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### 10.15. Homework Problems

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10.1 | For a separations process it is necessary to determine the VLE compositions of a mixture of ethyl bromide and n-heptane at 30°C. At this temperature the vapor pressure of pure ethyl bromide is 0.7569 bar, and the vapor pressure of pure n-heptane is 0.0773 bar. Calculate the bubble pressure and the composition of the vapor in equilibrium with a liquid containing 47.23 mol% ethyl bromide assuming ideal solution behavior. Compare the calculated pressure to the experimental value of 0.4537 bar. | |||||||||||||||||||||||||||||||||||||||

10.2 | Benzene and ethanol (e) form azeotropic mixtures. Prepare a y-x and a P-x-y diagram for the benzene-ethanol system at 45°C assuming the mixture is ideal. Compare the results with the experimental data tabulated below of Brown and Smith, Austral. J. Chem. 264 (1954). (P in the data table is in bar.)
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10.3 | The following mixture of hydrocarbons is obtained as one stream in a petroleum refinery on a mole basis: 5% ethane, 10% propane, 40% n-butane, 45% isobutane. Assuming the shortcut K-ratio model: (a) compute the bubble point of the mixture at 5 bar; (b) compute the dew point of the mixture at 5 bar; (c) find the amounts and compositions of the vapor and liquid phases that would result if this mixture were to be isothermally flash vaporized at 30°C from a high pressure to 5 bar. | |||||||||||||||||||||||||||||||||||||||

10.4 | Consider a mixture of 50 mol% n-pentane and 50 mol% n-butane at 14 bar.
What is the dew-point temperature? What is the composition of the first drop of liquid? At what temperature is the vapor completely condensed if the pressure is maintained at 14 bar? What is the composition of the last drop of vapor?
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10.5 | A 50 mol% mixture of propane(1) and n-butane(2) enters an isothermal flash drum at 37°C. If the flash drum is maintained at 0.6 MPa, what fraction of the feed exits as liquid? What are the compositions of the phases exiting the flash drum? Work the problem in the following two ways.
Use Raoult’s law (use the Peng-Robinson equation to calculate pure component vapor pressures). Assume ideal mixtures of vapor and liquid. (Use the Peng-Robinson equation to obtain f ^{sat}for each component.)
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10.6 | A mixture of 55 mol% ethanol in n-propanol is at 0.2MPa and 80°C at 70 mol/s. The stream is fed to a adiabatic flash drum. Calculate the outlet stream flow rates, temperatures, and compositions at 0.05MPa.
Use the path of Fig. 2.6(a). Use the path of Fig. 2.6(c).
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10.7 | An equimolar ternary mixture of acetone, n-butane, and ammonia at 1 MPa is to be flashed. List the known variables, unknown variables, and constraining equations to solve each of the cases below. Assume ideal solution thermodynamics and write the flash equations in terms of K-ratios, with the equations for calculating K-ratios written separately.
Bubble temperature Dew temperature Flash temperature at 25 mol% vapor. Raised to midway between the bubble and dew temperature, then adiabatically flashed
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10.8 | Tank A is rapidly half-filled with volatile hydrocarbon. Tank B is 10 times as large and rapidly half-filled with the same hydrocarbon. Initially the gas space can be considered to be free of volatile organic and at the same pressure. The tanks are then closed. The tanks warm 20°C and the pressure in both tanks goes up. After warming, does one tank have a higher pressure than the other, or are the final pressures the same? Show your result with equations. Your answer should be general; it should not depend on numerical calculations.
Do not confuse a flash point calculation with an isothermal flash calculation. | |||||||||||||||||||||||||||||||||||||||

10.9 | Above a solvent’s flash point temperature, the vapor concentration in the headspace is sufficient that a spark will initiate combustion; therefore, extreme care must be exercised to avoid ignition sources. Calculate the vapor phase mole fraction for the following liquid solvents using flash points listed, which were obtained from the manufacturer’s material safety data sheets (MSDS). The calculated vapor concentration is an estimate of the lower flammability limit (LFL). Assume that the headspace is an equilibrium mixture of air and solvent at 760 mmHg. The mole fraction of air dissolved in the liquid solvent is negligible for this calculation.
Methane, – 187.8°C Propane, – 104.5°C Pentane, – 48.9°C Hexane, – 21.7°C Ethanol, 12.7°C 2-butanone, – 5.6°C Toluene, 4.4°C m-xylene, 28.8°C Ethyl acetate, – 4.5°C
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10.10 | Solvent vessels must be purged before maintenance personnel enter in order to ensure that: (1) sufficient oxygen is available for breathing; (2) vapor concentrations are below the flash point; (3) vapor concentrations are below the Occupational Safety and Health Administration (OSHA) limits if breathing apparatus is not to be used. Assuming that a 8 m^{3} fixed-roof solvent tank has just been drained of all liquid and that the vapor phase is initially saturated at 22°C, estimate the length of purge necessary with 2 m^{3}/min of gas at 0.1 MPa and 22°C to reach the OSHA 8-hr exposure limit.^{[13]}
Hexane 500 ppm 1-butanol 100 ppm Chloroform 50 ppm Ethanol 1000 ppm Toluene 200 ppm
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10.11 | A pharmaceutical product is crystallized and washed with absolute ethanol. A 100 kg batch of product containing 10% ethanol by weight is to be dried to 0.1% ethanol by weight by passing 0.2 m^{3}/min of 50°C nitrogen through the dryer. Estimate the rate (mol/min) that ethanol is removed from the crystals, assuming that ethanol exerts the same vapor pressure as if it were pure liquid. Based on this assumption, estimate the residence time for the crystals in the dryer. The dryer operates at 0.1 MPa and the vapor pressure of the pharmaceutical is negligible.
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10.12 | Benzyl chloride is manufactured by the thermal or photochemical chlorination of toluene. The chlorination is usually carried out to no more than 50% toluene conversion to minimize the benzal chloride formed. Suppose reactor effluent emissions can be modeled ignoring by-products, and the effluent is 50 mol% toluene and 50 mol% benzyl chloride. Estimate the emission of toluene and benzyl chloride (moles of each) when an initially empty 4 m^{3} holding tank is filled with the reactor effluent at 30°C and 0.1 MPa.
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10.13 | This problem explores emissions during heating of hexane(1) and toluene(2) in a tank with a fixed roof that is vented to the atmosphere through an open pipe in the roof. Atmospheric pressure is 760 mmHg. The tank volume is 2000 L, but the maximum operating liquid level is 1800 L. Determine the emissions of each VOC (in g) when the tank is heated.
The liquid volume is 1800 L, x _{1}= 0.5, T^{i}= 10°C, ΔT = 15°C.The liquid volume is 1800 L, x _{1}= 0.5, T^{i}= 25°C, ΔT = 15°C.The liquid volume is 1500 L, x _{1}= 0.5, T^{i}= 25°C, ΔT = 15°C.The liquid volume is 1800 L, x _{1}= 1.0, T^{i}= 25°C, ΔT = 15°C.Explain why the ratio [(emission of toluene in part (b))/(emission of toluene in part (a))] is different from the corresponding ratio of hexane emissions.
Do not confuse a flash point calculation with an isothermal flash calculation. | |||||||||||||||||||||||||||||||||||||||

10.14 | Use Raoult’s law to estimate the flash point temperature for the following equimolar liquid mixtures in an air atmosphere at 750 mmHg total pressure:
Pentane (LFL = 1.5%) and hexane (LFL = 1.2%) Methanol (LFL = 7.3%) and ethanol (LFL = 4.3%) Benzene (LFL = 1.3%) and toluene (LFL = 1.27%)
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10.15 | Go to www.csb.gov and watch a video assigned by your instructor. For the substance involved, look up the LFL. Use Raoult’s law to estimate the flash point temperature and compare it with a literature value. For the scenario in the video, offer an explanation of how easy or difficult is was to reach the LFL under the conditions, and comment on the recommendations of the CSB. |