Homework 05

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University of Illinois, Urbana Champaign *

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422

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Mechanical Engineering

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Apr 3, 2024

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CHBE 422, Mass Transfer Operations HW #5 Due on Friday, March 8 th 1. Adsorption Equilibrium . Experimental equilibrium data for the adsorption of methane on Calgon Carbon Corp. PCB activated carbon are listed in table below. Determine if the Langmuir isotherm is a good fit to the data at 𝑇 = 373 K . (Hint: From the given p/q and p , solve for 𝑞 ?,max and 𝐾 ?,𝑝 . Plot your own isotherm ( q vs. p ) (you can use the p values, but you need an expression for q as a function of p ) and see if that agrees with the given values. Equilibrium data for methane on Calgon PCB activated carbon (Ritter and Yang 1987; Valenzuela and Myers, 1989) p (kPa) q (mmol/g) p (kPa) q (mmol/g) p/q p (kPa) q (mmol/g) 275.788 2.0299 482.629 1.1153 432.735 637.7598 0.3569 1137.6255 4.0822 1123.8361 1.8515 606.987 1296.2036 0.7584 2413.145 5.0414 1620.2545 2.2307 726.344 2378.6716 1.2046 3757.6116 5.3983 1999.463 2.543 786.262 3709.3486 1.6061 5239.9722 5.5767 3447.3501 3.1676 1088.316 5329.603 1.9184 6274.1772 5.6213 4929.7104 3.4799 1416.624 6246.5981 2.0745 6687.8589 5.6213 6156.9673 3.6806 1672.816 6687.8589 2.1415 6584.4385 3.7699 1746.582 T = 296 K T = 373 K T = 480 K

2. Adsorption Column. Air at 26.7°C, 1 atm, with a humidity of 0.003 kg water/kg dry air must be dehumidified by passing through a fixed bed of silica gel. The following data give the concentrations of water during a breakthrough curve. a) If the break point concentration is set at 𝑐 = 1.12 × 10 −4 kg water/kg dry air , determine 𝑡 𝑏 , the breakthrough time. b) What is the total capacity of the bed? You only need to determine 𝑡 ? , the time- equivalent of total capacity of bed. You DO NOT need to numerically integrate, but estimate the area instead. c) If the curve is shifted to the right by 1 hour, what would be the new capacity of the bed? For this to occur, how much larger must the silica bed be? d) What is the usable capacity of the bed for part b? Again, determine 𝑡 ? which is the time-equivalent term of capacity. You DO NOT need to numerically integrate, but estimate the area instead. t (hr) c/c 0 0 0 0.5 0 0.7 0 0.9 0.0187 1 0.0374 1.12 0.0749 1.24 0.1498 1.31 0.2247 1.37 0.2996 1.43 0.3745 1.48 0.4494 1.53 0.5243 1.58 0.5992 1.64 0.7116 1.71 0.8052 1.78 0.88 1.86 0.936 2 1

3. Langmuir Isotherm of a 2-component system. Volatile organic compounds (VOCs, a health hazard) are present in water from some sources. They can be removed by adsorption onto high surface area activated carbon supports (i.e., a Brita water-filter). An aqueous stream containing small amounts of acetone (A) and propionitrile (B) will be treated using an activated carbon adsorbent. Equilibrium adsorption data (measured by an EPA research group) for adsorption of these individual solutes onto activated carbon are described by the Langmuir isotherm and are accurate for solute concentrations up to 50 mmol L -1 . 𝑞 ? = 0.18 ∙ 𝑐 ? 1 + 0.14 ∙ 𝑐 ? 𝑞 ? = 0.17 ∙ 𝑐 ? 1 + 0.1 ∙ 𝑐 ? Where 𝑞 has units of mmol/g and 𝑐 ? , 𝑐 ? have units of mmol/L. a) Combine these single-solute results into an extended Langmuir type isotherm to predict the equilibrium adsorption of each component in a binary system (i.e., when both acetone and propionitrile are present). You will need to start by considering how to derive the Langmuir isotherm for a two-component system, and you will end up with new expressions for 𝑞 ? and for 𝑞 ? . b) Calculate the equilibrium uptakes of acetone and of propionitrile when 𝑐 ? = 15 mmol L -1 and 𝑐 ? = 40 mmol L -1 .

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