382
NOTES
EXPERIMENTAL DETERMINATIONS OF THE DIFFUSION COEFFICIENTS OF GASES THROUGH WATER: NITROGEN AND ARGON1 BYROBERT E. SMITH,EUQENIA TARVER FRIESS AND
VOl. 59 D = (n/4a2@)(V/t)
(1)
which, in the differential form more convenient for computing, is D = (n/4a2pz)(Av/4t~ &')z
(2)
Here, V represents volume of gas displaced in time MANUELF. MORALES t, q the area at the absorbing interface, and a equal Department of Physiology School of Medicine University of California Medical Center, Lo8 Angeies, Calif., and N o d l Medical Research In+ t*o a~(T/273)(P/760),where a! is the Bunsen abtute, National Naval Medical Center, Bethesda, Maryland sorption coefficient at the temperature T of the exReceived January 84, 1966 periment; P is the partial pressure of gasander General theoretical studies on the physiological study within the gas space of the capillary tube. exchange of inert gases, e.g.,2Jas well as measureTo increase sensitivity Ringbom changed the ments of the permeability of tissues to inert gases,4 relative bore of the stationaw, gas-free side to have emphasized the importance of precise meas- about two times the bore of the saturated side, and urements of the diffusion coefficients of gases derived the above expression in terms of the centithrough liquids. N o measurements have appeared meters displacement, n, of the small bore meniscus, for the rare gases, and the values for nitrogen avail- namely able in the literature include only the two early D = k ( A n / d t + At - l/ts2 (3) determinations of Hiifnerb and Exnere for nitrogen in which k = ( 6 ~ / a ~ ) ( d ~ / with d ~ ) ~ dl , and d 2 the through water, that of Tamman and Jessen' for nitrogen through agar gel, and more recently those small and large capillary diameters, respectively. If An is taken in centimeters and t in hours, D of Eggleton, et u Z . , ~ for nitrogen through agar gel, olive oil and animal fat. In the present paper are wilI be in ern., day-'; as reported here these have sec.-l. reported the diffusion coefficients obtained experi- been divided by 86400 to give units of mentally for the passage through water of two Experimental gases, namely, nitrogen and argon; additional difThe apparatus as modified12consisted of a capillary confusion studies have been conducted with helium nected through 3-way stopcocks to two reservoir flasks. and sulfur hexafluoride (SFs),but the results do not The capillary was constructed by fusing together two tubes different bore, one 3.09 X 10+ cm. in diameter, the other appear acceptable without further t e ~ t i n g . ~The of 6.80 X 10+ cm. The fine, tube was 32 cm. in length and values reported for nitrogen are generally confirma- was graduated in mm.; the coarser tube was 15 cm. in tory of earIier measurements cited; so far as is length. Modifications in the original desi n which offered known no other data have been reported for trans- advantages in operation and minimized t f e possibility of diffusion through joints included the use of mercury seal fer of argon through water. with 120' angle plug bore, and on the left reservoir The apparatus of Ringbom'O with a few modifi- astopcocks ground-glass joint with mercury well and a side arm mancations was used. In this, a gas-saturated and a ometer. Water, triply distilled in glass, was degassed by boiling gas-free water column, introduced from either end into a capillary tube, are separated by a pure gas for 10 min. in a closed system under slightly reduced ressure introduced while hot into the reservoir flasks anffurther phase. With the gas-saturated water connected and degassed by evacuation until all bubbling ceased. The to a large reservoir and the pure water fixed as a test gas was passed into the flask until the pressure inside dead end column of sufficient length, the volume of was equal to or slightly greater than atmospheric, and the gas moving into the pure water is obtained by ob- gas allowed to bubble through the water until saturatlon was achieved. The apparatus was placed in a large glass serving the movement of the gas-saturated water water-bath maintained at 25 f 0.05'. At the end of one column into the displaced gas space. The rate a t hour of equilibration in the bath, the venting manometer which this displacement occurs gives a measure of was sealed off with mercury, and gas saturation was immethe diffusion coefficient of the gas through water, diately discontinued. The capillary wa8 first dried by passdry gas through it, then filled with test gas saturated provided the tube diameter is small enough to mini- ing with water vapor by bubbling the gas through H20. The mize convection and that suitable temperature pressure in the capillary was then reduced by an amount sufficient to permit entry of the water column into the capilcontrol is maintained. Under these conditions, the governing equation lary for a suitable distance. The pure water was allowed almost .to fill the coarser segment, then cut off from the is that of Stefan,l' Le. reservoir. The gas saturated water column was then al-
-
(1) The opinions contained herein are the personal one8 of the authors and do not necessarily reflect those of the Navy Department or the Naval Service a t large. (2) R. E. Smith and M. F. Morales, BUZZ. Math. Eiophus., 6 , 125 (1944). (3) M. F.Morales and R. E . Smith, ibid., 10, 191 (1948). (4) M.Krogh. J . Phyeiol., 49, 271 (1914). (5) G:Hiifner, Ann. p h y s i k . Chem., 60, 134 (1897). (6) F. Exner, Physik, 166, 321 (1875). (7) G. Tammann and V. Jessen, Z . anow. aZZgem. Chem., 179, 125 (1929). (8) P.Eggleton, 9. R. Elsden, J. Fegler and C. 0. Hebb, J . Physiol., 104, 129 (1945). (9) The highly improbable value of D = 10.37zt 0.815 X lo-* cm.2 sec.-1 was obtained for He, while the experimental value for SFs of D = 4.51 =t0.97 X 10-6 also appeared too high for immediate acceptance. (10) Von A. Ringbom, Z . anorg. aZlg,em. Chem., 138, 94 (1938). (11) J. Stefan, K.Akademie Wiseensch. Wiener Berichte,77, (11) 371 (1878).
lowed to enter and come to rest a t some point in the graduated segment of the tube, whereafter it was left confluent with its reservoir flask. The system was fully closed to prevent any effect from atmospheric fluctuation. The pressure of the test gas in the capillary was determined from the flask pressure by correcting for water vapor pressure and pressure due to the weight of the water column plus any residual differential in the heights of the Hg of the side arm manometer following final closure of its external arm. For analysis, plots were made of the displacement of the free meniscus in cm. us. d/t7and the slopes of the region beyond the initial equilibration determined by the method of least squares.
Results and Discussion Calculations based on twelve trials with N2 (99.58% N2; 0.42% 0,; 0.02% CO,) gave for the (12) To be desoribed in greater detail in Research Report from Naval Medical Research Institute, Bethesda, Maryland.
April, 1955
COMMUNICATION TO THE EDITOR
diffusion coefficient D = 2.246 f 0.106 X lod cm.2 sec.-l. Eleven trials using argon (>99,5% pure) gave D = 1.463 f 0.138 X 10" cm.2sec.-1. The ratio DnitrogmJDargon = 1.53 conforms grossly to the inverse ratio of the square roots of the respective molecular weights = 1.2. The coefficient obtained with Nz agrees quite closely with the experimental value obtained by Hufner6 a t 22" (Le., D = 2.12 X 10--6), when the latter is corrected for temperature by a factor 1.145, derived empirically from the data of Tamman and Jessen? on diffusion of Nzthrough agar as a function of temperature. When corrected for partial pressure of water vapor the absolute coefficients of the latter authors give for Nz a t 25", D X lo6 = (1.56/8640O)(76Oz/ 736.2) = 1.92, which is still somewhat lower than
383
the values obtained in the present study. A calculation of D from the Stokes-Einstein formula would give for Nz at 25" the value D X lo6 = 1.55, assuming a molecular radius of 1.575 8 . 1 8 A similar calculation using Hill's14 values for radii as r*/2 = 2.085 8. for Nz and 1.915 A. for argon gives DN, X lo6 = 1.171 and D A X lo6 = 1.275 which does not alter the previous conclusion. Summary.-Using a slightly modified Ringbom apparatus, measurements have been made of the diffusion of argon and of nitrogen into pure water at 25"; the respective coefficients of diffusion calculated from the data are D X lo6 = 1.463 f 0.138 and 2.246 f 0.106 cm.2 set.-'. (13) Taken as l/n molecular diameters based on van der Waals equation ("Handbook of Chemistry and Physics," Chemioal Rubber Publ. Go., 29 Ed., Cleveland, Ohio, 1945, p. 2581). (14) T. L. Hill, J . Chem. Phus., 16, 141, 399 (1948).
COMMUNICATION TO THE EDITOR ON FIRST ORDER TRANSITIONS I N ADSORPTION SYSTEMS Sir : It has been demonstrated in several cases1s2 that gas-solid absorption systems can have discontinuous adsorption isotherms on a short-time basis and completely continuous isotherms on a long-time basis. It is the purpose of this communication to comment on the above phenomenon. For a discussion of total or thermodynamic equilibrium in an adsorption system, the following partial equilibria will be introduced: (a) gaskinetic-the concentration of gas molecules on or near the surface of the solid until, over a small time interval, kinetic equilibrium subsists (number of molecules striking surface of solid S number leaving). (b) Swelling3-the adjustment or response (swelling) of the solid to the adsorptive stresses of the surroundings. (c) Thermal-the establishment of uniform temperature throughout the solid component after dissipation of the heat introduced by a heater or liberated as heat of adsorption. When there are simultaneous, time independent kinetic, swelling, and thermal equilibria, total (thermodynamic) equilibrium is said to exist. It is conjectured that the establishment of kinetic equilibrium is a short-time process (seconds, minutes); i.e. it is postulated that entering gas molecules quickly come to equilibrium with their surroundings, but these same surroundings are themselves changing (in the thermal and swelling senses). Thus, the rapidly established kinetic equilibrium will be reversibly displaced as the (1) E. V. Ballou, J . A m . Chem. SOC.,76, 1199 (1954). (2) M. L. Corrin and C. P. Rutkowski, J . P h w . Chem., 18, 1089 (1954). (3) R.J. Tykodi, J . Chem. Phus., 88, 1647 (1954).
system approaches a state of swelling and thermal equilibrium. There is evidence that the establishment of thermal equilibrium can be a long-time process (minutes, hours) ,45 particularly so in the absence of a significant gas pressure in the ~ y s t e m . ~ As to swelling equilibrium, the swelling rate is usually greatest at low coverage and decreases with increasing coverage. Since the establishment of swelling equilibrium requires the dissipation of adsorptive stresses by a bulk (not merely surface) response3 of the solid component, it will generally be a slow process. In a system in which kinetic equilibrium has been established and in which the approach to swelling and/or thermal equilibria is slow, it is possible to observe, on a short-time basis, reasonably complete adsorption-desorption reversibility (both adsorption and desorption points fall on the same curve) even though the system is not in total equilibrium. It is suggested that the discontinuous isothermswith adsorption-desorption reversibility-mentioned above are probably exemplifications of such a state of partial equilibrium. It has been argued elsewhere3that adsorption systems in total (thermodynamic) equilibrium are not likely to exhibit first order transitions. Finally, it is asserted that for adsorption systems with isothermal surroundings the only unambiguous test of total equilibrium is the time independence, on a long-time basis, of the pertinent system variables (usually pressure and temperature). 250 RIDGEAVENUE R. J. TYKODI UNIVERSITY PARK,PENNSYLVANIA RECEIVED FEBRUARY 12, 1955 (4) J. A. Morrison, J. M. Los and L. E. Drain, Trans. Faradau Soc., 47, 1023 (1951). (5) E. L. Pace and S. A. Greene, J . A m . Chem. Soc., 76, 3286 (1954).
