a. NA + NB = cV
b. nA + nB = ρv
c. jA + jB = 0
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22.2 In a gas-phase diffusion mass-transfer process, the steady-state flux of species A in a binary mixture of A and B is 5.0 × 10–5 kgmole A/m2s, and the A,z + NB;z flux of B is 0 (zero). At a particular point in the diffusion space, the concentration of species A is 0.005 kgmole/m3 and the concentration of species B is 0.036 kgmole/m3. Estimate the individual net velocities of species A and B along the direction of mass transfer, and the average molar velocity.
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22.3 Estimate the molar concentration of 0.50 wt% (0.0050 mass fraction) benzene (C6H6) dissolved in liquid ethanol (C2H5OH) at 20°C. The density of liquid ethanol is 789 kg/m3 at 20°C. This solution of the solute benzene dissolved in the solvent ethanol is considered dilute.
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22.4 Tetrachlorosilane (SiCl4) gas is reacted with hydrogen gas (H2) to produce electronic-grade polycrystalline silicon at 800°C and 1.5 × 105 Pa according to the reaction equation:...The reaction rate may experience diffusion limitations at the growing Si solid surface. To address this concern, the diffusion coefficient coefficients in this system must be estimated.
a. Estimate the binary diffusion coefficient of SiCl4 in H2 gas.
b. Estimate the diffusion coefficient of SiCl4 in a mixture containing 40 mole% SiCl4, 40 mole% H2, and 20 mole% HCl. Is this diffusion coefficient substantively different than the diffusion coefficient estimated in part (a)? The Lennard–Jones parameters for SiCl4 are σ = 5.08 Å and ε/κ = 358 K.
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22.5 A gas separation process has been proposed to remove selectively two pollutants, hydrogen sulfide (H2S) and sulfur dioxide (SO2), from an exhaust gas stream containing 3.0 mole% H2S, 5.0 mole% SO2, and 92 mole% N2. The temperature is 350 K, and the total system pressure is 1.0 atm,
a. Determine the total molar concentration, molar concentration of H2S, and mass concentration of H2S of the gas mixture.
b. Estimate the binary gas-phase molecular diffusion coefficient of H2S in N2. The critical temperature of H2S is 373.2 K and the critical volume is 98.5 cm3/gmole.
c. Estimate the molecular diffusion coefficient of H2S in the gas mixture. Is this diffusion coefficient substantively different than the diffusion coefficient for the H2S-N2 binary pair? Why, or why not?
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22.6 “Sour” natural gas is contaminated with hydrogen sulfide. The H2S vapors are commonly treated removed by passing the gas through a packed bed of adsorbent particles. In the present process, natural gas with a bulk gas composition is 99 mole% methane (CH4) and 1.0 mole% H2S will be treated with a porous adsorbent material of void fraction of 0.50 and mean pore diameter of 20 nm at 30°C and 15.0 atm total system pressure. To design the adsorption bed, it is necessary to estimate the diffusion coefficient of H2S within the porous adsorbent. The Lennard–Jones parameters for H2S are s . 3.623 Å and e/k . 301.1 K.
a. What is molar concentration of H2S in the gas mixture?
b. Estimate the binary gas-phase molecular diffusion coefficient of methane in H2S by two methods, and compare the results.
c. Estimate the effective diffusion coefficient of H2S within the porous material, assuming methane and hydrogen sulfide fill the gas void space within the porous material.
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22.7 A process is being developed to deposit a thin film of silicon electronic grade silicon (Si) onto the inner surface of a hollow glass optical fiber by thermal decomposition of silane (SiH4) to solid Si. Silane gas is diluted in inert He gas to a composition of 1.0 mole% SiH4 and fed into the hollow glass fiber, which has an inner diameter of 10.0 microns (10.0 mm). The CVD process is carried out at 900 K and a very low total system pressure of only 100 Pa. The Lennard–Jones parameters for silane are s . 4.08Å and e/k . 207.6 K.
a. Determine the mass fraction of silane in the gas mixture....is a dimensionless parameter used to assess the importance of dispersion of species undergoing diffusion in a flowing stream of bulk velocity v∞ through a tube of diameter d. At low values for Pe, diffusion dominates the dispersion process. Estimate the gas velocity and volumetric flow rate of gas within a single hollow fiber if it is desired to maintain Pe equal to 5.0 × 10–4.
b. Estimate the binary gas-phase molecular diffusion coefficient of silane vapor in He gas at 900 K for total system pressures of 1.0 atm and 100 Pa. Why is the value at 100 Pa so large?
c. Assess the importance of Knudsen diffusion of silane vapor within the hollow glass fiber.
d. The Peclet number (Pe), defined as
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22.8 The Stokes–Einstein equation is often used to estimate the molecular diameter of large spherical molecules from the molecular diffusion coefficient. The measured molecular diffusion coefficient of the serum albumin (an important blood protein) in water at infinite dilution is 5.94 × 10−7 cm2/s at 293 K. Estimate the mean diameter of a serum albumin molecule. The known value is 7.22 nm.
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22.9 The diffusion of oxygen (O2) through living tissue is often first approximated as the diffusion of dissolved O2 in liquid water. Estimate the diffusion coefficient of O2 in water by the Wilke–Chang and Hayduk–Laudie correlations at 37°C.
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22.10 The rate of an electrochemical process for plating of solid copper onto a surface from a cupric chloride solution is affected by mass-transfer processes. Estimate the molecular diffusion coefficient of copper II chloride (CuCl2) dissolved in water at infinite dilution at 25°C.
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22.11 As part of a bioseparations process, glucose (solute A) in aqueous solution (solvent B) is diffusing across a microporous membrane. The thickness of the membrane is 2.0 mm, and the pores running through the membrane consists of parallel cylindrical channels of 3.0 nm diameter (1 nm is a nanometer, 1 × 109 nm = 1 m). The temperature is 30°C. The mean diameter of a single glucose molecule is 0.86 nm.
a. Estimate the molecular diffusion coefficient of glucose in water by the Stokes–Einstein relationship.
b. What is the effective diffusion coefficient of glucose through the membrane?
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22.12 The diffusion rate of the enzyme ribonuclease into a porous chromatography support material was measured at 298 K. An effective diffusion coefficient of 5.0 × 10−7 cm2/s was obtained from an experiment based on diffusion of the enzyme through a single cylindrical pore. Estimate the pore diameter (dpore) needed to achieve this effective diffusion coefficient. The molecular diffusion coefficient of ribonuclease in water is 1.19 × 10−6 cm2/s at 298 K, and the diameter of this molecule is 3.6 nm.
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22.13 A size-exclusion based molecular separation process is being developed to purify a mixture of proteins dissolved in aqueous solution at 20°C. The solution is dilute and approximates the properties of water, which has a viscosity of 1.0 cP at 20°C. One protein of interest (protein A) is spherical with a mean molecular diameter of 25 nm. It is desired to design a porous membrane that has a stearic partition coefficient of no more than 0.64 for this protein—i.e., F1(φ) = 0.64.
a. Estimate the molecular diffusion coefficient of protein A in dissolved in solution at 20°C.
b. What is the effective diffusion coefficient of the protein A within a single cylindrical desired membrane material?
c. At what pore diameter will all proteins other than protein A will be “excluded” from the membrane?
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22.14 Electronic properties are imparted to crystalline silicon by diffusing an elemental impurity called a “dopant” into this material at high temperature. At 1316 K, the diffusion coefficient of one particular dopant in silicon is 1.0 × 10−13 cm2/s; at 1408 K, the diffusion coefficient has increased to 1.0 × 10−12 cm2/s. Based on Table 24.7, what is a likely candidate for the dopant material?Table 24.7 Diffusion parameters common substitutional dopants in polycrystalline silicon, using data obtained from Ghandhi...
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