404
D. K. ANDERSON, J. R. HALLAND A. L. BABB
scribing the diffusion and solubility of a vapor in a membrane without recourse to a separate solubility measurement. In practice it is clear from the foregoing that in order to obtain even the correct order of magnitude of these characteristic parameters the basic experimental observables must be known to within a few per cent. of their accurate values. The methods described above can be extended to cases where h contains other parameters besides c y ; e.g., even if nothing is known concerning the form of h we could fit a polynomial to the time lag data to any desired degree of accuracy. Needless to say the degree of complication of such procedures increases sharply with the number of parameters. It should also be noted that if besides time lag and steady-state data we know the solubility a t one pressure (only one cy) we can still use the foregoing formulas (cf., equations 2, 12 and 13, etc.) to find DOand a separately if we assume a suitable fgnctional form for h. Without time lag data only D(co)can be found. If an isotope of the given vapor (preferably a radioactive one) is available then a transmission experiment can yield directly (if we neglect a small isotope effect) D without the necessity of knowing anything about the functional form of a. The membrane is initially uniformly saturated at a concentration of co of isotope 1; the vapor reservoirs (at z = 0 and I) being maintained at a constant pressure po = co/S(co) of isotope 1. At time t = O the reservoir at x = 0 is exchanged for another maintaining a pressure PO of isotope 2. The amount of isotope 2 appearing at the reservoir at x = I is now measured as a function of time.1° Since the total vapor concentration is constant throughout the membrane the time lag of isotope 2 is given by L
= Z2/6D(c0)
(10) The author is indebted to Prof. M. Sswarc for a discussion of this method clarifying certain details.
Vol. 62
Isotope experiments such as this are necessary in any case if we desire to know the true binary diffusion coefficients in order to make frame of reference corrections. We will not comment further here on this topic. Discussion We can conclude from the foregoing that if we can guess the form of the concentration dependence of 3 then time lag data are as useful as in the case where 3 is constant. Even if we cannot say anything about the concentration dependence of 3 we can still use L to obtain an idea of the order of magnitude of a if we make certain assumptions (generally rather harmless ones) concerning a. Thus in the absence of phase separation (in the diffusant-membrane system), phenomenological diffusion theory and the thermodynamics of irreversible processes (since entropy production is positive) assure us that 0 < Do 5 D(c) 0 5 c < (14) where c, is the equilibrium saturation concentration, Le., "up-hill" diffusion does not occur. I n this case P(co)satisfies the inequality CS
Since D(c0) is bounded (13)allows us to estimate the order of magnitude of D(c0). In particular for a large class of D's including all shown in Table I and n
a's which are polynomials 3 = Do[l
+ i=
bci] 1
with bi 2 0 the lower bound on F is 1/6. Thus the estimate
-
~ ( c o ) 12/6L(~)
is at worst too small by a factor of three. The author is indebted to Miss M. C. Gray and her computing staff for the numerical calculations leading to Figs. 1 and 2 and to Prof. R. M. Barrer for his continued interest in this work.
RIUTUAL DIFFUSION I N NON-IDEAL BINARY LIQUID MIXTURES' BY D. K. ANDERSON, J. R. HALLAND A. L. BABB Department of Chemical Engineering, University of Washington, Seattle, Washington Received October $3. 1967
As part of a comprehensive study of the mutual and self-diffusion behavior of non-ideal binary liquid mixtures, experimental data for six systems are presented. Mutual diffusion data for the following solutions are given over the complete composition range: acetone-benzene at 25.15'; acetone-water a t 25.15'; acetone-chloroform a t 25.15 and 39.95'; acetonecarbon tetrachloride at 25.15'; ethanol-benzene at 25.15 and 39.98". and methanol-benzene a t 39.95". For the two systems involving ethanol and methanol, the new results are combined &th previously reported data to evaluate the activation energies of both the diffusion and viscous flow mechanisms. Curves for the function Dv/(d In al/d In NI) also have been evaluated for the systems studied experimentally. At present no attempt will be made to interpret the results theoretically.
Introduction Diffusion studies in this Laboratory have two general aim^.^-^ For both ideal and non-ideal liquid systems, current theories relating mutual ( I ) This work was supported in part by the Offiae of Ordnance Researah, U. 8. Army. (2) C. S. Caldwell and A. L. Babb, THIS JOURNAL, 60, 51 (1956); 59, 1113 (1955).
(3) P. A. Johnson and A. L. Babb, i b i d . , 60, 14 (1856). (4) P. A. Johnson and A. L. Babb, Chem. Reus., 56, 387 (1956).
and self-diffusivities may be compared with recently available results. Secondly, for systems where association of one component is known to occur, or where there are solvent-solute interactions, it is hoped that with the present knowledge of association mechanisms some progress may be made toward predicting experimental diffusion. As part of this comprehensive program, mutual diffusion data for six non-ideal systems are reported
L
MUTUAL DIFFUSION IN NON-IDEAL BINARY LIQUIDMIXTURES
April, 1958
TABLE I SUMMARY OF
A
Ethanol
Acetone
Acetone
Acetone
Acetone
Benzene
25.15
EXPERIMENTAL DIFFUSION DATA
System
B
Methanol Benzene
Etlianol
Acetone
Benzene
Benzene
Water
Temp., O C .
0.00470 .01536 ,1094 .2559 .5034 .6567 .8163 ,9966 25.15 .00225 .00471 .09574 .2034 .3415 .5068 .7022 .9961 39.98 .00372 .00372 .09574 .2034 .3415 .5068 ,7022 .9961 .9961
40.0
25.0
Carbon tetrachloride 25.15
Chloroform
Chloroform
Av. compn. of A D X 10s. mole cm.21 fraction 8ec.
26.15
39.95
4.67 4.22 1.88 1.30 '1.28 1.68 2.22 3.15 3.02 2.86 1.30 0.993 0.901 1.01 1.35 1.81 3.72 3.76 1.89 1.46 1.30 1.42 1.76 2.36 2.38
,00216 .OS309 .2392 ,4893 .SO36 ,6653 .9265 .9696
1.28 0.854 0.635 0.819 2.39 1.43 3.80 4.56
,00390 .00390 .2056 .3942 .7934 .9953 .9953
1.69 1.71 1.45 1.65 2.63 3.59 3.54
.00548 .2081 ,3903 .6061 .7472 .8641 ,9948 .9953
2.35 2.97 3.29 3.45 3.52 3.59 3.63 3.63
.00548 .00548 .2013 .2013 .3984 .4989 .4989 .6040 ,8592
2.90 2.87 3.57 3.59 4.05 4.14 4.16 4.24 4.27 4.28 4.31
,8641
.9948
405 .00369 .00369 .1000 .2027 .2027 .3941 .3930 ,3939 .5994 .5994 .7808 .9967 .9973 .9973
2.75 2.74 2.58 2.55 2.56 2.70 2.69 2.70 2.98 2.96 3.35 4.14 4.18 4.15
6.0
8 5.c Q-. 4 -e
3
(j
4.0
8 b F
c,
e-. Q 3.c 4 Q
2.c
0.5
I .o
MOL. FRACTION ACETONE. Fig. 1.-Diffusion and viscosity data for the acetonebenzene system a t 25.15' left hand scale; Dq and activity corrected Dq(Dq*),right hand scale.
in this paper together with snme energies of activation for both viscosity and diffusion. A t present, no attempt will be made to interpret the results theoretically. Experimental The solvents used were the highest grades commercially available and were for the most part used without further purification. Particular care was taken in handling hygroscopic liquids, as the slightest traces of water were found to affect the diffusion results markedly. The ethanol stabilizer was removed from chloroform with anhydrous calcium chloride, and benzene was stored over metallic sodium. The mutual diffusion measurements were made with a Mach-Zehnder type diffusiometer, described fully elsewhere .6 ( 5 ) C. 8 . Caldwell, J. R. Hall and A. L. Babb. Rev, Sei. Inst., 28, 816 (1957).
D. I
