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engineering
chemical engineering

Transport Operations 2nd Edition Allen Stuart - Solutions

Transient thermal behavior of a chromatographic device (Fig. 15B.7), you are a consultant to an industrial concern that is experimenting, among other things, with transient thermal phenomena in gas chromatography. One of the employees first shows you some reprints of a well-known researcher and
Derivation of the macroscopic energy balance, show how to integrate Eq. (N) of Table 11.4-1 over the entire volume V of a flow system, which, because of moving parts, may be a function of time. With the help of the Gauss divergence theorem and the Leibniz formula for differentiating an integral,
The classical Bernoulli equation, below Eq. 15.2-5 we have emphasized that the mechanical energy balance and the total energy balance contain different information, since the first is a consequence of conservation of momentum, whereas the second is a consequence of conservation of energy. For the
Approximation of a black body by a hole in a sphere, a thin sphere of copper, with its internal surface highly oxidized, has a diameter of 6 in. How small a hole must be made in the sphere to make an opening that will have an absorptivity of 0.99?
Efficiency of a solar engine, a device for utilizing solar energy, developed by Abbot,’ consists of a parabolic mirror that focuses the impinging sunlight onto a Pyrex tube containing a high-boiling, nearly black liquid. This liquid is circulated to a heat exchanger in which the heat energy is
Radiant heating requirement, a shed is rectangular in shape, with the floor 15 ft by 30 ft and the roof 7.5 ft above the floor. The floor is heated by hot water running through coils. On cold winter days the exterior walls and roof are about -10°F. At what rate must heat be supplied through the
Steady-state temperature of a roof, estimate the maximum temperature attained by a level roof at 45° north latitude on June 21 in clear weather. Radiation from sources other than the sun may be neglected, and a convection heat transfer coefficient of 2.0 Btu/hr ∙ ft2 ∙ F may be assumed. A
Radiation errors in temperature measurements The temperature of an air stream in a duct is being measured by means of a thermocouple. The thermocouple wires and junction are cylindrical, 0.05 in. in diameter, and extend across the duct perpendicular to the flow with the junction in the center
Surface temperatures on the Earth's moon(a) Estimate the surface temperature of our moon at the point nearest the sun by a quasi-steady-state radiant energy balance, regarding the lunar surface as gray. Neglect radiation and reflection from the planetsc the solar constant at Earth is given in
Reference temperature for effective emissivity show that, if the emissivity increases linearly with the temperature, Eq. 16.5-3 may be written as in which eo1 is the emissivity of surface 1 evaluated at a reference temperature To given by
Radiation across an annular gap, Develop an expression for the radiant heat transfer between two long gray coaxial cylinders 1 and 2. Show that where A1 is the surface area of the innercylinder.
Multiple radiation shields (a) Develop an equation for the rate of radiant heat transfer through a series of n very thin, fiat, parallel metal sheets, each having a different emissivity e, when the first sheet is at temperature T1 and the nth sheet is at temperature Tn. Give your result in terms of
Radiation and conduction through absorbing media a glass slab, bounded by planes z = 0 and z = δ, is of infinite extent in the x and y directions. The temperatures of the surfaces at z = 0 and z = δ are maintained at Tδ, and Ta, respectively. A uniform monochromatic radiant beam of intensity
Cooling of a black body in vacuo a thin black body of very high thermal conductivity has a volume V, surface area A, density p, and heat capacity Cp. At time t = 0, this body at temperature T1 is placed in a black enclosure, the walls of which are maintained permanently at temperature T2 (with T2
Prediction of a low-density binary diffusivity estimate DAB for the system methane-ethane at 293K and 1atm by the following methods: (a) Equation 17.2-1. (b) The corresponding-states chart in Fig. 17.2-1 along with Eq. 17.2-3. (c) The Chapman-Enskog relation (Eq. 17.3-12) with
Extrapolation of binary diffusivity to a very high temperature, a value of DAB = 0.151 cm2/s has been reported1 for the system CO2-air at 293K and 1 atm. Extrapolate DAB to 1500K by the following methods:(a) Equation 17.2-1.(b) Equation 17.3-10.(c) Equations 17.3-12 and 15, with Table E.2,What do
Self-diffusion in liquid mercury, the diffusivity of Hg203 in normal liquid Hg has been measured2 along with viscosity and volume per unit mass. Compare the experimentally measured DAA, with the values calculated with Eq.17.4-5.
Schmidt numbers for binary gas mixtures at low density, use Eq. 17.3-11 and the data given in Problem 1A.4 to compute Sc = µ/pDAB for binary mixtures of hydrogen and Freon 12 at xA = 0.00, 0.25, 0.50, 0.75, and 1.00, at 25°C and 1atm.
Estimation of diffusivity for a binary mixture at high density, Predict CDAB for an equimolar mixture of N2 and C2H6 at 288.2K and 40atm (a) Use the value of DAB at 1atm from Table 17.1-1, along 'with Fig. 17.2-1. (b) Use Eq. 17.2-3 and Fig. 17.2-1.
Diffusivity and Schmidt number for chlorine-air mixtures (a) Predict DAB for chlorine-air mixtures at 75°F and 1atm. Treat air as a single substance with Lennard-Jones parameters as given in Appendix E. Use the Chapman-Enskog theory results in S17.3. (b) Repeat (a) using Eq.
The Schmidt number for self-diffusion at high density (a) Use Eqs. 1.3-1b and 17.2-2 to predict the self-diffusion Schmidt number Sc = µ/pDAA ∙ at the critical point for a system with MA ≈ MA. (b) Use the above result, along with Fig. 1.3-1 and Fig. 17.2-1, to predict Sc = µ/pDAA
Corrcection of high-density diffusivity for temperature, the measured value3 of CDAB for a mixture of 80 mole% CH4 and 20 mole% C2H6 at 313K and 136 atm is 6.0 x 10-6 g-mol/cm ∙ s (see Example 17.2-3). Predict CDAB for the same mixture at 136 atm at 351K, using Fig. 17.2-1.
Estimation of liquid diffusivities (a) Estimate the diffusivity for a dilute aqueous solution of acetic acid at 12.5°C, using the Wilke-Chang equation, the density of pure acetic acid is 0.937 g/cm3 at its boiling point. (b) The diffusivity of a dilute aqueous solution of methanol at
Relations among fluxes in multi component systems, verify Eqs. (K), (O), (T), and (X) Table 17.8-1 using only the definitions of concentrations, velocities, and fluxes.
Interrelation of composition variables in mixtures(a) Using the basic definitions in Eqs. (A) to (G) of Table 17.7-1, verify the algebraic relations in Eqs. (H) to (O).(b) Verify that, in Table 17.7-1, Eqs. (P) and (Q) simplify to Eqs. (P') and (Q') for binary mixtures.(c) Derive Eqs. (P') and (Q')
Relations between fluxes in binary systems, the following equation is useful for interrelating expressions in mass units and those in molar units in two-component systems: Verify the correctness of this relation.
Equivalence of various forms of Fick's law for binary mixtures (a) Starting with Eq. (A) of Table 17.8-2, derive Eqs. (B), (D), and (F). (b) Starting with Eq. (A) of Table 17.8-2, derive the folowing flux expressions: what conclusions can be drawn from these two equations? (c) Show
Mass flux with respect to the solvent velocity (a) In a system with N chemical species, choose component N to be the solvent. Then define jNa = pa (va – VN) (17C.2-1) to be the mass flux with respect to the solvent velocity. Verify that jNa = ja – (pa /pN)j N (17C.2-2) (b) For a
Determination of Lennard-Jones potential parameters from diffusivity data of a binary, gas mixture(a) Use the following data5 for the system H2O-O2 at 1atm pressure to determine σAB and εAB/k:One way to do this is as follows: (i) Plot the data as log (T3/2/DAB) versus log T on a thin sheet of
Evaporation rate for the system shown in Fig. 18.2-1, what is the evaporation rate in g/hr of CC13NO2 (chloropicrin) into air at 25°C Make the customary assumption that air is a "pure substance."
Sub-limitation of small iodine spheres in still air. A sphere of iodine, 1 cm in diameter, is placed in still air at 40°C and 747 mm Hg pressure. At this temperature the vapor pressure of iodine is about 1.03 mm Hg. We want to determine the diffusivity of the iodine-air system by measuring the
Estimating the error in calculating the absorption rate, what is the maximum possible error in computing the absorption rate from Eq. 18.5-18, if the solubility of A in B is known within + 5% and the diffusivity of A in B is known within + 15%? Assume that the geometric quantities and the velocity
Chlorine absorption in a falling film (Fig. 18A.4), chlorine is being absorbed from a gas in a small experimental wetted-wall tower as shown in the figure. The absorbing fluid is water, which is moving with an average velocity of 17.7 cm/s. What is the absorption rate in g-moles/hr, if the
Measurement of diffusivity by the poinbsource method (Fig. 18C.1)1, we wish to design a flow system to utilize the results of Problem 18C.1 for the measure of DAB. The approaching stream of pure B will be directed vertically upward, and the gas composition will be measured at several points along
Determination of diffusivity for ether-air system the following data on the evaporation of ethyl ether (C2H5OC2H5) have been tabulated by Jost. 2 The data are for a tube of 6.16 mm diameter, a total pressure of 747 mm Hg, and a temperature of 22°C. The molecular weight of ethyl ether is 74.12, and
Mass flux from a circulating bubble (a) Use Eq. 18.5-20 to estimate the rate of absorption of CO2 (component A) from a carbon dioxide bubble 0.5 cm in diameter rising through pure water (component B) at 18°C and at a pressure of 1atm. The following data 3 may be used: DAB = 1.46 x 105 cm2/s,
Error in neglecting the convection term in evaporation(a) Rework the problem in the text in S18.2 by neglecting the term xA (NA + NB) in Eq. 18.0-1. Show that this leads to this is a useful approximation if A is present only in very low concentrations. (b) Obtain the result in (a) from Eq.
Effect of mass transfer rate on the concentration profiles (a) Combine the result in Eq. 18.2-11 with that in Eq. 18.2-14 to get(b) Obtain the same result by integrating Eq. 18.2-1 directly using the fact that NAz is constant. (c) Note what happens when the mass transfer rate becomes
Absorption with chernical reaction (a) Rework the problem discussed in the text in S18.4, but take z = 0 to be the bottom of the beaker and z = L at the gas-liquid interface. (b) In solving Eq. 18.4-7, we took the solution to be of the sum of two hyperbolic functions. Try solving the
Method for separating helium from natural gas (Fig. 18B.8), Pyrex glass is almost impermeable to all gases but helium. For example, the diffusivity of He through Pyrex is about 25 times the diffusivity of H2 through pyrex, hydrogen being the closest "competitor" in the diffusion process. This fact
Effect of temperature and pressure on evaporation rate (a) In S18.2 what is the effect of a change of temperature and pressure on the quantity xA1? (b) If the pressure is doubled, how is the evaporation rate in Eq. 18.2-14 affected? (c) How does the evaporation rate change when the
Evaporation rate for small mole fraction of the volatile liquid, in Eq 18.2-15, expand in a Taylor series appropriate for small mole fractions of A. First rewrite the logarithm of the quotient as the difference of the logarithms. Then expand ln (1 – XA1) and ln (1 – XA2) in Taylor series about
Effectiveness factors for long cylinder so derive the expression for ηA for long cylinders analogous to Eq. 18.7-16. Neglect the diffusion through the ends of the cylinders.
Gas absorption in a falling film with chemical reaction, rework the problem discussed in S18.5 and described in Fig. 18.5-1, when gas A reacts with liquid B by a first-order irreversible chemical reaction in the liquid phase, with rate constant k'''1. Specifically, find the expression for the total
Diffusion through a stagnant film--alternate derivation in S18.2 an expression for the evaporation rate was obtained in Eq. 18.2-14 by differentiating the concentration profile found a few lines before. Show that the same results may be derived without finding the concentration profile. Note that
Dehumidification of air (Fig. 19.4-1) for the system of Example 19.4-1 let the vapor is H20 and the stagnant gas is air. Assume the following conditions (which are representative in air conditioning): (i) at z = δ, T = 80°F and xH2O = 0.018; (ii) at z = 0, T = 50°F. (a) For p = 1atm,
Steady-state evaporation (Fig. 18.2-1), rework the problem solved in S18.2, dealing with the evaporation of liquid A into gas B, starting from Eq. 19.1-17. (a) First obtain an expression for v*, using Eq. (M) of Table 17.8-1, as well as Fick's law in the form of Eq. (D) of Table
Gas absorption with chemical reaction (Fig. 18.4-1), rework the problem solved in S18.4, by starting with Eq. 19.1-16. What assumptions do you have to make in order to get Eq. 18.4-4?
The Maxwell-Stefan equations for multicomponent gas mixtures. In Eq. 17.9-1 the Maxwell-Stefan equations for the mass fluxes in a multicomponent gas system are given. Show that these equations simplify for a binary system to Fick's first law, as given in Eq. 17.1-5.
Various forms of the species continuity equation(a) In this chapter the species equation of continuity is given in three different forms: Eq. 19.1-7, Eq. (A) of Table 19.2-1, and Eq. (B) in Table 19.2-3. Show that these three equations are equivalent.(b) Show how to get Eq. 19.1-15 from Eq. 19.1-11.
Alternate form of the binary diffusion equation, in the absence of chemical reactions, Eq. 19.1-17 can be written in terms of v rather than v* by using a different measure of concentration namely, the logarithm of the mean molecular weight: in which M = xAMA + xBMB. (Caution: Solution is lengthy.)
Derivation of the equation of continuity, in S19.1 the species equation of continuity is derived by making a mass balance on a small rectangular volume ∆x ∆y ∆z fixed in space. (a) Repeat the derivation for an arbitrarily shaped volume element V with a sufficiently smooth fixed boundary S.
Measurement of diffusivity by unsteady-state evaporation, use the following data to determine the diffusivity of ethyl propionate (species A) into a mixture of 20 mole% air and 80 mole% hydrogen (this mixture being treated as a pure gas B) These data were obtained by using a glass tube 200 cm
Absorption of oxygen from a growing bubble (Fig. 20A.2), oxygen is being injected into pure water from a capillary tube. The system is virtually isothermal and isobaric at 25°C and 1 atm. The solubility of oxygen in the liquid phase is wA0 = 7.78 x 10-4, and the liquid-phase diffusivity for the
Rate of evaporation of n-octane, at 20°C, how many grams of liquid n-octane will evaporate into N2 in 24.5 hr in a system such as that studied in Example 20.1-1 at system pressures of (a) 1atm, and (b) 2atm? The area of the liquid surface is 1.29 cm2, and the vapor pressure of n-octane
Absorption with rapid second-order reaction (Fig. 20.1-2), make the following calculations for the reacting system depicted in the figure: (a) Verify the location of the reaction zone, using Eq. 20.1-38. (b) Calculate NA0 at t = 2.5 s.
Rapid forced-convection mass transfer into a laminar boundary layer, calculate the evaporation rate nA0(x) for the system described under Eq. 20.2-52, given that wA0 = 0.9, wA∞ = 0.1, and Sc = 2.0. Begin by determining, by trial and error, the values of K and II'(0, Sc, K) consistent with Table
Slow forced convection mass transfer into a laminar boundary layer, this problem illustrates the use of Eqs. 20.2-55 and 57 and tests their accuracy. (a) Estimate the local evaporation rate, nA0, as a function of x for the drying of a porous water-saturated slab, shaped as in Fig. 20.2-2. The
Extension of the Arnold problem to account for interphase transfer of both species, show how to obtain Eqs. 20.1-23, 24, and 25 starting with the equations of continuity for species A and B (in molar units) and the appropriate initial and boundary conditions.
Stoichiometric boundary condition for rapid irreversible reaction, example 20.1-2 must satisfy the stoichiometric relation the reactant fluxes in which vR = dzR/dt. Show that this relation leads to Eq. 20.1-31 when use is made of Fick's first law, with the assumptions of constant c and
Taylor dispersion in slit flow (Fig. 2B.3), show that, for laminar flow in a plane slit of width 2B and length L, the Taylor dispersion coefficient is
Diffusion from an instantaneous point source, at time t = 0, a mass mA of species A is injected into a large body of fluid B. Take the point of injection to be the origin of coordinates. The material A diffuses radially in all directions. The solution may be found in Carslaw and Jaeger: 2(a) Verify
Simultaneous momentum, heat, and mass transfer: alternate boundary conditions (Fig. 20B.7). The dimensionless profiles II (η, Λ, K) in Eq. 20.2-43 are applicable to a variety of situations. Use Eqs. 20.2-49 to 52 to obtain equations for the evaluation of the dimensionless net mass flux K for the
Absorption from a pulsating bubble, use the results of Example 20.1-4 to calculate δ(t) and NA0(t) for a bubble whose radius undergoes a square-wave pulsation: Here w is a characteristic frequency, and n = 1, 2,....
Design of fluid control circuits, it is desired to control a reactor via continuous analysis of a side stream. Calculate the maximum frequency of concentration changes that can be detected as a function of the volumetric withdrawal rate, if the stream is drawn through a 10 cm length of tubing with
Dissociation of a gas caused by a temperature gradient, a dissociating gas (for example, Na2 → 2Na) is enclosed in a tube, sealed at both ends, and the two ends are maintained at different temperatures. Because of the temperature gradient established, there will be a continuous flow of Na2
Two-bulb experiment for measuring gas diffusivitiesmanalytical solution (Fig. 18B.6) this experiment, described in Problem 18B.6, is analyzed there by a quasi-steady-state method. The method of separation of variables gives the exact solution s for the compositions in the two bulbs as in which γn
Determination of eddy diffusivity (Figs. 18C.1 and 21A.1), in Problem 18C.1 we gave the formula for the concentration profiles in diffusion from a point source in a moving stream. In isotropic highly turbulent flow, Eq. 18C.1-2 may be modified by replacing DAB by the eddy diffusivity D (t) AB)
Heat and mass transfer analogy write the mass transfer analog of Eq. 13.4-19, what are the limitations of the resulting equation?
Wall mass flux for turbulent flow with no chemical reactions use the diffusional analog of Eq. 13.3-7 for turbulent flow in circular tubes, and the Blasius formula for the friction factor, to obtain the following expression for the Sherwood number, Sh = 0.0160Re7/8 Sc1/3 valid for large Schmidt
Deposition of silver from a turbulent stream (Fig. 21B.3), an approximately 0.1 N solution of KNO3 containing 1.00 x 10-6 g-equiv. AgNO3 per liter is flowing between parallel Ag plates, as shown in Fig. 21B.3 (a). A small voltage is applied across the plates to produce a deposition of Ag on the
Prediction of mass transfer coefficients in closed channels, estimate the gas-phase mass transfer coefficients for water vapor evaporating into air at 2 atm and 25°C, and a mass flow rate of 1570 lbm/hr, in the systems that follow. Take DAB = 0.130 cm2/s. (a) A 6-in. i.d. vertical pipe with a
Calculation of gas composition from psychometric data, a stream of moist air has a wet bulb temperature of 80°F and a dry-bulb temperature of 130°F, measured at 800 mm Hg total pressure and high air velocity. Compute the mole fraction of water vapor in the air stream. For simplicity, consider
Calculating the air temperature for drying in a fixed bed, a shallow bed of water-saturated granular solids is to be dried by blowing dry air through it at 1.1atm pressure and a superficial velocity of 15 ft/s. What air temperature is required initially to keep the solids at a surface temperature
Rate of drying of granular solids in a fixed bed calculate the initial rate of water removal in the drying operation described in Problem 22A.3, if the solids are cylinders with a = 180 ft-1.
Evaporation of a freely falling drop a drop of water, 1.00 mm in diameter, is falling freely through dry, still air at pressure of 1atm and a temperature of 100°F with no internal circulation. Assume quasi-steady-state behavior and a small mass-transfer rate to compute (a) The velocity of the
Effect of radiation on psychometric measurements, suppose that a wet-bulb and dry-bulb thermometer are installed in a long duct with constant inside surface temperature Ts and that the gas velocity is small. Then the dry-bulb temperature Tdb and the wet-bulb temperature Twb should be corrected
Film theory with variable transport properties (a) Show that for systems in which the transport properties are functions of y, Eqs. 19.4-12 and 13 may be integrated to give for y
An evaporative ice maker, consider a circular shallow dish of water 0.5 m in diameter and filled to the brim, resting on an insulating layer, such as loose straw, and in a windless area. At what air temperature can the water be cooled to freezing if the relative humidity of the air is 30%? Make the
Oxygen stripping, calculate the rate at which oxygen transfers from quiescent oxygen saturated water at 20°C to a bubble of pure nitrogen 1 mm in diameter, if the bubble acts as a rigid sphere. It will first be necessary to determine the bubble velocity of rise through the water.
Controlling diffusional resistance water drops 2 mm in diameter are being oxygenated by falling freely through pure oxygen at 20°C and a pressure of 1 atm. Do you need to know the gas-phase diffusivity to calculate the rate of oxygen transport? Why? The solubility of oxygen under these conditions
Determination of diffusivity (Fig. 22B.7) the diffusivity of water vapor in nitrogen is to be determined at a pressure of 1 atm over the temperature range from 0°C to 100°C by means of the "Arnold experiment" of Example 20.1-1. It will, therefore, be necessary to use the correction factor θAB to
Marangoni effects in condensation of vapors. In many situations the heat transfer coefficient for condensing vapors is given as h = k/& where k is the thermal conductivity of the condensate film, and 8 is the film thickness. Correlations available in the literature are normally based on the
Film model for spheres derive the results that correspond to Eqs. 22.8-3, 4 for simultaneous heat and mass transfer in a system with spherical symmetry that is, assume a spherical mass transfer surface and assume that T and xA depend only on the radial coordinate r. Show that Eqs. 22.8-7 and 8 do
Film model for cylinders derive the results that correspond to Eqs. 22.8-3, 4 for a system with cylindrical symmetry, that is, assume a cylindrical mass transfer surface and assume that T and XA depend only on r. Verify that Eqs. 22.8-7, 8 do not need to be changed.
Expansion of a gas mixture very slow reaction rate, estimate the temperature and velocity of the water-gas mixture at the discharge end of the nozzle in Example 23.5-3 if the reaction rate is very slow, use the following data' log10 K3 = –0.15, Cp,H2 = 7.217, Cp,CO2, = 12.995, Cp,H2O = 9.861,
Height of a packed-tower absorber a packed tower of the type described in Example 23.5-2 is to be used for removing 90% of the cyclohexane from a cyclohexane-air mixture by absorption into a non-volatile light oil. The gas stream enters the bottom of the tower at a volumetric rate of 363ft3/min at
Effective average driving forces in a gas absorber consider a packed-tower gas absorber of the type discussed in Example 23.5-2. Assume that the solute concentration is always low and that the equilibrium and operating lines are both very nearly straight. Under these conditions, both k0ya and k0x a
Irreversible first-order reaction in a continuous reactor, a well-stirred reactor of volume V is initially completely filled with a solution of solute A in a solvent S at concentration CAO. At time t = 0, an identical solution of a in S is introduced at a constant mass flow rate w. A small constant
Isotope separation and the value function, you wish to compare an existing isotope fractionators that processes 50 moles/hr of a feed containing 1.0 mole% of the desired isotope to a product of 90% purity and a waste of 1% with another that processes 50 moles/hr of 10 mole% material to product and
Irreversible second-order reaction in an agitated tank consider a system similar to that discussed in Problem 23B.4, except that the solute disappears according to a second-order reaction; that is, RA,tot = – k'''2 Vc2A. Develop an expression for c A as a function of time by the following
Start-up of a chemical reactor rework Example 23.6-1 by use of Laplace transforms of Eqs. 23.6-2 and 3
Transient behavior of N reactors in series2 there are N identical chemical reactors of volume V connected in series, each equipped with a perfect stirrer. Initially, each tank is filled with pure solvent S. At zero time, a solution of A in S is introduced to the first tank at a constant volumetric
Thermal diffusion(a) Estimate the steady-state separation of H2 and D2 occurring in the simple thermal diffusion apparatus shown in Fig. 24.3-1 under the following conditions: T1 is 200K, T2 is 600K the mole fraction of deuterium is initially 0.10 and the effective average kT is 0.0166. (b) At
Ultracentrifugation of proteins estimate the steady-state concentration profile when a typical albumin solution is subjected to a centrifugal field 50,000 times the force of gravity under the following conditions: Cell length = 1.0 cm Molecular weight of albumin =
The dimensions of the Lorentz force. Show how the Lorentz force on a charge moving through a magnetic field corresponds to the first term added to the linear da of Eq. 25.4-51 and gives a consistent set of units for this quantity. Suggestion: Note that cRTda represents the motive force for
Junction potentials, consider two well-mixed reservoirs of aqueous salt at 25°C, as in Fig. 24.4-2, separated by a stagnant region. Salt concentrations are 1.0 N on the left (1) and 0.1 N on the right (2). Estimate junction potentials for NaC1 and for KC1 using the ion diffusivities of Problem
Osmotic pressure, typical sea water, containing 3.45% by weight of dissolved salts, has a vapor pressure 1.84% below that of pure water. Estimate the minimum possible trans-membrane pressure required to produce pure water, if the membrane is ideally selective.
Permeability of a perfectly selective filtration membrane develops an expression for the hydraulic permeability of the perfectly selective membrane described in Example 22.8-5 in terms of the diffusional parameters introduced in S24.5.
Expressions for the mass flux (a) Show how to transform the left side of Eq. 24.2-8 into the left side of Eq. 24.2-9. First rewrite the former as follows: Rewrite the second term as a sum over all 13, and then add a term to compensate for the modification of the sum. Note that this change

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