NOTES
4699
The Diffusion of Gases i n Nonpolar Liquids.
where a! is the reciprocal of the interfacial resistance and C, is the concentration of the solute at the interface. Combining eq 5 with eq 1 and 2, the solution now becomes3
The Open-Tube Method by Lorna Bennett, Wing Y. Ng, and John Walkley
c
=
c0erfc(x/2dDi) -
Department of Chemistry, Simon Fraser University, Burnaby 2, British Columbia, Canada (Received J u l y 8, 1968)
ehx+h*Dt
Hildebrand’ has recently made use of the diaphragm method for the measurement of the diffusion of gases in nonpolar solvents. This is a pseudo-steady-state method and relies upon measuring the change in volume of the gas in equilibrium with the saturated solution above the diaphragm. The gas in the solution diffuses through a diaphragm of macroscopic size holes into the bulk solvent of essentially infinitely dilute solute concentration. This method is often lengthy, and the conditions which give rise to a steady-state system are sometimes difficult to attain. We now report some measurements of the diffusion of gases in nonpolar solvents using a n open-tube method. This method is a nonsteady-state one and has the advantage that a value of both the diffusion coefficient and the interfacial resistance can be measured.
Theory The solution for Fick’s law of linear diffusion, uix., using the usual definition of terms
J,
=
-D-
BC
bX
and satisfying the conditions that C = Co if x = 0 and t > 0, C = 0 if x > 0 and t = 0, is
c
=
c0e r f c ( z / 2 d E )
(3)
where Co is the saturation solubility of the solute and erfc(y) is the complement of the error function. Thus the volume of gas dissolved at time t in a previously degassed solvent is given as
2RTA P
(4)
where A is the cross-sectional area of the cell and P and T are the pressure and temperature, respectively, of the gas. Experiments show that the observed V us. curve is displaced from that expected using eq 4. It is seen that the slope of the curve rapidly approaches, as a limiting value, that expected from eq 4. The basic equation for mass transfer across an interface2 is
di
J,,o = - D ( E )
230
= -a!(C,
- CO)
(5)
erfc(
&+ h 6 t )
(6)
where h = a / D . The volume of gas crossing the interface is given by
V
=
...[,” Ph
erfc(hdB) - 1
+2 h d 9
(7)
where P is the partial pressure of the gas and R is the gas constant. It is seen from eq 7 that the limiting behavior will be given by an equation identical with eq 4, hence giving a value of D. By curve fitting eq 7 to the complete set of data (from t = 0), a value of D and h can be found. It is found that these two values of D are in good agreement.
Experimental Section The apparatus used was similar to that of Houghton,
et aL4 The diffusion cell was a uniform tube of 24 cm2 in cross-sectional area and 25 cm long. The average diffusion length for 200 min (the duration of a typical run) was less than 2 cm. The volume of gas diffusing into the solvent was measured with a calibrated manometer. After filling the diffusion cellwith the degassed solvent, a good thermal equilibrium was established by keeping the cell thermostated (to *O.Olo) for at least 24 hr prior to allowing gas into the cell above the solvent. Solvents were spectroquality reagents supplied by Matheson Coleman and Bell, and the gases were research grade, supplied by IIatheson.
Results and Discussion
di
Figure 1 shows the experimental V us. curve for N2 in C6H6. The dotted line shows the expected relationship in the absence of interfacial resistance. Owing to the nature of eq 7, D may be estimated from the limiting slope of the experimental curve. The expected relationship between V and as given by eq 7, is also shown in Figure 1for various values of h. I n no experiment is it found possible to reproduce the data at the beginning of a run ( t --t 0). This is undoubtedly due to a time lag in setting up the gas-vapor equilibrium above the solvent,
di,
(1) M.Ross and J. H. Hildebrand, J . Chem. Phys., 40, 2397 (1964); K. Nakanishi, E. M. Voigt, and J. H. Hildebrand, ibid., 42, 1860 (1965). (2) J. T. Davies and E. K. Rideal, “Interfacial Phenomena,” 2nd ed, Academic Press, New York, N. Y., 1963, Chapter 7. (3) H. S. Carslaw and J. C. Jaeger, “Conduction of Heat in Solids,” 2nd ed, Oxford University Press, London, 1959, Chapter 2. (4) G . Houghton, A. 8. Kesten, J. E. Funk, and J. Coull, J. Phys. Chem., 65, 649 (1961).
Volume 72, Number 18 December 1968
4700
NOTEB Data for this open-tube method have not previously been analyzed by curve fitting to eq 7 . We are unable to comment upon the h values with the limited data available. It is pertinent to note, however, that the linear portion of the curve is only strongly dependent upon h, for small h values, ie., less than 15. This method is excellent for measuring the diffusion coefficient D and this coefficient, unlike h, is not sensitive to interfacial impurity,
Quantum Yield of the Photonitrosation of Cyclohexane
by Hajime Miyama, Noriho Harumiya, Basic Research Laboratories, Toyo Rayon Company, Ltd., Tebiro, Kamakura, J a p a n
Yoshikazu Ito, and Shigeru Wakamatsu h7ag0ya Laboratory, Toyo Ravon Company, Ltd., Tebiro, Kamakura, J a p a n (Received J u l y 10, 1968)
Figure 1. Diffusion of nitrogen gas in benzene at 25" (D = 7.23 oma sec-l): 0, experimental results; - - -, eq 4 (no interfacial resistance).
The D and h values for several gas-solvent systems are given in Table I together with the D values obtained using the Hildebrand diaphragm method. It is seen that, in general, good agreement between the two D values exists. It is seen from Table I that the D
Table I: Diffusion Coefficients and Permeability Values at 25' lOSD, om2 see-'-
Leastsquares System
Ar-CClP NI-CC14 Ar-CeHe Na-CJh
Diaphram method
(3.63)a (3.42)a 11.2 6.93
From the
slope
fit of eq 7
om-1
3.71 3.63
3.73 3.79
11.3 8.1
7.20
7.23
9.5
...
...
h,
...
Reference 1.
value for argon in benzene is anomalously high when measured by the diaphragm method. No sensible value of D could be obtained from the open-tube method for this system. From the data obtained it would appear that this system behaves as if the flux at the interface were constant. Such a condition is incompatible with eq 7, and as such no value of D or of a can be obtained from the data. The Journal of Physical Chemistry
The photonitrosation of cyclohexane is one of the important processes of synthesizing caprolactam.' However, not much is known about the quantum yield of this reaction. A value of 0.7 was obtained by Torimitsu, et aL12 in the wavelength range 365-560 mp, and a value of 1.48 was obtained by Baumgartner, et aL3 The latter value was later corrected to 0.87 (420 mp) and 0.68 (580 m ~ ) .Fukuzawa ~ and iVIiyama6 obtained, under a flash lamp, 0.65 in the range 360505 mp. The accuracy of most of these values cannot be estimated because the oxime hydrochloride produced does not dissolve in cyclohexane, and the scattering of the incident light by suspended oxime particles becomes marked as the reaction proceeds. Therefore, in order to obtain a more reliable value without being disturbed by the light scattering, we used an integrating sphere in the wavelength range 365-589 mp. The integrating sphere6 made from mild steel has a diameter of 1.3 m and its inside wall is coated with white paint, containing barium sulfate as a main component, in order t o obtain uniformly reflected light (the reflectance is about 90%). The reaction vessel is a Pyrex (1) Y. Ito, Bull. Chem. Sac. Jap., 2 9 , 227 (1956); E. &faller and H. Metrger, Chem. Ber., 8 7 , 1282 (1954). (2) S. Torimitsu, S. Wakamatsu, and Y . Ito, unpublished work. (3) P. Baumgartner, A. Seschamps, and C. Roux-Guerraz, Compt. Rend., 259, 4021 (1964). (4) A. Deschamp, Ph.D. Thesis, Faculty of Science, University of Paris, 1966. ( 5 ) D. Fukusawa and H. Miyama, J. Phys. Chem., 7 2 , 371 (1968). (6) B. J. Hisdak, J. Opt. Sac. Amer., 5 5 , 1122 (1965). The theoretical details of the integrating sphere were described in the references cited in this paper.
