Page 543 - Bird R.B. Transport phenomena

§17.2 Temperature and Pressure Dependence of Diffusivities 523

EXAMPLE 17.2-1 Estimate ЯЬ for the system CO-CO at 296.IK and 1 atm total pressure.
2
АВ
Estimation of SOLUTION
Diffusivity at Low
Density The properties needed for Eq. 17.2-1 are (see Table E.I):

Label Species M T (K) p (atm)
c
A CO 28.01 133 34.5
В co 44.01 304.2 72.9
2
Therefore,

(РСАРСВУ = (34.5 X 72.9) 1/3 - 13.60
/3
(T T ) 5/u = (133 X 304.2) 5712 = 83.1
cA
cB
/2
V _
, 0.2417
M 28.01 44.01/
A
296.1 V 8 2 3
= 2.745 X 10" = 5.56 X 10"
f
T Tj \Vl33 X 304.2/
cA
Substitution of these values into Eq. 17.2-1 gives
4
(1Ш АВ = (5.56 X 10~ )(13.60)(83.1)(24.17) (17.2-4)
2
This gives %b = 0.152 cm /s, in agreement with the experimental value. 5 This is unusually
AB
good agreement.
This problem can also be solved by means of Fig. 17.2-1 and Eq. 17.2-3, together with the
2
ideal gas law p = cRT. The result is ЯЬ = 0.140 cm /s, in fair agreement with the data.
АВ
EXAMPLE 17.2-2 Estimate c£b AA* for C O 2 in ordinary CO 2 at 171.7 atm and 373K. It is known 6 that ЯЬ * =
14
АА
5
3
2
0.113 cm /s at 1.00 atm and 298K, at which condition с = p/RT = 4.12 X 10" g-mole/cm .
Estimation of Self-
Diffusivity at High SOLUTION
Density
Since a measured value of 0)дл* is given, we use method (i). The reduced conditions of the
measurement are T = 298/304.2 = 0.980 and p = 1.00/72.9 = 0.014. Then from Fig. 17.2-1 we
r
r
get the value (с2) *) = 0.98. Hence
лл
г
(4.12 X 10" )(0.113)
5
:
(сЯЬ *) 0.98
АА г
6
= 4.75 X 10~ g-mol/cm • s (17.2-5)
At the conditions of prediction (T = 373/304.2 = 1.23 and p = 171.7/72.9 = 2.36), we read
r r
(сЯЬ *) = 1.21. The predicted value is then
АА г
6
= (<® .) (c® .) c = (1.21)(4.75 X 10" )
AA
AA
r
6
= 5.75 X 10~ g-mole/cm • s (17.2-6)
6
The data of O'Hern and Martin give сЯЬ * = 5.89 X 10 g-mole/cm • s at these conditions.
7
АА
This good agreement is not unexpected, inasmuch as their low-pressure data were used in the
estimation of (c% *) .
AA c
В. A. Ivakin, P. E. Suetin, Sov. Phys. Tech. Phys. (English translation), 8, 748-751 (1964).
5
6
E. B. Wynn, Phys. Rev., 80,1024-1027 (1950).
7
H. A. O'Hern and J. J. Martin, Ind. Eng. Chem., 47, 2081-2086 (1955).