Page 544 - Bird R.B. Transport phenomena

524 Chapter 17 Diffusivity and the Mechanisms of Mass Transport

This problem can also be solved by method (iii) without an experimental value of сЯЬ *.
АА
Equation 17.4-2 gives directly
eM i_Y /2 ,2/3
\ = 2.96 X 1(Г +
^44.01 46^ (304.2) 1
6
= 4.20 X 10~ g-mole/cm • s (17.2-7)
The resulting predicted value of сЭ)^* is 5.1 X 10" g-mole/cm • s.
6

EXAMPLE 17.2-3 Estimate c9) AB for a mixture of 80 mole% CH and 20 mole% C H 6 at 136 atm and 313K. It is
2
4
5
known that, at 1 atm and 293K, the molar density is с = 4.17 X 10~ g-mole/cm 3 and 9) AB =
Estimation of Binary 0.163 cm7s.
Diffusivity at High
Density
SOLUTION
Figure 17.2-1 is used, with method (i). The reduced conditions for the known data are
T 293
= 1.22 (17.2-8)
V(190.7)(305.4)
1.0
Pr = = = 0.021 (17.2-9)
/p p V(45.8)(48.2)
cA cB
From Fig. 17.2-1 at these conditions we obtain (c%b ) = 1.21. The critical value (c$) ) is
AB r AB c
therefore
5
c4b AB _ (4.17 X l(T X0.163)
~~ (c4b ) ~ 1.21
AB r
6
= 5.62 X 10" g-mol/cm-s (17.2-10)
Next we calculate the reduced conditions for the prediction (T = 1.30, p = 2.90) and read the
r r
value (c£b AB) r = 1.31 from Fig. 17.2-1. The predicted value of сЯЬ is therefore
АВ
6
) c = (1.31)(5.62 X 10~ )
6
= 7.4X 10~ g-mole/cm -s (17.2-11)
6
Experimental measurements 8 give сЯЬ АВ = 6.0 X 10 , so that the predicted value is
23% high. Deviations of this magnitude are not unusual in the estimation of c£b AB at high
densities.
An alternative solution may be obtained by method (iii). Substitution into Eq. 17.4-3
gives
V / 2 (45.8 X 48.2) 1/3
6
(c% AB) c = 2.96 X 10~ |
6
= 4.78 X 10" g-mole/cm • s (17.2-12)
Multiplication by (сЯЬ ) . at the desired condition gives
АВ }
6
сЯЬ = (4.78 X 10~ )(1.31)
АВ
6
= 6.26 X 10~ g-mole/cm • s (17.2-13)
This is in closer agreement with the measured value. 8

s V. J. Berry, Jr., and R. C. Koeller, AIChE Journal, 6,274-280 (1960).