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 0.1inch (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/scm2 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. (333).
Note that for an ideal gas, product cDH,A is independent of total pressure because c is
directly proportional to P, while from Eq. (336), cDH,A is inversely proportional to
P.
At P = 1 atm, c = P/RT = 1/(82.06)(293) = 4.16 x 105 mol/cm3.
Therefore, cDH,A = (4.16 x 105)(0.145) = 6.03 x 106
(a) P = 10 atm. By Dalton's law, at (yH)1 = 0.08/10 = 0.008
From Eq. (333), NH = cDH,A ∆z ln 1 − ( yH ) 2
(6.03 × 10 −6 )
1− 0
=
ln
= 1.91× 10−7 mol HCl/scm 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 106 mol/scm2
(c) For P = 0.1 atm, (yH)1 = 0.08/0.1 = 0.8, which gives, NH =3.82 x 105 mol/scm2 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. (336), 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 oxygenbenzene system at 38oC (311 K) and 2 atm, which
give, DAB = 0.0494 cm2/s
Find: Diffusivity at 100 atm.
Analysis: If Eq. (336) 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 infinitedilution 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) nhexane.
Find: Diffusivities by the methods of Wilke and Chang (WC), and of Hayduk and Minhas
(HM). Compare predicted values to given experimental values.
Analysis: Let:A = the solute, CCl4; and B = solvent. The WilkeChang equation, Eq. (339), is
DA,...
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 Spring '11
 Levicky
 The Land

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