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

Given air film of 01 inch 0254 cm thickness hcl

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Unformatted text preview: 4 0.333 5 0.167 6 0 1 0.9 Hydrogen mole fraction 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.5 1 1.5 2 2.5 3 Distance from End 1, inches 3.5 4 4.5 5 Exercise 3.8 Subject: Molecular diffusion of HCl (H) across an air (A) film at 20oC. Given: Air film of 0.1-inch (0.254 cm) thickness. HCl partial pressure of 0.08 atm on side 1 of the film and 0 on the other side 2. Diffusivity of HCl in air at 20oC (293 K) and 1 atm = 0.145 cm2/s. Assumptions: Ideal gas law. Unimolecular diffusion of HCl. Find: Diffusion flux of HCl in mol/s-cm2 for the following total pressures: (a) 10 atm (b) 1 atm (c) 0.1 atm Analysis: Fick's law applies. Use the form of Eq. (3-33). Note that for an ideal gas, product cDH,A is independent of total pressure because c is directly proportional to P, while from Eq. (3-36), cDH,A is inversely proportional to P. At P = 1 atm, c = P/RT = 1/(82.06)(293) = 4.16 x 10-5 mol/cm3. Therefore, cDH,A = (4.16 x 10-5)(0.145) = 6.03 x 10-6 (a) P = 10 atm. By Dalton's law, at (yH)1 = 0.08/10 = 0.008 From Eq. (3-33), NH = cDH,A ∆z ln 1 − ( yH ) 2 (6.03 × 10 −6 ) 1− 0 = ln = 1.91× 10−7 mol HCl/s-cm 2 1 − ( yH )1 1 − 0.008 ( 0.254) ) (b) For P = 1 atm, (yH)1 = 0.08/1 = 0.08, which gives, NH = 1.98 x 10-6 mol/s-cm2 (c) For P = 0.1 atm, (yH)1 = 0.08/0.1 = 0.8, which gives, NH =3.82 x 10-5 mol/s-cm2 Exercise 3.9 Subject: Estimation of the binary gas diffusivity for nitrogen (A) - toluene (B) at 25o C (298 K) and 3 atm Assumptions: No need to correct diffusivity for high pressure with Takahashi method. Find: Binary gas diffusivity using the method of Fuller, Shettler, and Giddings. Analysis: Use Eq. (3-36), with, M A,B = From Table 3.1, VA = 18.5, DA,B = 2 1 1 + 28 92 = 42.9 VB = 7(15.9) + 8(2.31) − 18.3 = 1115 . 0.00143(298)1.75 = 0.028 cm 2 / s (3)(42.9)1/ 2 [18.51/ 3 + 111.51/ 3 ]2 Exercise 3.10 Subject: Correction of gas binary diffusivity for high pressure. Given: Results of Example 3.3 for oxygen-benzene system at 38oC (311 K) and 2 atm, which give, DAB = 0.0494 cm2/s Find: Diffusivity at 100 atm. Analysis: If Eq. (3-36) is applied, DAB = 0.0494 (3/100) = 0.00148 cm2/s Apply the Takahashi correlation of Fig. 3.3, based on reduced T and P. For equimolar mixture, Tr=T/Tc and Pr=P/Pc where, Tc = 0.5(154 + 563) = 359 K and Pc = 0.5(48.6+49.7) = 49.1 atm Therefore, Tr = 311/359 = 0.866, and Pr = 100/49.1 = 2.04 We are outside the range of the Takahashi correlation, but it appears that the correction would greatly decrease the diffusivity, by a factor of 10 or more. Exercise 3.11 Subject: Estimation of infinite-dilution liquid diffusivity for carbon tetrachloride at 25oC (298 K) in four different solvents. Given: Experimental values diffusivity for solvents of (a) methanol, (b) ethanol, (c) benzene, and (d) n-hexane. Find: Diffusivities by the methods of Wilke and Chang (W-C), and of Hayduk and Minhas (H-M). Compare predicted values to given experimental values. Analysis: Let:A = the solute, CCl4; and B = solvent. The Wilke-Chang equation, Eq. (3-39), is DA,...
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