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Separation Process Principles- 2n - Seader &amp; Henley - Solutions Manual

# Adsorption equilibrium data at 547 k for

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Unformatted text preview: 21 x 105 cm2/g or 52.1 m2/g This is much smaller than the values given for silica gel in Table 15.2. Exercise 15.5 Subject: Maximum ion-exchange capacity of a resin. Given: Ion-exchange resin made from 8 wt% divinylbenzene and 92 wt% styrene. Find: Maximum ion-exchange capacity in meq/g resin. Analysis: Compute the moles of each aromatic component per 100 grams of resin: Styrene Divinylbenzene Total MW 104.14 130.18 grams 92 8 100 gmol 0.8834 0.0615 0.9449 Therefore, need 0.9449 mol H2SO4 or 0.9449(81.07) = 76.6 g. Total resin weight after sulfonation = 100 + 76.6 = 176.6 g. Maximum ion-exchange capacity = 0.9449(1000)/176.6 = 5.35 meq/g of resin. Exercise 15.6 Subject: Fitting adsorption data to linear, Freundlich, and Langmuir isotherms and computing the heat of adsorption. Given: Silica gel adsorbent with: surface area = Sg = 832 m2/g, pore volume = Vp = 0.43 cm3/g, particle density = ρp = 1.13 g/cm3, and average pore diameter = dp = 22 angstroms. Equilibrium adsorption data for pure benzene vapor at 4 different temperatures as follows: q, moles adsorbed /g gel x 105: p, partial pressure, atm 70oC 90oC 110oC 130oC 0.0005 14.0 6.7 2.6 1.13 0.0010 22.0 11.2 4.5 2.0 0.0020 34.0 18.0 7.8 3.9 0.0050 68.0 33.0 17.0 8.6 0.0100 88.0 51.0 27.0 16.0 0.0200 78.0 42.0 26.0 Find: (a) For each temperature, best fits of the data to (1) linear, (2) Freundlich, and (3) Langmuir isotherms. Which give a reasonable fit? (b) Do data represent less than a monolayer? (c) Heat of adsorption, with comparison to heat of vaporization of benzene. Analysis: The regression program of POLYMATH can be used to do nonlinear curve fits or a spreadsheet program can be used to do least squares curve fits on the linearized isotherms. For the former, the following results are obtained for fitting Eqs. (15-16), (15-19), and (15-24). Somewhat different results would be obtained with the linearized equations (15-20) and (15-25). (1) q = kp Linear (2) q = kp1/n Freundlich (3) q = Kqmp/(1 + Kp) Langmuir Temperature, o C 70 90 110 130 Linear: k 0.1011 0.0431033 0.0229401 0.0138306 Freundlich: k 0.0132915 0.00944163 0.00653397 0.00595422 n 1.71882 1.57209 1.43190 1.25461 The linear equation is a poor fit for all 4 temperatures. The Freundlich equation a reasonably good fit for all 4 temperatures. The Langmuir equation gives the best fit for all 4 temperatures. Langmuir: K 188.18 67.55 50.0327 27.4455 qm 0.0013584 0.0013337 0.00083383 0.00073471 Exercise 15.6 (continued) Analysis: (continued) (b) The surface area covered by one adsorbed molecule is given by Eq. (15-8), where for benzene, M = 78.11 and the liquid density, from Fig. 2.3, ranges from 0.82 cm3/g at 90oC to 0.76 cm3/g at 130oC. At 90oC, M α = 1.091 N Aρ L 2/3 7811 . = 1091 . 6.023 × 1023 (0.82) 2/3 = 319 × 10 −15 cm2 . From the data, the maximum experimental adsorption is 0.00088 moles benzene/g silica gel. This is a coverage of 0.00088(6.023 x 1023)(3.19 x 10-15) = 1.69 x 106 cm2/g or 169 m2/g. This is far less than the given...
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