airplane in which the temperature is also 23C but the relative humidity is 10%.

Recovering and reusing organic solvents (rather than discharging the solvents in waste streams) is an important part of the operation of most chemical plants. The magnitude of these recovery efforts can be staggering: in recent years the Eastman Chemical Company used 3.6 billion pounds of solvents and recovered 3.5 billion pounds (97%). Eastman's installation of a $26 million acetone-recovery system reduced acetone emissions by 50% in the division that had been responsible for most of these emissions.s In an acetone-recovery process, a gas stream containing 20.0 mole% acetone and the remainder nitrogen leaves a chemical plant at 90C and 1 atm. The stream is cooled at constant pressure in a condenser, enabling some of the acetone vapor to be recovered as a liquid. The nitrogen and uncondensed acetone are discharged to the atmosphere. (a) Give two major benefits of recovering the acetone. (h) Two cooling fluids are available-cooling-tower water at 20C and a refrigerant at -35C. For each fluid, calculate the percentage acetone recovery [(mol acetone condensed/mol acetone fed to condenser) X 100%], assuming that the condenser temperature equals the coolant temperature. (c) What more would you need to know to decide which coolant to use? (d) In a real system. the condenser temperature could never be as low as the initial cooling fluid temperature. Why not? (Hint: In a condenser, heat is transferred from the process fluid to the cooling fluid.) Explain how this fact would affect the percentage solvent recovery.

On a hot summer day the temperature is 35C, barometric pressure is 103 kPa, and the relative humidity is 90%. An air conditioner draws in outside air, cools it to 20C, and delivers it at a rate of 12,500 Llh. Calculate the rate of moisture condensation (kg/h) and the volumetric flow rate of the air drawn from the outside.

An air conditioner is designed to bring 10,000 ft3/min of outside air (90F, 29.8 in Hg, 88% relative humidity) to 40F, thereby condensing a portion of the water vapor, and then to reheat the air. releasing it into a room at 65F. Calculate the rate of condensation (gallons H20/min) and the volumetric flow rate of the air delivered to the room. (Suggestion: On the flowchart, treat the cooling--eondensation and the reheating as separate process steps.)

The air in a building is to be maintained at 25C and 55% relative humidity by passing outside air through a water spray. The air enters the spray chamber at 32C and 70% relative humidity, leaves the chamber cooled and saturated with water vapor, and is then reheated to 25C. Estimate the temperature of the air leaving the spray chamber and the water (kg) added to or removed from (specify which) each kilogram of dry air processed.

A hygrometer is used to measure the moisture content of humid air. Calibration of the instrument leads to a straight line on a semilog plot of y, the mole fraction of water in air (logarithmic scale), versus H, the instrument reading (linear scale). Room air is charged into the hygrometer sample chamber on a day when the temperature is 22C, barometric pressure is 1.00 atm, and the relative humidity is 40%. The resulting meter reading is H = 5.0. A second measurement is then made by heating water to 50C in a sealed flask containing air. The system is allowed to equilibrate at a pressure of 839 mm Hg with liquid still present in the flask, and a sample of the air above the liquid is withdrawn and injected into the sample chamber (which is heated to prevent condensation). The meter reading in this case is H = 48.(a) Determine the expression for y as a function of H. (b) Suppose you wish to condition air at 35C and 1 atm to produce air at 22C, 1 atm, and 40% relative humidity. The air conditioner first cools the air, condensing the necessary amount of water, and then reheats the remaining air to 22e. A sample of the outside air is injected into the hygrometer chamber, and the resulting reading is H = 30. Calculate the temperature to which the air must be cooled before it is reheated and determine the amount of water condensed in kg/mJ of delivered conditioned air.

Recovery of a solvent vapor from a gas stream by condensation can be achieved by cooling the gas, by compressing it, or by a combination of these operations. The greater the compression, the less cooling is needed. (a) A gas mixture at a pressure Po and temperature To is the feed to a recovery process. A single condensable vapor and several noncondensable gases are present in the mixture, giving the feed a dew point of TdO ' A fraction f of the vapor is to be condensed. The vapor pressure p*(T) of the condensable component may be expressed as a function of temperature with the Antoine equation. For a gas feed rate of no, draw and label a flowchart. Then derive the following relationship for the final condenser pressure in terms of the final temperature Tf and the specified feed conditions and fractional solvent recovery: P f = p*(Tf)[l - f p*(Tdo)/ Pol (1 - f)p*(TdO )/ Po Crefr($/kmol feed gas) = 2000 + 27(6.T)2 Ccomp($lkmol feed gas) = 4500 + 5.58(6.P) where 6.T(C) = Tf - To and 6.P(mm Hg) = Pf - Po. Your task is to prepare a spreadsheet to estimate the operating cost of a process in which ethylbenzene is recovered from an ethylbenzene-nitrogen gas mixture. The spreadsheet should have the following form: (b) The cost of refrigeration equipment and the compressor can be estimated using the empirical formulas9 Condensation of ethylbenzene from nitrogen Antoine constants for ethylbenzene A= 6.95719 B= 1424.26 C= 213.206 Run To Po TdO f Tf p*(TdO ) p*(Tf ) Pf Crefr Ccomp Ctot 1 I 50 I 765 I I 40 0.95 45 I 21.493 27.62 19137 2675 107013 I 109688 ! I I I 2 I 50 765 40 0.95 40 '"' 50 I .J 765 I 40 0.95 35 4 50 765 40 0.95 45 Enter the values in the first six columns of the first row of the 12-column table (1,50, ... ,45) and enter formulas in the next six columns (including Clot = Crefr + Ccomp ). 'Computer problem. 9These formulas are fictitious. Real cost-estimation formulas can be found in a number of texts including M. S. Peters and K. D. Timmerhaus, Plant Design and Economics for Chemical Engineers, 4th Edition, McGraw-Hill, New York, 1991; W. D. Seider, J. D. Seader, and D. R. Lewin, Process Design Principles, John Wiley & Sons, NeW York, 1999; and G. D. Ulrich, A Guide to Chemical Engineering Process Design and Economics, John Wiley & Sons, New York, 1984. Student Workbook Encyclopedia Equipment absorber Encyclopedia Equipment dryer Encyclopedia Equipment dryer Encyclopedia Equipment extractor, dryer, condenser Problems 287 The row shown above for Run 1 contains results for a feed gas at 50C and 765 mm Hg with a dew point of 40C, from which 95 % of the ethylbenzene is to be recovered by cooling the mixture to 45C. The output shows that the mixture must be compressed to 19,137 mm Hg to achieve the desired recovery, and that the costs of refrigeration and compression and the total cost ($/kmol feed gas) are, respectively, $2675, $107,013, and $109,688. When you have constructed the spreadsheet and duplicated the results just described for Run 1, (i) copy that row into the next three rows and change the values in the first six columns to duplicate those shown above; (ii) let Runs 2 and 3 stand; and (iii) in Run 4, vary the value of Tr to find the most cost-effective final temperature and pressure for the given feed conditions and fractional recovery, noting what happens to Pr, Cefr, Ccomp , and COl as you carry out your search. (c) Use the results for Runs 1-3 to deduce the effect of lowering the final temperature on the pressure required to achieve a specified fractional recovery of ethylbenzene. Explain why this result makes sense. (d) Summarize the effect of Tr on the refrigeration and compression costs and explain why the total cost has a minimum.

A gas stream containing 40.0 mole% hydrogen, 35.0% carbon monoxide. 20.0% carbon dioxide. and 5.0% methane is cooled from 1000C to 10C at a constant absolute pressure of 35.0 atm. Gas enters the cooler at 120 m3/min and upon leaving the cooler is fed to an absorber. where it is contacted with refrigerated liquid methanol. The methanol is fed to the absorber at a molar flow rate 1.2 times that of the inlet gas and absorbs essentially all of the CO~, 98% of the methane, and none of the other components of the feed gas. The gas leaving the absorber, which is saturated with methanol at -12C, is fed to a cross-country pipeline. (a) Calculate the volumetric flow rate of methanol entering the absorber (m3/min) and the molar flow rate of methanol in the gas leaving the absorber. Do not assume ideal gas behavior when doing PVT calculations. (b) What is a possible intended use of the product gas? Why is it desirable to remove the CO~ from the gas prior to feeding it to the pipeline?

A hot-air dryer is used to reduce the moisture content of 1500 kg/min of wet wood pulp from 0.75 kg H20/kg dry pulp to 0.15 wt% H20. Air is drawn from the atmosphere at 28C, 760 mm Hg, and 50% relative humidity, sent through a blower-heater, and then fed to the dryer. The air leaves the dryer at 80C and 10 mm Hg (gauge). A sample of the exit air is drawn into a chamber containing a mirror and cooled slowly, keeping the gauge pressure at 10 mm Hg. A mist is observed to form on the mirror at a temperature of 40.0C. Calculate the mass of water removed from the pulp (kg/min) and the volumetric flow rate of air entering the system (m3/min).

Wet leather containing 61 % water enters a continuous tunnel dryer and leaves at a rate of 485 Ibmlh containing 6.0% water. Dry air enters the dryer at 140F and 1 atm, and the outlet air is at 130F and 1 atm with a relative humidity of 50%. Calculate the rate at which wet leather enters the dryer and the volumetric flow rate of the inlet air (ft3/h)

n-Hexane is used to extract oil from soybeans. The solid residue from the extraction unit, which contains 0.78 kg liquid hexane/kg dry solids, is contacted in a dryer with nitrogen that enters at 85C. The solids leave the dryer containing 0.05 kg liquid hexane/kg dry solids, and the gas leaves the dryer at 80C and 1.0 atm with a relative saturation of 70%. The gas is then fed to a condenser in which it is compressed to 5.0 atm and cooled to 28C. enabling some of the hexane to be recovered as condensate. (a) Calculate the fractional recovery of hexane (kg condensed/kg fed in wet solids). (b) A proposal has been made to split the gas stream leaving the condenser. combining 90% of it with fresh makeup nitrogen, heating the combined stream to 85C, and recycling the heated stream to the dryer inlet. What fraction of the fresh nitrogen required in the process of part (a) would be saved by introducing the recycle? What costs would be incurred by introducing the recycle?

In the final stage of the manufacturing process for a solid organic product. the product is cleaned with liquid toluene and then dried in a process whose flowchart is shown on the next page. IO lOAdapted from Professional Engineering Examinations, Vol. 1 (1965-1971), National Council of Engineering Examiners, p. 60. 288 Chapter 6 Multiphase Systems dryer, Encyclopedia Equipment condenser, heat exchanger The wet product enters the dryer at a rate of 300 Ibm/h containing 0.200 Ibm toluene/lbmdry solids. A stream of nitrogen at 2ooF, 1.2 atm, and containing a small amount of toluene vapor also enters the dryer. (A higher temperature would cause the product to soften and degrade.) Heat is transferred in the dryer from the gas to the wet solids, causing most of the toluene to evaporate. The final product contains 0.020 Ibm toluene/Ibm dry solids. Gas leaves the dryer at 150F and 1.2 atm with a relative saturation of 70% and passes through a water-cooled condenser. Gas and liquid streams leave the condenser in equilibrium at 90F and 1 atm. The gas is reheated to 2ooF and reenters the dryer. (a) Briefly explain this process in your own words. In your explanation, include the purposes of the condenser and the nitrogen reheater and a likely reason that nitrogen rather than air is used as the recirculating gas. What do you suppose happens to the liquid toluene leaving the condenser? Nz C7H8(v) 150F, 1.2 atm 70% Relative saturation Cooling water -11 CONDENSER Product Nz, C7H8(v) gOF, 1 atm saturated ~~_t BLOWER C7H8 (1) gOF. 1 atm Nz C7H8(v) 200F, 1.2 atm Steam Condensate Student Workbook Encyclopedia Equipment absorber (b) Calculate the compositions (component mole fractions) of the gas streams entering and leaving the dryer, the circulation rate of dry nitrogen (Ibm/h), and the volumetric flow rate of gas entering the dryer (ft3/h).

n-Hexane is burned with excess air. An analysis of the product gas yields the following dry-basis molar composition: 6.9% CO2, 2.1 % CO, 0.265% C6H 14 (+ O2 and N2). The stack gas emerges at 760 mm Hg. Calculate the percentage conversion of hexane, the percentage excess air fed to the burner, and the dew point of the stack gas, taking water to be the only condensable species.

A fuel gas containing methane and ethane is burned with air in a furnace. producing a stack gas at 300C and 105 kPa (absolute). The stack gas contains CO2 at a partial pressure of 80 mm Hg and no CO, O2, methane, or ethane. Calculate the mole fraction of methane in the fuel and the dew-point temperature of the stack gas.

A mixture of propane and butane is burned with air. Partial analysis of the stack gas produces the following dry-basis volume percentages: 0.0527% C3Hg, 0.0527% C4HlO , 1.48% CO, and 7.12% C02' The stack gas is at an absolute pressure of 780 mm Hg and the dew point of the gas is 46SC. Calculate the molar composition of the fuel.

An important parameter in the design of gas absorbers is the ratio of the flow rate of the feed liquid to that of the feed gas. The lower the value of this ratio, the lower the cost of the solvent required to process a given quantity of gas but the taller the absorber must be to achieve a specified separation.

An important parameter in the design of gas absorbers is the ratio of the flow rate of the feed liquid to that of the feed gas. The lower the value of this ratio, the lower the cost of the solvent required to process a given quantity of gas but the taller the absorber must be to achieve a specified separation. Propane is recovered from a 7 mole % propane-93% nitrogen mixture by contacting the mixture with liquid n-decane. An insignificant amount of decane is vaporized in the process, and 98.5% of the propane entering the unit is absorbed. Problems 289 Product liquid nL2 (1b-mole/hl Feed liquid Ii L j (Ib-mole/h) Feed gas ---4=--_2!11 nG2 (lb-mole/h) 0.07 Ib-mole C3Hg/lb-mole Product gas nG, (Ib-mole/h) ABSORBER T = 80F, P = 1 atm Encyclopedia Equipment stripper (a) The highest possible propane mole fraction in the exiting liquid would be that in equilibrium with the propane mole fraction in the entering gas (a condition requiring an infinitely tall column). Using the Cox chart (Figure 6.1-4) and Raoult's law to relate the mole fractions of propane in the entering gas and exiting liquid, calculate the ratio (nLI nC2) corresponding to this limiting condition. (b) Suppose the actual feed ratio (nLj nC2) is 1.2 times the value calculated in part (a) and the percentage of the entering propane absorbed is the same (98.5%). Calculate the mole fraction of propane in the exiting liquid. (c) What are the costs and benefits associated with increasing (nL,,/ nc2) from its minimum value [the value calculated in part (a)]? What would you have to know to determine the most cost-effective value of this ratio?

Nitric acid is used extensively for the production of inorganic and organic nitrates, for metal treatments of various kinds, and for photoengraving. It is produced by oxidizing ammonia to nitric oxide over a platinum-rhodium catalyst, oxidizing the nitric oxide to nitrogen dioxide, and dissolving the NOz in water: 4 NH3 (g) + 5 Oz(g) ---+ 4 NO(g) + 6 HzO(g) 2 NO(g) + Oz(g) ---+ 2 NOz(g) 3 NOz(g) + HzO(I) ---+ 2 HN03 (aq) + NO(g) A side reaction that lowers the product yield is the oxidation of ammonia to nitrogen and water vapor: 4 NH3 (g) + 3 Oz(g) ---+ 2 Nz(g) + 6 HzO(g) Saturated ammonia vapor, produced by vaporizing pure liquid ammonia at 820 kPa absolute, is mixed with a stoichiometric quantity of air. and the combined stream enters a converter. Prior to being mixed with the ammonia, the air is compressed and passed through a preheater. It enters the compressor at 30C and 1 atm with a relative humidity of 50%, and it exchanges heat in the preheater with the gases emerging from the converter. The quantity of oxygen in the feed is the amount theoretically required to convert all of the ammonia to HN03 In the converter, the ammonia reacts completely, with 97% forming NO and the balance forming Nz. In the short time in which the reaction mixture is in the presence of the catalyst (less than 0.001 s), a negligible amount of NOz is formed. The product gas is subjected to a series of cooling and hydration steps in which the NO is completely oxidized to NOz, which in turn combines with water (some of which is present in the product gas, the rest of which is added) to form a 55 wt% aqueous nitric acid solution. The NO formed in the latter reaction is reoxidized and the added N02 is hydrated to form still more HN03 . The product gas from the process may be taken to contain only Nz and Oz. A simplified flowchart of the process follows. t t R COOLING 55"10 HN03(aq) AND HYDRATION 2 (g) Air Preheated air NH 3(gl PREHEATE ,,~ CONVERTER \...~ NO O2 N2 H 0 (a) Taking a basis of 100 mol of ammonia fed to the process, calculate (i) the volume (m3) of the ammonia vapor and of the air fed to the process, using the compressibility factor equation of state for the ammonia calculation; (ii) the moles and molar composition of the gas leaving the converter; and (iii) the required feed of liquid water (m3) to the cooling and hydration step. (b) Scale up the results calculated in part (a) to a new basis of 1000 metric tons of 55% nitric acid solution produced

A dry gas containing 10.0% NH3 by volume is contacted with water at lOo e and 1 atm in a singlestage bubble contactor. The effluent liquid and gas streams may be considered to be in equilibrium with each other. A small slip stream taken from the effluent liquid is fed to a continuous densitometer, which indicates that the liquid density is 0.9534 glmL. (a) Using tabulated data from Perry's Chemical Engineers' Handbook (pp. 2-85, 2-87, and 2-99),11 estimate the percentage of the ammonia in the feed that is removed in the contactor. 11 R. H. Perry and D. W. Green, Eds., Perry's Chemical Engineers' Handbook, 7th Edition. McGraw-Hill, New York, 1997. Problems 291 (b) Why is it important to maintain the slip stream and densitometer chamber at a known temperature at or below the temperature of the contactor?

Sulfur trioxide (S03) dissolves in and reacts with water to form an aqueous solution ofsulfuric acid (H2S04 ), The vapor in equilibrium with the solution contains both S03 and H20. If enough S03 is added, all of the water reacts and the solution becomes pure H2S04 If still more S03 is added, it dissolves to form a solution of S03 in H2S04 , called oleum or fuming sulfuric acid. The vapor in equilibrium with oleum is pure S03. A 20% oleum by definition contains 20 kg of dissolved S03 and 80 kg of H2S04 per hundred kilograms of solution. Alternatively, the oleum composition can be expressed as % S03 by mass, with the constituents of the oleum considered to be S03 and H20. (a) Prove that a 15.0% oleum contains 84.4% S03' (b) Suppose a gas stream at 40C and 1.2 atm containing 90 mole% S03 and 10% N2 contacts a liquid stream of 98 wt% H2S04 (aq), producing 15% oleum at the tower outlet. Tabulated equilibrium data indicate that the partial pressure of S03 in equilibrium with this oleum is 1.15 mm Hg. Calculate (i) the mole fraction of S03 in the outlet gas if this gas is in equilibrium with the liquid product at 40C and 1 atm, and (ii) the ratio (m3 gas feed)/(kg liquid feed).

State whether you would use Raoult's law or Henry's law to perform vapor-liquid equilibrium calculations for each component in the following liquid mixtures: (a) water and dissolved nitrogen; (b) hexane, octane, and decane; and (c) club soda or any other carbonated beverage

A gas containing nitrogen, benzene, and toluene is in equilibrium with a 40 mole% benzene- 60 mole% toluene liquid mixture at 100C and 10 atm. Estimate the gas-phase composition (mole fractions) using Raoult's law.

Using Raoult's law or Henry's law for each substance (whichever one you think appropriate), calculate the pressure and gas-phase composition (mole fractions) in a system containing a liquid that is 0.3 mole% N2 and 99.7 mole% water in equilibrium with nitrogen gas and water vapor at 80C.

The pressure in a vessel containing methane and water at 70C is 10 atm. At the given temperature. the Henry's law constant for methane is 6.66 X 104 atm/mole fraction. Estimate the mole fraction of methane in the liquid

When air (=21 mole% O2, 79 mole % N2) is placed in contact with 1000 cm3 of liquid water at body temperature, 36.9C, and 1 atm absolute, approximately 14.1 standard cubic centimeters (cm3 (STP)] of gas are absorbed in the water at equilibrium. Subsequent analysis of the liquid reveals that 33.4 mole% of the dissolved gas is oxygen and the balance is nitrogen. (a) Estimate the Henry's law coefficients (atm/mole fraction) of oxygen and nitrogen at 36.9C. (b) An adult absorbs approximately 0.4 g 02/min in the blood flowing though the lungs. Assuming that blood behaves like water and that it enters the lungs free of oxygen, estimate the flow rate of blood into the lungs in Llmin. (c) The actual flow rate of blood into the lungs is roughly 5 Llmin. Identify the assumptions made in the calculation of part (b) that are likely causes of the discrepancy between the calculated and actual blood flows.

The solubility coefficient of a gas may be defined as the number of cubic centimeters (STP) of the gas that dissolves in 1 cm3 of a solvent under a partial pressure of 1 atm. The solubility coefficient of CO2 in water at 20C is 0.0901 cm3 CO2(STP)/cm3 H20(l). (a) Calculate the Henry's law constant in atm/mole fraction for CO2 in H20 at 20C from the given solubility coefficient. (b) How many grams of CO2 can be dissolved in a 12-oz bottle of soda at 20C if the gas above the soda is pure CO2 at a gauge pressure of 2.5 atm (1 liter = 33.8 fluid ounces)? Assume the liquid properties are those of water. (c) What volume would the dissolved CO2 occupy if it were released from solution at body temperature and pressure-37C and 1 atm?

The sulfur dioxide content of a stack gas is monitored by passing a sample stream of the gas through an S02 analyzer. The analyzer reading is 1000 ppm S02 (parts per million on a molar basis). The sample gas leaves the analyzer at a rate of 1.50 Llmin at 30C and 10.0 mm Hg gauge and is bubbled through a tank containing 140 liters of initially pure water. In the bubbler, S02 is absorbed and water evaporates. The gas leaving the bubbler is in equilibrium with the liquid in the bubbler at 30C and 1 atm absolute. The S02 content of the gas leaving the bubbler is periodically monitored with the 292 Chapter 6 MuItiphase Systems SO~ analyzer. and when it reaches 100 ppm S02 the water in the bubbler is replaced with 140 liters of fresh water. (3) Speculate on why the sample gas is not just discharged directly into the atmosphere after leaving the analyzer. Assuming that the equilibrium between S02 in the gas and dissolved S02 is described by Henry's law, explain why the S02 content of the gas leaving the bubbler increases with time. What value would it approach if the water were never replaced? Explain. (The word "solubility" should appear in your explanation.) (b) Use the following data for aqueous solutions of S02 at 30C12 to estimate the Henry's law constant in units of mm Hg/mole fraction: I g S02 dissolved/lOa g H2O(l) 0.0 0.5 1.0 1.5 2.0 ! Pso2 (mm Hg) 0.0 42 85 129 176 I i (c) Estimate the S02 concentration of the bubbler solution (mol S02/1iter), the total moles of S02 dissolved. and the molar composition of the gas leaving the bubbler (mole fractions of air, S02, and water vapor) at the moment when the bubblersolution must be changed. Make the following assumptions: The feed and outlet streams behave as ideal gases. Dissolved S02 is uniformly distributed throughout the liquid. The liquid volume remains essentially constant at 140 liters. The water lost by evaporation is small enough for the total moles of water in the tank to be considered constant. The distribution of S02 between the exiting gas and the liquid in the vessel at any instant of time is governed by Henry's law, and the distribution of water is governed by Raoult's law (assume XH20 = 1). (d) Suggest changes in both scrubbing conditions and the scrubbing solution that might lead to an increased removal of S02 from the feed gas.

A vapor stream that is 65 mole% styrene and 35 mole% toluene is in equilibrium with a liquid mixture of the same two species. The pressure in the system is 150 mm Hg absolute. Use Raoult's law to estimate the composition of the liquid and the system temperature.

A gas containing nitrogen, benzene, and toluene is in equilibrium with a liquid consisting of 35 mole% benzene and 65 mole% toluene at 85C and 10 atm. Estimate the gas composition (mole fractions) using Raoult's law and assuming ideal gas behavior.

A liquid mixture containing 50 mole% propane, 30% n-butane, and 20% isobutane is stored in a rigid container at nOE The container has a maximum allowable working pressure of 200 psig. The Student head space above the liquid contains only vapors of the three hydrocarbons. Workbook (3) Show that the container is currently safe, using Raoult's law and the Cox chart (Figure 6.1-4) in your calculations. (b) Obtain a rough estimate of the temperature above which the maximum allowable pressure would be exceeded. Comment on the suitability of the container to store the given mixture.

A closed system contains an equimolar mixture of n-pentane and isopentane. (3) Suppose the system is initially all liquid at 120C and a high pressure, and the pressure is gradually reduced at a constant temperature. Estimate the pressures at which the first bubble of vapor forms and at which the last drop of liquid evaporates. Also calculate the liquid and vapor compositions (mole fractions) at those two conditions. (Suggestion: Use a spreadsheet.) (b) Now suppose the system starts as a vapor at 1200 mm Hg gauge and a high temperature, and the temperature is gradually reduced at constant pressure. Estimate the temperatures at which the first drop of liquid forms and at which the last bubble of vapor condenses. Also calculate the liquid and vapor compositions (mole fractions) at those two conditions.

Nitrogen is bubbled through a liquid mixture that initially contains equimolar amounts of benzene and toluene. The system pressure is 3 atm and the temperature is 80C. The nitrogen flow rate is 12R. H. Perry and D. W. Green, Eds., Perry's Chemical Engineers' Handbook, 7th Edition, McGraw-Hili, New York. 1997, p. 2-77. Problems 293 10.0 standard liters per minute. The gas leaving the bubbler is saturated with benzene and toluene vapors. (a) Estimate the initial rates (mol/min) at which benzene and toluene leave the bubbler. (b) How will the mole fractions of benzene and toluene in the liquid change with time (increase, decrease, or remain constant)? Explain your answer. (c) How will the mole fractions of benzene and toluene in the exiting gas change with time (increase, decrease, or remain constant)? Explain your answer.

Calculate the following: (a) The bubble-point temperature of an equimolar mixture of liquid n-hexane and n-heptane at 1.0 atm and the composition (mole fractions) of the vapor in equilibrium with this mixture. (b) The dew-point temperature of a gas mixture with a molar composition of 30% n-hexane, 30% nheptane, and 40% air at 1 atm and the composition (mole fractions) of the liquid in equilibrium with this mixture

A liquid mixture contains N components (N may be any number from 2 to 10) at pressure P(mm Hg). The mole fraction of the ith component is Xi (i = L 2, ... , N), and the vapor pressure of that component is given by the Antoine equation (see Table B.4) with constants Ai, Bi , and Ci Raoult's law may be applied to each component. (a) Write the equations you would use to calculate the bubble-point temperature of the mixture, ending with an equation of the form f(T) = O. (The value of T that satisfies this equation is the bubble-point temperature.) Then write the equations for the component mole fractions (Yl, Y2, . .. , Yv) in the first bubble that forms, assuming that the temperature is now known. (b) Prepare a spreadsheet to perform the calculations of part (a). The spreadsheet should include a title line and two tables: the first table should contain the Antoine-equation constants and the total pressure, and the second should contain columns for the liquid-phase mole fractions, guessed values of the bubble-point temperature, any intermediate quantities generated in the bubble-point calculation (such as vapor pressures at the guessed temperatures), the function f(T), and the values of the vapor-phase mole fractions. Enter the values of Ai, Bi , Ci , P, and Xi for each species in the mixture, assume a value of T. and enter formulas for the other variables in the spreadsheet including f. Then determine the bubble-point temperature by using the goalseek tool (or simple trial and error) to find the value of T for which f = O. Test your program by calculating the bubble-point temperatures and vapor compositions for liquids at 760 mm Hg containing (i) 22.6 mole% benzene, 44.3 mole% ethylbenzene, and the balance toluene; (ii) 44.3 mole% benzene, 22.6% ethylbenzene, and the balance toluene; and (iii) 22.6 mole% benzene. 22.6% ethylbenzene, and the balance toluene. Briefly explain why the variations in bubble-point temperature for these three cases make sense. (c) Write a computer program to perform the calculations of part (b), and test it using the same three cases. To calculate the bubble-point temperature, evaluate f for the first guessed value of T, and then vary T in increments of ::::5C until the value of f changes sign from its initial value. Use the two values of T for which the corresponding values of f bracket 0 as the starting point for a regula-falsi method calculation (Appendix A.2c), stopping when If(T)1 < 1.0 X 10- 4 .

A vapor mixture of n-butane (B) and n-hexane (H) contains 50.0 mole% butane at 120C and 1.0 atm. A stream of this mixture flowing at a rate of 150.0 Lis is cooled and compressed, causing some but not all of the vapor to condense. (Treat this process as a single-unit operation.) Liquid and vapor product streams emerge from the process in equilibrium at TeC) and 1100 mm Hg. The vapor product contains 60.0 mole% butane. (a) Draw and label a flowchart. Perform a degree-of-freedom analysis to show that you have enough information to determine the required final temperature (T), the composition of the liquid product (component mole fractions), and the molar flow rates of the liquid and vapor products from the given information and Antoine expressions for the vapor pressures Ps(T) and PH(T). JllSt identify the equations-for example, mole balance on butane or Raoult's law for hexane-but don't write them yet. (b) Write in order the equations that you would use to determine the quantities listed in part (a) and also the fractional condensation of hexane (mol H condensed/mol H fed). In each equation, circle the variable for which you would solve. Do no algebra or calculations. (c) Complete the calculations either manually or with an equation-solving program. (d) State three assumptions you made that could lead to errors in the calculated quantities.

The feed to a distillation column is a 45.0 mole% n-pentane-55.0 mole% n-hexane liquid mixture. The vaporstream leaving the top of the column, which contains 98.0 mole% pentane and the balance hexane, goes to a total condenser (in which all the vapor is condensed). Half of the liquid condensate is returned to the top of the column as reflux and the rest is withdrawn as overhead product (distillate) at a rate of 85.0 kmollh. The distillate contains 95.0% of the pentane fed to the column. The liquid stream leaving the bottom of the column goes to a reboi/er. Part of the stream is vaporized; the vapor is recycled to the bottom of the column as boi/up, and the residual liquid is withdrawn as bottoms product. (a) Calculate the molar flow rate of the feed stream and the molar flow rate and composition of the bottoms product stream. (b) Estimate the temperature of the vapor entering the condenser, assuming that it is saturated (at its dew point) at an absolute pressure of 1 atm and that Raoult's law applies to both pentane and hexane. Then estimate the volumetric flow rates of the vapor stream leaving the column and of the liquid distillate product. State any assumptions you make. (c) Estimate the temperature of the reboiler and the composition of the vapor boilup, again assuming operation at 1 atm. DISTI LLATION COLUMN Boilup (vapor) Distillate (liquid) Bottoms product (liquid) CONDENSER Cooling fluid Reflux (liquid) Vapor from top of column Liqu id from '------;VV) bottom of column REBOILER Heating fluid Feed to column Encyclopedia Equipment condenser (d) Calculate the minimum diameter of the pipe connecting the column and the condenser if the maximum allowable velocity in the pipe is 10 m/s. Then list all the assumptions underlying the calculation of that number.

The vapor leaving the top of a distillation column goes to a condenser in which either total or partial condensation takes place. If a total condenser is used, a portion of the condensate is returned to the top of the column as reflux and the remaining liquid is taken off as the overhead product (or distillate). (See Problem 6.60.) If a partial condenser is used, the liquid condensate is returned as reflux and the uncondensed vapor is taken off as the overhead product. Vapor from top of column Reflux (liqUid) PARTIAL CONDENSER Cooling fluid Overhead product (vapor) The overhead product from an n-butane-n-pentane distillation column is 96 mole% butane. The temperature of the cooling fluid limits the condenser temperature to 40C or higher. Problems 295 (a) Using Raoult's law, estimate the minimum pressure at which the condenser can operate as a partial condenser (i.e., at which it can produce liquid for reflux) and the minimum pressure at which it can operate as a total condenser. In terms of dew point and bubble point, what do each of these pressures represent for the given temperature? (b) Suppose the condenser operates as a total condenser at 40C, the production rate of overhead product is 75 kmollh, and the mole ratio of reflux to overhead product is 1.5: 1. Calculate the molar flow rates and compositions of the reflux stream and the vapor feed to the condenser. (c) Suppose now that a partial condenser is used, with the reflux and overhead product in equilibrium at 40C and the overhead product flow rate and reflux-to-overhead product ratio having the values given in part (b). Calculate the operating pressure of the condenser and the compositions of the reflux and vapor feed to the condenser.

Vapor-liquid equilibrium calculations can sometimes be simplified through the use of a quantity called the relative volatility, which may be defined in terms of the tollowmg depiction of vapor and liquid phases in equilibrium: Vapor: Yi. Yi- Yk' The relative volatility of species i to species j is Yi =mole fraction of species i in vapor x, = mole fraction of species i in liquid Encyclopedia Equipment distillation column Yi/ x, aij = -,-- Yj/ Xj If al} is much greater than 1, species i is much more volatile than species j (i.e., it has a much greater tendency to vaporize at the system temperature and pressure); conversely, if aij 1, species i is much less volatile than species j. The closer aij is to 1, the more difficult it is to separate species i from species j by a process such as distillation or partial condensation of a vapor mixture. (a) Show that the relative volatility of species A to species B, aAB, equals the ratio of vapor pressures at the system temperature, p~/ PB' if both species obey Raoult's law and follow ideal gas behavior. (b) Determine the relative volatility of styrene to ethylbenzene at 85C and the relative volatility of benzene to ethylbenzene at the same temperature. Which pair would you classify as more difficult to separate by distillation? (c) Show that for a binary mixture of i and j aijX, Y- ='1+(aij-l)x, (d) Apply the equation from part (c) to a benzene-ethylbenzene system at 85C, using it to estimate the mole fractions of benzene in the vapor phase in equilibrium with liquids having benzene mole fractions of 0.0,0.2,0.4,0.6,0.8, and 1.0. Then calculate the total system pressure for each of these six conditions.

A stage of a separation process is defined as an operation in which components of one or more feed streams divide themselves between two phases, and the phases are taken off separately. In an ideal stage or equilibrium stage, the effluent (exiting) streams are in equilibrium with each other. Distillation columns often consist of a series of vertically distributed stages. Vapor flows upward and liquid flows downward between adjacent stages; some of the liquid fed to each stage vaporizes, and some of the vapor fed to each stage condenses. A representation of the top section of a distillation column is shown on the next page. (See Problem 4.26 for a more realistic representation.) Consider a distillation column operating at 0.4 atm absolute in which benzene and styrene are being separated. A vapor stream containing 65 mole% benzene and 35 mole% styrene enters stage 1 at a rate of 200 mollh, and liquid containing 55 mole% benzene and 45 mole% styrene leaves this stage at a rate of 150 mollh. You may assume (1) the stages are ideal, (2) Raoult's law can be used to relate the compositions of the streams leaving each stage, and (3) the total vapor and liquid molar flow rates do not change by a significant amount from one stage to the next. 296 Chapter 6 Multiphase Systems Stage n - 1 Stage 1 Stage n Stage 2 U",d I Vapor n/(mol/s) nu(molls) Xn + I (mol S/mol) yn(mol S/mol) n[ nu X n Yn -1 n/ Inu ~~ ":,1 T::' " "/ X3 Y2 nt nv X2 Yl n/molls) rnv(molls) Xl (mol S/mol) Yo(mol S/mol) (a) How would you expect the mole fraction of benzene in the liquid to vary from one stage to another, beginning with stage 1 and moving up the column? In light of your answer and consid ering that the pressure remains essentially constant from one stage to another, how would you then expect the temperature to vary at progressively higher stages'? Briefly explain. (b) Estimate the temperature at stage 1 and the compositions of the vapor stream leaving this stage and the liquid stream entering it. Then repeat these calculations for stage 2. (c) Describe how you would calculate the number of ideal stages required to reduce the styrene content of the vapor to less than 5 mole%.

The following diagram shows a staged absorption column in which n-hexane (H) is absorbed from a gas into a heavy oil. Equipment Encyclopedia absorber Gas effluent ncN(mol/s) YN(mol H/moll 1-----"""1 Stage N nc(mol/s) nL(mol/s) Yi(mol H/mol) Xi _ 1(mol H/mol) ..-- 8 Stagei+l Stage i - - - -~ H Stage i I---,;,j Stage 2 I---+~ Stage 1 nc(molls) nL(molls) Yi + I (mol H/mol) x/(mol H/mol) Liquid effluent nL1(mOl/s) xI(mol H/mol) Liquid feed 200 mol oil/s Gas feed nc = 100 molls 0 Yo =0.050 mol H/mol A gas feed stream containing 5.0 mole% hexane vapor and the balance nitrogen enters at the bottom of an absorption column at a basis rate of 100 molls, and a nonvolatile oil enters the top of the column in a ratio 2 mol oil fed/mol gas fed. The absorber consists of a series ofideal stages (see Problem 6.63), arranged so that gas flows upward and liquid flows downward. The liquid and gas streams leaving each stage are in equilibrium with each other (by the definition of an ideal stage), with compositions related by Raoult's law. The absorber operates at an approximately constant temperature T cae) and pressure P(mm Hg). Of the hexane entering the column, 99.5% is absorbed and leaves in the *Computer problem. Problems 297 liquid column effluent. At the given conditions it may be assumed that N2 is insoluble in the oil and that none of the oil vaporizes. (a) Calculate the molar flow rates and mole fractions of hexane in the gas and liquid streams leaving the column. Then calculate the average values of the liquid and gas molar flow rates in the column, ndmol/s) and nc(moVs). For simplicity, in subsequent calculations use these values as the molar flow rates of the liquid and gas streams leaving each stage. (b) Estimate the mole fraction of hexane in the gas leaving the bottom stage of the column (YI) and in the liquid entering this stage (X2)' (c) Suppose that Xi and .Vi are the mole fractions of hexane in the liquid and gas streams leaving stage i. Derive the following formulas and verify that they yield the answers you calculated in part (b): (1) (2) (d) Create a spreadsheet to determine the number of stages (N) required to reduce the moie fraction of hexane to its required final value [calculated in part (a)] or less for P = 760 torr and temperatures of 30e. 50C, and 70C. The spreadsheet should have the following structure (some calculated values are shown): Hexane Absorption I I I I I I I I P=- I 760 PR =- 1 I I 0.05 I I I I Yo = Xl = Ye = . 2.63E-04 I i i I I nCN = nLl =- I nc = nL =- I I I A=- 6.8776 I B= I 1172 C= 224.366 ! i I I I I I I I I I ! T p*(T) I T p*(T) T p*(T) ! I I I I 30 187.1 II I I 50 I , 70 I I I I i I x(i) y(i) I i I x(i) y(i) i x(i) y(i) I 0 I 5.00E-02 I 0 5.00E-02 I 0 5.00E-02 ! I I I i I I 1 2.43E-02 5.98E-03 I i 1 I I I 1 ! I I I 7.56E-04 I , I 2 3.07E-03 2 I 2 ! ! I I I \ 3 5.57E-04 1.37E-04 I 3 3 Enter the values of Xi, YN, he"" nLt ' and the average flow rates hc and nL calculated in parts (a) and (b). Then in the appropriate cells for the calculation at 30C, enter the Antoine formula for the vapor pressure, the value of XI, the formula for YI (Equation 1), and the formulas for X2 and Y2 (Equations 2 and 1). Then copy the formulas into successive rows, proceeding until the value of Yi is less than or equal to the calculated effluent value (YN)' The results (which should match the ones shown) indicate that three stages are required to achieve the specified hexane recovery at 30e. Repeat the calculations for the other two temperatures. (You should be able to do so entirely by copying cells from one location to another on the spreadsheet.) Do not go beyond 25 stages for any temperature, whether or not you achieve the required separation. 298 Chapter 6 Multiphase Systems Encyclopedia Equipment evaporator (e) You should have found that at 70C and 760 mm Hg the hexane mole fraction in the vapor levels out at a value above the target value, which means that the specified separation cannot be achieved at those conditions. Explain this result. Then use your spreadsheet to determine the minimum pressure at which the target absorption can be achieved at that temperature.

A vapor mixture containing 30 mole% benzene and 70% toluene at 1 atm is cooled isobarically in a closed container from an initial temperature of 115e. Use the Txy diagram of Figure 6.4-1 to answer the following questions. (a) At what temperature does the first drop of condensate form? What is its composition? (b) At one point during the process the system temperature is 100e. Determine the mole fractions of benzene in the vapor and liquid phases and the ratio (total moles in vapor/total moles in liquid) at this point. (c) At what temperature does the last bubble of vapor condense? What is its composition?

Three gram-moles of benzene and 7 gram-moles of toluene are placed in a closed cylinder equipped with a piston. The cylinder is immersed in a boiling-water bath that maintains the temperature at 100e. The force exerted on the piston can be varied to adjust the cylinder pressure to any desired value. The pressure is initially 1000 mm Hg and is gradually lowered to 600 mm Hg. Use the Pxy diagram of Figure 6.4-1 to convince yourself that the cylinder initially contains only liquid benzene and toluene and to answer the following questions. (a) At what pressure does the first vapor bubble form? What is its composition? (b) At what pressure does the last droplet of liquid evaporate? What is its composition? (c) What are the liquid and vapor compositions in equilibrium with each other when the pressure is 750 mm Hg? What is the ratio (moles vapor/mole liquid) at this point? (d) Estimate the volume of the cylinder contents when the pressure is (i) 1000 mm Hg, (ii) 750 mm Hg, and (iii) 600 mm Hg

A methanol-water feed stream is introduced to a vaporizer in which a molar fraction f of the feed is vaporized. The feed has a methanol mole fraction of XF = 0.4, and the vaporizer operates at a pressure of 1 atm absolute and SOe. Vapor and liquid leaving the device are in equilibrium at the temperature and pressure of the system and have methanol mole fractions of y and x, respectively. A Txy diagram for methanol-water mixtures at 1 atm absolute is shown below. The feed to the vaporizer and the liquid and vapor product streams are shown as points B, A, and C, respectively. 110 100 CH 30H-water vapor-liqui~ equilibrium data 2 P =1 atm '" 90 Vapor .3 e '" a. 80 E I- '" 70 60 '-- .....1 o 0.2 0.4 0.6 0.8 x, y (CH 30H liquid and vapor mole fractions) (a) Prove that! can be determined from the equation moles of vapor XF - x f = moles of liquid = y - x Use this result to determine! for the specific conditions cited above (XF = 0.4, T = SOC). (b) Use the Txy diagram to estimate the minimum and maximum temperatures at which the given feed stream could be separated into vapor and liquid fractions at 1 atm. In each case, what fraction of the feed would be vaporized?

Vapor-liquid equilibrium data for mixtures of acetone (A) and ethanol at 1 atm are given in the following table: Encyclopedia Equipment evaporator Problems 299 T(C) 78.3 67.3 65.9 63.6 61.8 60.4 59.1 58.0 I : 57.0 56.1 XA 0.000 0.250 0.300 0.400 0.500 0.600 0.700 0.800 I 0.900 1.000 YA 0.000 0.478 0.524 0.605 0.674 0.739 0.802 0.865 I 0.929 1.000 (a) Use the given data to construct a Txy diagram for this system. (b) A thermocouple inserted into a two-phase mixture of acetone and ethanol at equilibrium reads 62.1C. The system pressure is 1 atm. Use the Txy diagram to estimate the mole fractions of acetone in the liquid and vapor phases. (c) An equimolar mixture of acetone and ethanol is fed to an evacuated vessel and allowed to come to equilibrium at 65C and 1.00 atm absolute. Estimate (i) the molar compositions of each phase, (ii) the percentage of the total moles in the vessel that are in the vapor phase. and (iii) the percentage of the vessel volume occupied by the vapor phase. (d) A liquid mixture containing 40.0 mole% acetone and 60.0 mole% ethanol is fed to a continuous flash evaporator. Vapor and product streams leave the unit in equilibrium at 1.00 atm. The molar flow rate of the vapor product stream is 20% of the molar flow rate of the feed stream. Estimate the operating temperature of the evaporator and the compositions of the liquid and vapor product streams. (e) Use Raoult's law to estimate the bubble-point temperature and vapor composition in equilibrium with an equimolar liquid mixture of acetone and ethanol. Calculate the percentage errors in the estimated values of h p and y. Propose a reason why Raoult's law produces poor estimates for this system. (Suggestion: Consider the molecular structure of the two components.)

Your task in this problem will be to use a spreadsheet to generate a Txy diagram for a two-component system, using Raoult's law to express the vapor-liquid equilibrium distribution of each species. The spreadsheet will be constructed for the chloroform-benzene system at 1 atm (for which Raoult's law is not a very good approximation), but it can then be used for any other system by substituting different Antoine equation constants. (a) Look up the normal boiling points of chloroform and benzene and sketch the expected shape of a Txy diagram for these two species at 1 atm. Do not perform any calculations. (b) Create a spreadsheet that contains a title line in Row 1 (Txy Diagram for an Ideal Binary Solution), the names of the two species (Chloroform and Benzene), and the labels (A, B. C) and values of their Antoine equation constants (Rows 3 and 4), and a label P(mrn Hg) = and in the adjacent cell the pressure for which the diagram is to be generated (760) (Row 5). Then insert column headings x, T, y, pI, p2, pI+p2 in Row 7. These headings denote the mole fraction of the first species in the liquid phase, the equilibrium temperature, the mole fraction of the first species in the vapor phase, the partial pressures of the first and second species in the vapor phase, and the sum of the partial pressures of the two species. In the first column (under the x heading) enter 0.0, 0.05, 0.10.... , 0.95, 1.0. (You should be able to enter a formula in the second cell and then copy it into the remaining cells of the column rather than entering each number individually.) Then carry out the following procedure for each x value, Enter a temperature (for all but x = 0 and x = 1 you will have to guess a value). Enter formulas for the two partial pressures (use Raoult's law) and for their sum, and then enter a formula for y. Vary the value of T to determine the temperature at which the sum of the component partial pressures equals the specified total pressure of the system (760 mm Hg). This calculation can easily be done using the goalseek tool on most spreadsheet programs, or it can be done by manual trial and error. The row now contains the correct x and y values for the given temperature, Once you have done the calculation for the first x value, you should be able to copy formulas into subsequent rows rather than having to enter them again. When the calculation has been *Computer problem. 300 Chapter 6 Multiphase Systems completed for all rows of the table, draw the Txy diagram (using the graphing facility of your spreadsheet program if possible, otherwise by hand). (c) Explain in your own words exactly what you are doing in the bulleted sequence of steps in part (b) and give the relevant formulas. The phrase "bubble point" should appear in your explanation. (d) The following vapor-liquid equilibrium data have been obtained for mixtures of chloroform (C) and benzene (B) at 1 atm. T(C) I 80.6 I 79.8 79.0 I 77.3 75.3 71.9 68.9 61.4 Xc ! 0.00 I 0.08 0.15 I 0.29 0.44 0.66 0.79 1.00 ! 0.00 I 0.10 0.20 I Yc 0.40 0.60 0.80 0.90 1.00 I I Encyclopedia Equipment reactor condenser, distillation column Plot these data on the graph generated in part (b). Estimate the percentage errors in the Raoult's law values of the bubble-point temperature and vapor mole fraction for Xc = 0.44, taking the tabulated values to be correct. Why does Raoult's law give poor estimates for this system?

A liquid mixture containing 40.0 mole% methanol and 60.0 mole% I-propanol is placed in an open vessel and heated slowly. Estimate the temperature at which the mixture begins to boil. List assumptions made in your calculations. If heat is supplied continuously, how will the liquid temperature and composition change with time?

Acetaldehyde is synthesized by the catalytic dehydrogenation of ethanol: C2HsOH CH3CHO + Hz Fresh feed (pure ethanol) is blended with a recycle stream (95 mole% ethanol and 5% acetaldehyde), and the combined stream is heated and vaporized, entering the reactor at 280C. Gases leaving the reactor are cooled to -40C to condense the acetaldehyde and unreacted ethanol. Off-gas from the condenser is sent to a scrubber, where the uncondensed organic compounds are removed and hydrogen is recovered as a by-product. The condensate from the condenser, which is 45 mole% ethanol, is sent to a distillation column that produces a distillate containing 97 mole% acetaldehyde and a bottoms product that constitutes the recycle blended with fresh feed to the process. The production rate of the distillate is 1000 kg/h. The pressure throughout the process may be taken as 1 atm absolute. CONDENSER Distillate 97 mole% CH3CHO(l) DISTILLATION 55 mole% CH COLUMN 3CHO(I) Condensate 45 mole% CZH50H(I) Off-gas to scrubber CONDENSER 95 mole% CzH50H(I) 5 mole% CH 3CHO(I) ,-__-, Reactor output: Hz, CZH50H(v), CH3CHO(v) Recycle (a) Calculate the molar flow rates (kmol/h) of the fresh feed, the recycle stream, and the hydrogen in the off-gas. Also determine the volumetric flow rate (m3/h) of the feed to the reactor. (Suggestion: Use Raoult's law in the analysis of the condenser.) (b) Estimate (i) the overall and single-pass conversions of ethanol and (ii) the rates (kmoi/h) at which ethanol and acetaldehyde are sent to the scrubber

Dehydration of natural gas is necessary to prevent the formation of gas hydrates, which can plug valves and other components of a gas pipeline, and also to reduce potential corrosion prob- Problems ~1 lems. Water removal can be accomplished as shown in the following schematic diagram: CONDENSER Overhead product "'---'---+ ; DISTILLATION COLUMN PUMP TEG(I) + HzO Encyclopedia Equipment absorber, distillation column, pump Bottoms product @ Air + HzS Natural gas containing 80 Ibm HzO/106 SCF gas [SCF = ft3 (STP)] enters the bottom of an al'- sorber at a rate of 4.0 X 106 SCF/day. A liquid stream containing triethylene glycol (TEG. molecu1:rr weight = 150.2) and a small amount of water is fed to the top of the absorber. The absorber operates at 500 psia and 90F. The dried gas leaving the absorber contains 10 Ibm HzO/1ao SCF gas. Th.:: solvent leaving the absorber. which contains all the TEG-water mixture fed to the column pius J1l the water absorbed from the natural gas. goes to a distillation column. The overhead product str~~ from the distillation column contains only liquid water. The bottoms product stream. which contains TEG and water, is the stream recycled to the absorber. (a) Draw and completely label a flowchart of this process. Calculate the mass flow rate (lb::"day' and volumetric flow rate (ft3/day) of the overhead product from the distillation column_ (b) The greatest possible amount of dehydration is achieved if the gas leaving the absorption column is in equilibrium with the solvent entering the column. If the Henry's law constant for wat~r in TEG at 90F is 0.398 psialmol fraction. what is the maximum allowable mole fraction oi W:H':::" in the solvent fed to the absorber? (c) A column of infinite height would be required to achieve equilibrium between the gas and liqlli.:i at the top of the absorber. For the desired separation to be achieved in practice. the mok fraction of water in the entering solvent must be less than the value calculated in part (b). S~it 80% of that value and the flow rate of TEG in the recirculating solvent is 37 Ibm TEG 1~ "3{cr absorbed in the column. Calculate the flow rate (Ibm/day) of the solvent stream enterin~ :.::.~ absorber and the mole fraction of water in the solvent stream leaving the absorber. (d) What is the purpose ofthe distillation column in the process? (Hint: Think about how the rro..~ would operate without it.)

A two-stage process is used to separate HzS from a gas containing 96% Hz and ~% H:S b~- yoiumc. The HzS is absorbed in a solvent, which is then regenerated by air in a stripping column. The Hcmy's law constant for the absorption of HzS in the solvent at OC is 22 atm/mole fraction. Data on Process Streams L 1: 0.200 mole% HzS L z: Assume at equilibrium with Gz at OC G1: 100 mol/h 96% Hz. 4% HzS. 1.8 atm Gz: 99.9% Hz. 0.1% HzS G3 : 200 mol air/h @ Feed gas Hz + HzS @ Clean air 6.73. Encyclopedia Equipment stripper, heater, absorber 302 Chapter 6 Multiphase Systems Encyclopedia Equipment crystallizer Encyclopedia Equipment crystallizer Encyclopedia Equipment crystallizer Encyclopedia Equipment crystallizer Encyclopedia Equipment crystallizer Encyclopedia Equipment crystallizer. filter. pump (a) Briefly explain in your own words the functions of the three process units. Include in your explanation the purpose of the air in the stripper and the reason the stripper operates at a higher temperature than the absorber. (b) Calculate the molar flow rate of pure solvent and the volumetric flow rate of the gas at G4, neglecting evaporation of solvent in both columns. (See flowchart.)

The solubility of sodium bicarbonate in water is 11.1 g NaHC03/100 g H2 0 at 30C and 16.4 g NaHC03/100 g H20 at 60C. If a saturated solution of NaHC03 at 60C is cooled and comes to equilibrium at 30C, what percentage of the dissolved salt crystallizes?

An aqueous solution of potassium hydroxide is fed at a rate of 875 kg/h to an evaporative crystallizer operating at lOC, producing crystals of KOH2H20. A 5 g aliquot of the feed solution is titrated to neutrality with 22.4 mL of 0.85 molar H2S04 The solubility of KOH at lOC is 103 kg KOH/100 kg H2 0. At what rate must water be evaporated to crystallize 60% of the KOH in the feed

A salt A is soluble in a solvent S. A conductivity meter used to measure the solute concentration in A-S solutions is calibrated by dissolving a known quantity of A in S, adding more S to bring the solution volume to a fixed value, and noting the conductivity meter reading. The data given below are taken at 30C: Solute Solution Meter Dissolved Volume Reading (g) (mL) R 0 100.0 0 20.0 100.0 30 30.0 100.0 45 The following experiment is performed. One hundred sixty grams of A is dissolved in S at 30C. S is added until a final solution volume of 500 mL is obtained. The solution is cooled slowly to OC while being stirred and is maintained at this temperature long enough for crystallization to be complete. The concentration of A in the supernatant liquid is then measured with the conductivity meter, yielding R = 17.5. The solution is next reheated in small temperature increments. The last crystal is observed to dissolve at 10.2C. A specific gravity of 1.10 may be assumed for all A-S solutions. (a) Derive an expression for C(g A/mL solution) in terms of R. (b) Calculate the solubilities (g A/100 g S) at lO.2C and OC and the mass of solid crystals in the beaker at OC. (c) If half the solvent in the flask were to evaporate at OC, how much more A would come out of solution?

A saturated MgS04 solution at 130F is fed to a crystallizer operating at SOap. The solution leaving the crystallizer is saturated. Magnesium sulfate solubilities are 35 wt% MgS04 at 130F and 23 wt% MgS04 at SOap. (a) Write the molecular formula for the crystalline product that forms. (See Table 6.5-1.) (b) A production rate of 1000 kg/h of crystalline material is desired. Calculate (i) the required feed rate to the crystallizer (kg/h), and (ii) the rate (kg/h) at which anhydrous MgS04 could be recovered from the crystals.

A solution containing 100 Ibm KN03/100 Ibm H20 at 80C is fed to a cooling crystallizer operated at 25C. Slurry from the crystallizer (KN03 crystals suspended in saturated solution) is fed to a filter, where the crystals are separated from the solution. Use the solubility data in Figure 6.5-1 to determine the production rate of crystals (Ibm/Ibm feed) and the solid-to-liquid mass ratio (Ibm crystals/Ibm liquid) in the slurry leaving the crystallizer.

A 10.0 wt% aqueous solution ofsodium chloride is fed to an evaporative crystallizer operated under a partial vacuum. Evaporation of water concentrates the remaining solution beyond its saturation point at the crystallizer temperature and causes crystallization of NaC!. The crystallizer product is a slurry of solute crystals suspended in a saturated solution at 80C. The unit is to produce 1000 kg NaCI(s)/h. The solubility of NaCI in water is given by Figure 6.5-1. (a) Derive expressions for the required rate of evaporation of water (kg/h) and the mass flow rate of solution in the exit slurry in terms of the mass flow rate of the feed stream to the crystallizer. Encyclopedia Equipment evaporator, crystallizer, dryer Encyclopedia Equipment reactor, filter Encyclopedia Equipment filter, crystallizer Prohlems 303 Determine the minimum possible feed rate (explain why it is the minimum rate) and the corresponding values of the evaporation rate and exit solution flow rate. (b) The pump that conveys the exit slurry from the crystallizer to a downstream filter cannot handle material containing more than 40 wt% solids. Determine the maximum feed rate to the crystallizer and the corresponding evaporation rate.

Potassium dichromate (KZCrZ07) is to be recovered from a 21 wt% aqueous solution in a continuous crystallization operation. The solution is joined by a recycle stream and fed to a vacuum evaporator where water is removed and the remaining solution is cooled to 30C, at which temperature the solubility of the salt is 0.20 kg KzCrz07/kg HzO. The solution and suspended potassium dichromate crystals flow to a centrifuge. The crystals and 5.0% of the solution constitute the solid effluent from the centrifuge, and the remaining solution is recycled to the evaporator. The solid effluent. which contains 90 wt% crystals and 10% entrained solution, is fed to a dryer. where it is contacted with hot air. The remaining water in the effluent is evaporated, leaving pure potassium dichromate crystals. The air leaves the dryer at 90C and 1 atm with a dew point of 39.2e. For a production rate of 1000 kg solid KzCr207/h. calculate the required feed rate (kg/h) of 21 % solution, the rate of evaporation of water in the evaporator (kg/h), the flow rate (kg/h) of the recycle stream, and the feed rate of air (standard liters/h).

Sodium bicarbonate is synthesized by reacting sodium carbonate with carbon dioxide and water at 70C and 2.0 atm gauge: NazC03 + COz + HzO 2 NaHC03 An aqueous solution containing 7.00 wt% sodium carbonate and a gas stream containing 70.0 mole% CO2 and the balance air are fed to the reactor. All of the sodium carbonate and some of the carbon dioxide in the feed react. The gas leaving the reactor, which contains the air and unreacted CO2 , is saturated with water vapor at the reactor conditions. A liquid-solid slurry of sodium bicarbonate crystals in a saturated aqueous solution containing 2.4 wt% dissolved sodium bicarbonate and no dissolved COz leaves the reactor and is pumped to a filter. The wet filter cake contains 86 wt% sodium bicarbonate crystals and the balance saturated solution, and the filtrate is also saturated solution. The production rate of solid crystals is 500 kg/h. Suggestion: Although the problems to be given can be solved in terms of the product flow rate of 500 kg NaHCOJ(s)/h, it might be easier to assume a different basis and then scale the process to the desired production rate of crystals. (a) Calculate the composition (component mole fractions) and volumetric flow rate (m3/min) of the gas stream leaving the reactor. (b) Calculate the feed rate of gas to the process in standard cubic meters/min [m3 (STP)/min]. (c) Calculate the flow rate (kg/h) of the liquid feed to the process. What more would you need to know to calculate the volumetric flow rate of this stream? (d) The filtrate was assumed to leave the filter as a saturated solution at 70e. What would be the effect on your calculations if the temperature of the filtrate actually dropped to 50C as it passed through the filter? (e) The reactor pressure of 2 atm gauge was arrived at in an optimization study. What benefit do you suppose would result from increasing the pressure? What penalty would be associated with this increase? The term "Henry's law" should appear in your explanation. (Hint: The reaction occurs in the liquid phase and the CO2 enters the reactor as a gas. What step must precede the reaction?)

An ore containing 90 wt% MgS04 7HzO and the balance insoluble minerals is fed to a dissolution tank at a rate of 60,000 Ibm/h along with fresh water and a recycle stream. The tank contents are heated to 110F, causing all of the magnesium sulfate heptahydrate in the ore to dissolve, forming a saturated solution. The resulting slurry of the insoluble minerals in saturated MgS04 solution is pumped to a heated filter, where a wet filter cake is separated from a solids-free filtrate. The filter cake retains 5 Ibm of saturated solution per 100 Ibm of minerals. The filtrate is sent to a crystallizer in which the temperature is reduced to 50F, producing a slurry of MgS04 ' 7H20 crystals in a saturated solution that is sent to another filter. The product filter cake contains all of the crystals and entrained solution, again in a ratio of 5 Ibm solution per 100 Ibm crystals. The filtrate from this filter is returned to the dissolution tank as the recycle stream. Solubility data: Saturated magnesium sulfate solutions at llOF and 50F contain 32 wt% MgS04 and 23 wt% MgS04 , respectively. 304 Chapter 6 Multiphase Systems FILTER Makeup water, mwllbdh) '----'t'----' --1------1 60,000 Ibm ore/h 90% MgS04 '7HzO/h 10% S(insoluble solids) ! Filter cake, mCake(lbdh) (5 Ibm sol'n/lOOlbm S) Recycle solution, mR(lbdhl Encyclopedia Equipment reactor, crystallizer, filter (a) Explain why the solution is first heated (in the dissolution tank) and filtered and then cooled (in the crystallizer) and filtered. (b) Calculate the production rate of crystals and the required feed rate of fresh water to the dissolution tank. (Note: Don't forget to include water of hydration when you write a mass balance on water.) (c) Calculate the ratio Ibm recyclellbmmakeup water.

An aqueous waste stream leaving a process contains 10.0 wt% sulfuric acid and 1 kg nitric acid per kg sulfuric acid. The flow rate ofsulfuric acid in the waste stream is 1000 kg/h. The acids are neutralized before being sent to a wastewater treatment facility by combining the waste stream with an aqueous slurry ofsolid calcium carbonate that contains 2 kg of recycled liquid per kg solid calcium carbonate. (The source of the recycled liquid will be given later in the process description.) The following neutralization reactions occur in the reactor: CaC03 + H2S04 CaS04 + H2 0 + CO2 CaC03 + 2 RN03 Ca(N03 )2 + H2 0 + CO2 The sulfuric and nitric acids and calcium carbonate fed to the reactor are completely consumed. The carbon dioxide leaving the reactor is compressed to 30 atm absolute and 40C and sent elsewhere in the plant. The remaining reactor effluents are sent to a crystallizer operating at 30C, at which temperature the solubility of calcium sulfate is 2.0 g CaS04/1000 g H2O. Calcium sulfate crystals form in the crystallizer and all other species remain in solution. The slurry leaving the crystallizer is filtered to produce (i) a filter cake containing 96% calcium sulfate crystals and the remainder entrained saturated calcium sulfate solution, and (ii) a filtrate solution saturated with CaS04 at 30C that also contains dissolved calcium nitrate. The filtrate is split, with a portion being recycled to mix with the solid calcium carbonate to form the slurry fed to the reactor, and the remainder being sent to the wastewater treatment facility. (a) Draw and completely label a flowchart for this process. (b) Speculate on why the acids must be neutralized before being sent to the wastewater treatment facility. (c) Calculate the mass flow rates (kg/h) of the calcium carbonate fed to the process and of the filter cake; also determine the mass flow rates and compositions of the solution sent to the wastewater facility and of the recycle stream. (Caution: If you write a water balance around the reactor or the overall system, remember that water is a reaction product and not just an inert solvent.) (d) Calculate the volumetric flow rate (Llh) of the carbon dioxide leaving the process at 30 atm absolute and 40e. Do not assume ideal gas behavior. (e) The solubility of Ca(N03h at 30C is 152.6 kg Ca(N03)2 per 100 kg H2O. What is the maximum ratio of nitric acid to sulfuric acid in the feed that can be tolerated without encountering difficulties associated with contamination of the calcium sulfate by-product by Ca(N03h?

A solution of diphenyl (MW = 154.2) in benzene is formed by mixing 56.0 g diphenyl with 550.0 mL of benzene. Estimate the effective vapor pressure of the solution at 30C and the melting and boiling points of the solution at 1 atm.

An aqueous solution of urea (MW = 60.06) freezes at -4.6C and 1 atm. Estimate the normal boiling point of the solution; then calculate the mass of urea (grams) that would have to be added to 1.00 kg of water to raise the normal boiling point by 3e

A solution is prepared by dissolving 0.5150 g of a solute (MW = 110.1) in 100.0 g of an organic solvent (MW = 94.10). The solution is observed to have a freezing point 0.41C below that of the pure Encyclopedia Equipment extractor Problems 305 solvent. A second solution is prepared by dissolving 0.4460 g of a solute having an unknown molecular weight in 95.60 g of the original solvent. A freezing point depression of 0.49C is observed. Determine the molecular weight of the second solute and the heat of fusion (kl/mol) of the solvent. The melting point of the pure solvent is -5.000C.

Derive Equation 6.5-4 for the boiling-point elevation of a dilute solution of a nonvolatile solute with mole fraction x in a solvent that has a pure-component vapor pressure p; (T). To do so, suppose that when the pressure is Po, the pure solvent boils at temperature TbO [so that Po = p;(TbO )] and the solvent in the solution boils at Tbs > TbOo Further suppose that at temperature ToO the effective vapor pressure of the solvent is Ps = (p;).(TbO ) < Po. (See diagram.) Solution Solvent \ \ 'I' I I I -y I ,: ~:.,' I ~~ . To T Temperature The procedure is as follows. (a) Write the Clausius-Clapeyron equation (Equation 6.1-3) for Ps (the effective solvent vapor pressure at TbO ) and then for Po (the effective solvent vapor pressure at Tbs), assuming that at the low solute concentrations in question the heat of vaporization is the same at both temperatures. Subtract the two equations. Simplify the equation algebraically, assuming that TbO and T bs are close enough together to say that TbOTbs = T~(). (b) Substitute the Raoult's law expression (Equation 6.5-2) for Ps = (P;)e(TbO)' Observe that if x 1 (which it is for highly dilute solutions), then In(l - x) = - X. The desired result follows.

The distribution coefficient ofstyrene distributed between ethylbenzene and ethylene glycol at 25C is 0.19 mass fraction in the ethylene glycol phase per mass fraction in the ethylbenzene phase. One hundred grams of pure ethylene glycol is added to 120 g of a mixture containing containing 75 wt% ethylbenzene and 25% styrene, and the resulting blend is allowed to equilibrate. How much styrene transfers to the ethylene glycol phase, assuming that ethylene gylcol and ethylbenzene are immiscible?

A stream of 5.00 wt% oleic acid in cottonseed oil enters an extraction unit at a rate of 100.0 kg/h. The unit operates as an equilibrium stage (the streams leaving the unit are in equilibrium) at 85C. At this temperature, propane and cottonseed oil are essentially immiscible, and the distribution coefficient (oleic acid mass fraction in propane/oleic acid mass fraction in cottonseed oil) is 0.15. (a) Calculate the rate at which liquid propane must be fed to the unit to extract 90% of the oleic acid. (b) Estimate the minimum operating pressure of the extraction unit (i.e., the pressure required to keep the propane liquid at 85C). (c) High-pressure operation is costly and introduces potential safety hazards. Suggest two possible reasons for using propane as the solvent when other less volatile hydrocarbons are equally good solvents for oleic acid.

Benzene and hexane are being considered as solvents to extract acetic acid from aqueous mixtures. At 30C, distribution coefficients for the two solvents are KB = 0.098 mass fraction acetic acid in benzene/mass fraction acetic acid in water and KH = 0.017 mass fraction acetic acid in hexane/mass fraction acetic acid in water. (a) Based on the distribution coefficients only, which of the two solvents would you use and why? Demonstrate the logic of your decision by comparing the quantities of the two solvents required to reduce the acetic acid content in 100 kg of an aqueous solution from 30 wt% to 10 wt%. (b) What other factors may be important in choosing between benzene and cyclohexane?

Acetone is to be extracted with n-hexane from a 40.0 wt% acetone-60.0 wt% water mixture at 25C. The acetone distribution coefficient (mass fraction acetone in the hexane-rich phase/mass fraction acetone in the water-rich phase) is 0.343. 13 Water and hexane may be considered immiscible. Three different processing alternatives are to be considered: a two-stage process and two single-stage processes. (a) In the first stage of the proposed two-stage process, equal masses of the feed mixture and pure hexane are blended vigorously and then allowed to settle. The organic phase is withdrawn and the aqueous phase is mixed with 75% of the amount of hexane added in the first stage. The mixture is allowed to settle and the two phases are separated. What percentage of the acetone in the original feed solution remains in the water at the end of the process? (b) Suppose all of the hexane added in the two-stage process of part (a) is instead added to the feed mixture and the process is carried out in a single equilibrium stage. What percentage of the acetone in the feed solution remains in the water at the end of the process? (c) Finally, suppose a single-stage process is used but it is desired to reduce the acetone content of the water to the final value of part (a). How much hexane must be added to the feed solution? (d) Under what circumstances would each of the three processes be the most cost-effective? What additional information would you need to make the choice?

Penicillin is produced by fermentation and recovered from the resulting aqueous broth by extraction with butyl acetate. The penicillin distribution coefficient K (mass fraction of penicillin in the butyl acetate phase/mass fraction of penicillin in the water phase) depends strongly on the pH in the aqueous phase: pH 2.1 I 4.4 5.8 K 25.0 1.38 0.10 This dependence provides the basis for the process to be described. Water and butyl acetate may be considered immiscibile. The extraction is performed in the following three-unit process: Fermentation broth Organic extract Aqueous raffinate (pH 2.1) Alkaline solution Aqueous extract (product solution, pH 5.8) Broth from a fermentor containing dissolved penicillin, other dissolved impurities, and water is acidified in a mixing tank. The acidified broth, which contains 1.5 wt% penicillin, is contacted with liquid butyl acetate in an extraction unit consisting of a mixer, in which the aqueous and organic phases are brought into intimate contact with each other, followed by a settling tank, in which the two phases separate under the influence of gravity. The pH of the aqueous phase in the extraction unit equals 2.1. In the mixer 90% of the penicillin in the feed broth transfers from the aqueous phase to the organic phase. The two streams leaving the settler are in equilibrium with each other-that is, the ratio of the penicillin mass fractions in the two phases equals the value of K corresponding to the pH of the aqueous phase (= 2.1 in Unit 1). The impurities in the feed broth remain in the aqueouS phase. The raffinate (by definition, the product stream containing the feed-solution solvent) leav- 13 Perry's Chemical Engineers' Handbook, 7th Edition, McGraw-Hill, New York, 1997. Problems 307 ing Extraction Unit 1 is sent elsewhere for further processing, and the organic extract (the product stream containing the extracting solvent) is sent to a second mixer-settler unit. In the second unit, the organic solution fed to the mixing stage is contacted with an alkaline aqueous solution that adjusts the pH of the aqueous phase in the unit to 5.8. In the mixer, 90% of the penicillin entering in the organic feed solution transfers to the aqueous phase. Once again, the two streams emerging from the settler are in equilibrium. The aqueous extract is the process product. (a) Taking a basis of 100 kg of acidified broth fed to the first extraction unit, draw and completely label a flowchart of this process and carry out the degree-of-freedom analysis to show that all labeled variables can be determined. (Suggestion: Consider the combination of water, impurities, and acid as a single species and the alkaline solution as a second single species, since the components of these "pseudospecies" always stay together in the process.) (b) Calculate the ratios (kg butyl acetate required/kg acidified broth) and (kg alkaline solution required/kg acidified broth) and the mass fraction of penicillin in the product solution. (c) Briefly explain the following: (i) What is the likely reason for transferring most of the penicillin from an aqueous phase to an organic phase and then transferring most of it back to an aqueous phase. when each transfer leads to a loss of some of the drug? (ii) What is the purpose of acidifying the broth prior to the first extraction stage, and why is the extracting solution added to the second unit a base? (iii) Why are the two "raffinates" in the process the aqueous phase leaving the first unit and the organic phase leaving the second unit, and vice versa for the "extracts"? (Look again at the definitions of these terms.)

A mixture of 20 wt% water, 33% acetone. and the remainder methyl isobutyl ketone is brought to equilibrium at 25C. If the total mass of the system is 1.2 kg, use the data in Figure 6.6-1 to estimate the composition and mass of each phase of the mixture

Five kilograms of a 30 wt% acetone-70% water mixture is added to 3.5 kg of a 20 wt% acetone-80% MIBK mixture at 25C. Use Figure 6.6-1 to estimate the mass and composition of each phase of the resulting mixture.

An aqueous acetone solution is fed at a rate of 32.0 Ibm /h to a stirred tank. A stream of pure methyl isobutyl ketone is also fed to the tank. and the resulting mixture is sent to a settler operating at 25C. One of the phases formed has a flow rate of 41.0 Ibm/h and contains 70 wt% MIBK. Use Figure 6.6-1 to determine the flow rate and composition of the second product stream and the rate at which MIBK is fed to the unit

Two systems contain water, acetone. and methyl isobutyl ketone in equilibrium at 25C. The first system contains equal masses of the three species, and the second one contains 9.0% acetone, 21.0% water, and 70.0% MIBK by mass. Let xa.aq and xa.org , respectively, denote the mass fractions of acetone in the aqueous phase (the phase that contains most of the water in the system) and the organic phase (the phase that contains most of the MIBK), and let xw.aq and Xw,org denote the mass fractions of water in the two phases. (a) Use Figure 6.6-1 to estimate the mass and composition (component mass fractions) of each phase of the mixtures in System 1 and in System 2. (b) Determine the distribution coefficient of acetone in the organic phase relative to the aqueous phase in each system, Ka = X,,-org i xa.aq ' If a process is being designed to extract acetone from one of the two solvents (water and MIBK) to the other one, when would a high value of Ka be desirable and when would a low value be desirable? (c) Determine the selectivity, l3aw, of acetone relative to water in the two systems, where (mass fraction acetone/mass fraction water)extract phase l3aw = (mass f' / f' ) ractlOn acetone mass ractlOn water raffinate phase What would be the value of l3aw if water and MIBK were completely immiscible? (d) Express the selectivity, l3aw, in terms of the distribution coefficients of acetone and water, Ka and Kw [Start with the formula given in part (c).) If MIBK is being used to extract acetone from an aqueous phase. under what circumstances might it be important to have a very high value of l3aw, even if it means that less acetone is being extracted?

Water is used to extract acetone from a 30 wt% acetone-70% MIBK mixture flowing at a rate of 200 kg/h. Two equilibrium stages at 25C are used as shown in the following diagram. If 300 kg H20/h is fed to each extraction unit, what fraction of the acetone in the feed solution would be removed and what would be the composition of the combined extract?

Air at 25C and 1 atm with a relative humidity of25% is to be dehumidified in an adsorption column packed with silica gel. The equilibrium adsorptivity of water on silica gel is given by the expression14 X*(kg water/lOO kg silica gel) = 12.5 p~,o PH,O where PH,O is the partial pressure of water in the gas contacting the silica gel and P~20 is the vapor pressure of water at the system temperature. Air is fed to the column at a rate of 1.50 Umin until the silica gel is saturated (i.e., until it reaches equilibrium with the feed air), at which point the flow is stopped and the silica gel replaced. (a) Calculate the minimum amount ofsilica gel needed in the column if replacement is to take place no more frequently than every two hours. State any assumptions you make. (b) Briefly describe this process in terms that a high school student would have no trouble understanding. (What is the process designed to do, what happens within the column, and why is replacement of the column packing necessary?)

A 50.0-L tank contains an air-carbon tetrachloride gas mixture at an absolute pressure of 1 atm, a temperature of 34C, and a relative saturation of 30%. Activated carbon is added to the tank to remove the CCl4 from the gas by adsorption and the tank is then sealed. The volume of added activated carbon may be assumed negligible in comparison to the tank volume. (a) Calculate PCCl4 at the moment the tank is sealed, assuming ideal gas behavior and neglecting adsorption that occurs prior to sealing. (b) Calculate the total pressure in the tank and the partial pressure of carbon tetrachloride at a point when half of the CCI4 initially in the tank has been adsorbed. Note: It was shown in Example 6.7-1 that at 34C X* (g CCl4 adsorbed) = 0.0762pcC14 g carbon 1 + 0.096pCCl4 where PCCl4 is the partial pressure (mm Hg) of carbon tetrachloride in the gas contacting the carbon. (c) How much activated carbon must be added to the tank to reduce the mole fraction of CCl4 in the gas to 0.001?

The following equilibrium data 15 have been obtained for the adsorption of nitrogen dioxide, N02l on silica gel at 25C and 1 atm: PN02 (mm Hg) 0 2 I 4 6 t 8 10 12 X*(kg N02/100 kg silica gel) 0 0.4 0.9 I 1.65 I 2.60 3.65 4.85 (a) Confirm that these data are reasonably correlated by the Freundlich isotherm X* = KFP~02 I 4R. Yang, Gas Separation by Adsorption Processes, Butterworths, London. 1987. p. 13. 15Adapted from R. E. Treybal, Mass- Transfer Operations, 3rd Edition. McGraw-HilI. New York. 1980. p. 653. Problems 309 and determine the values of KF and {3 that provide the best correlation. (Use one of the graphical methods introduced in Section 2.7c.) (b) The adsorption column shown in the figure below has an internal diameter of 10.0 em and a bed height of 1.00 m. The bed of silica gel has a bulk density of 0.75 kg/L. The adsorber is to remove N02 from a stream containing 1.0 mole% N02 and the balance air that enters the adsorber at 8.00 kg/h. The pressure and temperature are maintained at 1 atm and 25C. Past experience with this system has shown that a plot of the partial pressure ratio [(PNOz)outJet/(PNO, )inler] versus time produces a breakthrough curve with the following appearance. Inlet gas 8 kg/min 1.0 vol% N02(g) l ADSORPTION COLUMN T 1 m 1 1.0 (PN02)outler (PN02)lOlet Breakthrough curve Breakthrough ;e Time (min) Using the isotherm derived in part (a), determine the time (in min) required for breakthrough of the N02. (c) Silica gel in the column can be regenerated (i.e., adsorbed NOz can be removed so that the silica gel column can be reused) by elevating the bed temperature and/or purging the bed with clean air. Suppose such a regeneration process requires 1.5 hours to accomplish. Process shutdowns can be avoided by installing several silica gel columns in parallel, using one to carry out the purification while the others are being regenerated. What is the minimum number of columns required to achieve continuous process operation?

Various amounts of activated carbon were added to a fixed amount of raw cane sugar solution (48 wt% sucrose in water) at 80C. A colorimeter was used to measure the color of the solutions. R. which is proportional to the concentration of trace unknown impurities in the solution. The following data were obtained (See footnote 15, p. 654.) Equipment Encyclopedia adsorber kg carbon/kg dry sucrose I R (color units/kg sucrose) I : o I 0.005 20.0 I 10.6 0.010 I 0.015 I 0.020 6.0 I 3.4 I 2.0 0.030 1.0 The reduction in color units is a measure of the mass of impurities (the adsorbate) adsorbed on the carbon (the adsorbent). (a) The general form of the Freundlich isotherm is X = K (.13 , f I where X; is the mass of i adsorbed/mass of adsorbent and Cj is the concentration of i in solution. Demonstrate that the Freundlich isotherm may be formulated for the system described above as it = K~Rf3 where it is the % removal of color / [mass of carbon / mass of dissolved sucrose]. Then determine K~ and {3 by fitting this expression to the given data, using one of the graphical methods in Section 2.7. (b) Calculate the amount of carbon that would have to be added to a vat containing 1000 kg of the 48 wt% sugar solution at 80a C for a reduction in color content to 2.5% of the original value. this page inten