Page 149 - Separation process principles 2

114 Chapter 3 Mass Transfer and Diffusion

3.9 Estimate the diffusion coefficient for the gaseous binary sys- 3.16 Experimental liquid-phase activity-coefficient data are
tem nitrogen (A)/toluene (B) at 2S°C and 3 atm using the method of given in Exercise 2.23 for the ethanolhenzene system at 45°C. Es-
Fuller et al. timate and plot diffusion coefficients for both ethanol and benzene
3.10 For the mixture of Example 3.3, estimate the diffusion coef- over the entire composition range.
ficient if the pressure is increased to 100 atm using the method of 3.17 Estimate the diffusion coefficient of NaOH in a I-M aqueous
Takahashi. solution at 25°C.
3.11 Estimate the diffusivity of carbon tetrachloride at 25°C in a 3.18 Estimate the diffusion coefficient of NaCl in a 2-M aqueous
dilute solution of: (a) Methanol, (b) Ethanol, (c) Benzene, and solution at 18OC. Compare your estimate with the experimental
(d) n-Hexane by the method of Wilke-Chang and Hayduk-Minhas. value of 1.28 x lo-' cm2/s.
Compare the estimated values with the following experimental 3.19 Estimate the diffusivity of N2 in H2 in the pores of a catalyst
observations: at 300°C and 20 atm if the porosity is 0.45 and the tortuosity is 2.5.
Assume ordinary molecular diffusion in the pores.
Solvent Experimental DAB, cm2/s
3.20 Gaseous hydrogen at 150 psia and 80°F is stored in a small,
Methanol 1.69 x cm2/s at 15°C
spherical, steel pressure vessel having an inside diameter of 4 in. and
Ethanol 1.50 x lop5 cm2/s at 25°C
a wall thickness of 0.125 in. At these conditions, the solubility of hy-
Benzene 1.92 x cm2/s at 25°C
drogen in steel is 0.094 lbmol/ft3 and the diffusivity of hydrogen in
n-Hexane 3.70 x lop5 cm2/s at 25°C
steel is 3.0 x lod9 cm2/s. If the inner surface of the vessel remains
3.12 Estimate the liquid diffusivity of benzene (A) in formic acid saturated at the existing hydrogen pressure and the hydrogen partial
(B) at 25°C and infinite dilution. Compare the estimated value to pressure at the outer surface is assumed to be zero, estimate:
that of Example 3.6 for formic acid at infinite dilution in benzene. (a) The initial rate of mass transfer of hydrogen through the metal
3.13 Estimate the liquid diffusivity of acetic acid at 25°C in a wall
dilute solution of: (a) Benzene, (b) Acetone, (c) Ethyl acetate, and (b) The initial rate of pressure decrease inside the vessel
(d) Water by an appropriate method. Compare the estimated values (c) The time in hours for the pressure to decrease to 50 psia,
with the following experimental values! assuming the temperature stays constant at 80°F
3.21 Apolyisoprene membrane of 0.8-pm thickness is to be used
Solvent Experimental DAB, cm2/s
to separate a mixture of methane and H2. Using the data in
Benzene 2.09 x cm2/s at 25°C Table 14.9 and the following compositions, estimate the mass-
Acetone 2.92 x lop5 cm2/s at 25°C transfer flux of each of the two species.
Ethyl acetate 2.18 x lop5 cm2/s at 25°C
Water 1.19 x lo-' cm2/s at 20°C
Partial Pressures, MPa
3.14 Water in an open dish exposed to dry air at 25°C is found to
Membrane Side 1 Membrane Side 2
vaporize at a constant rate of 0.04 g/h-cm2. Assuming the water
surface to be at the wet-bulb temperature of ll.O°C, calculate the Methane 2.5 0.05
effective gas-film thickness (i.e., the thickness of a stagnant air film Hydrogen 2.0 0.20
that would offer the same resistance to vapor diffusion as is actually
encountered at the water surface). Section 3.3
3.15 Isopropyl alcohol is undergoing mass transfer at 35°C and
3.22 A 3-ft depth of stagnant water at 25°C lies on top of a
2 atm under dilute conditions through water, across a phase bound-
0.10-in. thickness of NaC1. At time < 0, the water is pure. At time =
ary, and then through nitrogen. Based on the date given below,
0, the salt begins to dissolve and diffuse into the water. If the con-
estimate for isopropyl alcohol:
centration of salt in the water at the solid-liquid interface is main-
(a) The diffusivity in water using the Wilke-Chang equation tained at saturation (36 g NaCVlOO g H20) and the diffusivity of
(b) The diffusivity in nitrogen using the Fuller et al. equation NaCl in water is 1.2 x cm2/s, independent of concentration,
(c) The product, DABpM. in water estimate, by assuming the water to act as a semi-infinite medium,
the time and the concentration profile of salt in the water when
(d) The product, DABpM, in air
where p~ is the molar density of the mixture. (a) 10% of the salt has dissolved
(b) 50% of the salt has dissolved
Using the above results, compare:
(c) 90% of the salt has dissolved
(e) The diffusivities in parts (a) and (b)
(f) The diffusivity-molar density products in Parts (c) and (d) 3.23 A slab of dry wood of 4-in. thickness and sealed edges is
exposed to air of 40% relative humidity. Assuming that the two
Lastly:
unsealed faces of the wood immediately jump to an equilibrium
(g) What conclusions can you come to about molecular diffusion moisture content of 10 lb H20 per 100 lb of dry wood, determine
in the liquid phase versus the gaseous phase? the time for the moisture to penetrate to the center of the slab (2 in.
Data: from either face). Assume a diffusivity of water in the wood as
8.3 x cm2/s.
Component Tc, OR PC, psia 2, UL, cm3/mol
3.24 A wet, clay brick measuring 2 x 4 x 6 in. has an initial uni-
Nitrogen 227.3 492.9 0.289 - form moisture content of 12 wt%..At time = 0, the brick is exposed
Isopropyl alcohol 915 69 1 0.249 76.5 on all sides to air such that the surface moisture content is