Measurement of the Gas Permeability of Sheet Materials L. C. CARTWRIGHT, Foster D. Snell, Znc., 29 West 15th S t . , ,Yew York 11, S.Y. Several types of gas permeability testers previously reported in the literature are discussed and their sensitivities compared. -An instrument of new design, made entirely of Pyrex, is described. Its sensitivity is some six times that of previous gas permeability instruments, permitting detection within 24 hours of permeabilities as low as 0.052 cc. (N.T.P.)per square meter per 24 hours per atmosphere.
B
ECAUSE of the increasing use of plastic films, plastic-
coated paper, and other flexible sheet materials for the protection of packaged products against atmospheric moisture and oxygen, attention has been given by many laboratories to methods of determining water vapor permeability and gas permeability of sheet materials. For a number of reasons considerably more rapid progress was made in the determination of water vapor permeability. Relatively simple, convenient, and accurate gravimetric methods have been developed, adopted as standard methods by interested technical societies, and included in numerous specifications for packaging materials. Doty et al. (W) have described a method for water vapor permeability determinations, made in a vacuumized system, in which the water vapor transmitted is retained in gaseous form Fhile pressure, Lrolume, temperature, and time data are taken to permit calculation of the permeability rate. Their method appears to yield very accurate results, and they have present,ed an interesting interpretation of the mechanism of water vapor permeation Fhich may be equally applicable to the transmission of other gases through permeable membranes. Indeed, their equipment should be quite as effective for gas permeability measurements with other gases as with water vapor, but, it is rather too elaborate and its use requires too much time and effort for the routine determination of the permeabilities of large numhers of sheet materials to various gases. Excluding certain earlier work on the gas permeability of relat'ively permeable materials, such as balloon fabrics, other coated or impregnated fabrics, and thin rubber membranes, one of the frrst gas permeability methods described in the literahre is that of Eldcr ( 3 ) and Shuman ( 4 ) . These authors have discussed at some length the import,ance of gas permeability measurements, especially of oxygen permeability in connection with t'he packaging of certain foods, drugs, and other products. They have indi(sated thr wide range of permeability of different sheet materials t o t h e same gas and of the same sheet material to different gases, and have dealt with the numerous difficulties involved in the accurate measurement of gas permeabilities over these ranges. Their instrument, described in detail by Shuman ( 4 ) , indicates the increase in pressure in a vacuurnized chamber of approximately 2-02. volume as the test, gas, at, 1-atmosphere pressure, pvrmeates t,hrough a test specimen some 32 sq. cm. in area. .issuming no leaks in t,he system and no gas pressure from ot,her sources, such as volatilization of plasticizer from t,he test specinic~n,a perceptible change in pressure of 0.5 mm. on t,he lowpressure side is obtained in 24 hours with a test specimen whose pmncahility to the t'est gas is only 0.37 cc. (S.T.P.) per sq. meter per 24 hours per atmosphere. Alany plastic films have pernic~ahilitiesto ordinary gases, such as nitrogen, oxygen, and c4:trhon dioxide, much greater than this value, some being more than 100,000 times as great, and relatively accurate measurements of these higher permeabilities may be made in a few minutes to a friv hours by Shuman's method. Todd (6) developed an inst,rument in which a 10-cc. volume of test gas, held at, atomspheric pressure in a closed chamber, inrluding a 1.854-mm. inside diameter, horizontal glass capillary, 1)ermeat'esthrough a t,est specimen some 46 sq. cm. in area int'o a idativcly large vacuumized chamber, and the decrease in volume of the test gas is read on a scale along the capillary, as a short indicat,ing column of liquid, separat,ingthe t,est gas from the outside air, moves along to maintain pressure equilibrium. Assuming no leaks in the system, no temperat,ure change, and no failure of the indicating column to maintain perfect pressure equilibrium, a perceptible movement of the indicator of 0.5 mm. would occur in 24 hours for a permeability of 0.30 r r . (K.T.P.) per sq. meter per
24 hours per atmosphere. Thus the sensitivity of Todd's apparat'us is just slightly greater than that of Shuman's, but Todd's apparatus is subject t o considerably greater error due to slight temperature and barometric changes. A decrease in t,emperature of only 0.13" C., or an increase in barometric pressure of only 0.34 mm., during a test period of 24 hours xvould cause a movement of the indicating column in Todd's instrument corresponding to a permeability of 1 cc. (S.T.P.) per sq. meter per 24 hours per atmosphere, m-hereas the reading of Shuman's instrument is not significantly affected by minor changes in temperat,ure and baromet8ricpressure. . h o t her apparatus for measuring gas permeabilit,y of sheet , intended primaterials, devised by Smith and Kleiber (j)was marily for determining the rate of oxygen permeation into gaspacked or vacuum-packed food products in flexible packaging materials. I n their method, air a t atmospheric pressure is in contact yith a relatively large area of the sheet material under tt.st,, rvhich serves as a portion of the confining walls of a relatively large volume of nitrogen, also at atmospheric pressure. Thus, the total gas pressure is the same on both sides of the test specimen, but the partial pressure of oxygen differs by approximately 0.2 atmosphere, and atmospheric oxygen permeates into the nitrogen-filled space. This simulates the conditions of use of the packaging material, at least for nitrogen-packed product's. By analyzing the gas in the nitrogen chamber for oxygen content at, the beginning and a t t,he end of a suitable test period, knowing the volume of the nitrogen chamber and the area of the t'est specimen, the oxygen permeability may be calculated. I n a specific example given, the test area of a sample of laminated MSAT cellophane was 500 sq. em., the nitrogen chamber volume was 900 cc., and the oxygen content of the nitrogen increased from 0.054 to 0.175 volume % during a test period of 555 hours, indleating an oxygen permeability of 0.0000039 cc. per sq. cm. per hour a t 30" C., which is equivalent to 4.2 cc. (X.T.P.) per sq. meter per 24 hours per atmosphere. The stated probable error of h 0 . 0 1 volume % of oxygen for the gas analysis apparatus used by Smith and Kleiber indicates a limiting sensit,ivity of 2.2 cc. (N.T.P.) per sq. meter per 24 hours per atmosphere for a 24-hour test period with their apparatus in the dimensions described, which is only about one sixth the sensitivity of Shuman's instrument', and one seventh that of Todd's instrument, for the same test period. More recently, another isost,atic met,hod of measuring gas permeability, utilizing equal total gas pressures but different partial pressures on the t n o sides of the test specimen, has been described by Davis ( 1 ) . I n this method, separate streams of two gases are passed through a series of cells in which the gases are separated only by the sheet material under test,. The test, area by increasing the number of cells. The niay he increased a t 1%-ill pressures and rates of flow of the trvo gases are equalized by suitable control devices and the effluent stream of each gas is collected and analyzed for its content of t.he other gas. Thus each gas serves as a test gas and a t the same time as a reference gas for the other, the partial pressure differential through the test sheet being substantially 1 atmosphere for each gas. Davis reported a sensitivity for a 24-hour test period of the order of 1 cc. (X.T.P.) per sq. meter per 24 hours per atmosphere for his method with the dimensions, conditions, and gas analysis methods described in his paper, which is slightly less than the sensitivities of the instruments of Shuman and of Todd and slightly greater than that of Smith and Kleiber. However, as Davis pointed out, it is important that very small leaks m the system may have relatively little effect on the accuracy of results obtained by the EOstatic method, whereas even a very small leak may invalidate the results when a total gas pressure differential of 1 at,mosphere is maintained through the t,est sheet,, as in the cases of the EldrrShuman and Todd methods.
In an effort to find a rapid and convenient method for determining the permeability of sheet materials to various gases, the author first devised a modification of Todd's instrument. The 393
V O L U M E 19, NO. 6
394 test area was increased to 64 sq. cm. and the horizontal capillary reduced to 1.1-mm. inside diameter, which increased the sensitivity some fourfold to 0.07 cc. (S.T.P.) per sq. meter per 24 hours per atmosphere for a 24-hour test period. At the same time the test gas chamber volume was reduced to 2.1 cc., decreasing the error due to uncorrected temperature and barometric changes some fivefold, although this was still a serious problem, and very careful application of temperature and pressure corrections to all readings was necessary in order to take advantage of the increased sensitivity of the modified Todd apparatus. Although this apparatus was used successfully for determining the permeability of a large number of sheet materials to air, oxygen, and carbon dioxide, including permeabilities ranging from 5 to 500,000 cc. (K.T.P.) per sq. meter per 24 hours per atmosphere, its operation was tedious and time-consuming, application of temperature and pressure corrections was almost always required, even for short test periods in a temperature-controlled room, and difficulties due to leaks were frequently encountered. To eliminate these difficulties and yet achieve the even greater sensitivity required for reasonably rapid determination of the gas permeability of materials with very low permeabilities, the author designed an instrument similar in principle to that of Elder and Shuman, but differing in important details of construction and operation. CONSTRUCTION AND OPERATIOh OF APPARATUS
The apparatus, shown in Figure 1, is constructed entirely of Pyrex. Although i t is not indicated in the drawing, the lower surface of the flat cover plate is plane-ground. The test specimen of sheet material separates the lower chamber, which holds the test gas, from the vacuumized capillary chamber into which the test gas permeates. The test area is defined by the inside diameter of the top edge of the test gas chamber, and a sheet of tissue paper, very slightly smaller than the test area, placed between the test specimen and the cover plate, permits the permeated gas to pass freely along the upper surface of the test specimen, into the capillary chamber where its pressure is read on the mercury manometer. The test specimen extends slightly beyond the outer circumference of the test gas chamber and cover plate and is hermetically sealed between them in a manner described below. The capillary system is vacuumized through its side arm, any desired test gas is introduced into the lower chamber under suitable known conditions, and its rate of permeation through !he test specimen is determined by observing the rate of pressure increase shown by the manometer. It is essential to the calculations that the volume of the low-pressure chamber be known fairly accurately. This is readily determined in a manner described below. Any convenient wax or wax-resin blend that is tough, flexible, and adherent to glass and the test specimen a t the test temperature, as well as relatively impermeable to gases, may be used to seal the test specimen in place. A mixture that has been found very satisfactory for use with most sheet materials over a test temperature range of 20' to 40" C., is equal parts Ay,weight ?f beeswax, amorphous petroleum wax, and a polymerized rosin known as Polypale resin. Another suitable mixture is the 40-60 blend of amorphous wax and paraffin given in TAPPI Standard T464m-46 for sealing viater vapor permeability test dishes. To assemble the apparatus for a series of determinations of the permeability of a particular test specimen to a number of gases a t given temperature and humidity conditions, say 75" F., 50% relative humidity, the following procedures have been found convenient. The assembly operations are preferably carried out in air maintained at the test conditions of 76" F., 507, relative humidity. The capillary system is removed from the cover plate and laid aside. A piece of the sheet material to be tested, somewhat larger than the cover plate, is laid on a clean sheet of paper on a smooth, flat surface, such as a glass plate. A disk of tissue paper, some 2 mm. smaller in diameter than the test area, of the same grade as that used in calibrating the instrument as described below, and conditioned to moisture equilibrium a t the test conditions, is placed on the test specimen. The
cover plate is centered over the tissue paper and held down firmly. The wax sealing mixture, heated some 30" to 50" above its melting point, is applied neatly from a medicine dropper all the way around the outer edge of the cover plate, sealing it firmly to the test, specimen. Nest, a thin film of petrolatum is applied uniformly all t,he way around to t h e plane-ground top edge of the test gas chamber, where it serves t o ensure sharp definit,ion of the test area, and the cover plate, with test specimen and tissue paper attached, is lowered carefully into place, well centered so as not to smear t,he petrolat,um over the test area. Held firmly together with the thumb and fingers to avoid slippage, the apparatus is now inverted, and t,he molten sealing composition applied all the way around to seal the test gas chamber to the t,est specimen. Then, with a knife or a pair of shears, the t,est specimen is trimmed, all the way around, flush with the solidified wax seal, and a third application of the molten sealing composition is made directly around the outer edge of the test specimen, flowing over onto the upper and lower sealing composition surfaces, and effectively complet,ing a vacuum-tight seal. ;is an added precaution, a heated glass rod or a micro flame may be applied all the way around, at the line There the top of t h e sealing composition meets the cover plate, to ensure perfect cont.act of the seal with the plate. The apparatus is now placed in an upright, posit,ion and the capillary system is replaced, being seated carefully with a suitable stopcock grease to ensure against leaks. The side arm of t h e capillary system is connected to a vacuum pump and the stopcock is opened briefly to remove the air from the low-pressure chamber, then closed again. Under test conditions other than a t zero relative humidity, excessive pumping out of the low-pressure chamber is avoided in order not to decrease the moisture content of the tissue paper appreciably. Actually, a little moisture is removed from the tissue paper each time the low-pressure chamber is pumped out,
1 mm. I.D
n
u f
-
ro F / r Fi USH
in. M/N.
WITH BOTTOM SURFACE O F COV€R Jo/Nr
/
PLANE GROUND TOP €DG€
Figure 1. Diagram of Apparatus
J U N E 1947 but the amount removed in the few seconds required to remove most of the air or other gas from this chamber is an insignificantly small fraction of the equilibrium moisture content of the paper. Most plastic sheet materials have sufficient water vapor permeability to permit complete restoration of this small moisture loss in a very short time by permeation through the test specimen from the conditioned gas in the test gas chamber. When the test gas is air and the work is done in a room main-tained a t the test conditions, the test gas chamber stopcocks may be left open. After the low-pressure chamber is pumped down to near or slightly below 11 mm., the equilibrium water vapor pressure of the tissue paper a t the stated conditions, and the side.arm stopcocks are closed, manometer readings are taken a t suitable intervals until a definite and uniform rate of pressure increase with time has been established. The low-pressure chamber may be pumped out again, and t'he determination repeated as many times as appears desirable. To use another test gas, it is passed through a suitable humidity conditioning system, such as bubbling through saturated calcium nitrate solution for conditioning to 75' F., 50% relative humidity, and swept through the test gas chamber until all the air has been ,displaced. A slow stream of the new test gas may be maintained through the test gas chamber during tests wit'h it, or the test gas chamber stopcocks may merely be closed, once that chamber is filled with conditioned gas, and the supply shut off .during the tests, since the ratio of the volume of the test gas ,chamber to that of the low-pressure chamber is so great that a large number of repeat determinations may be made without, significantly reducing the pressure in the test gas chamber. After all the desired tests on one test specimen, have been completed, the apparatus is readily taken apart and cleaned. The most convenient way of removing the sealing composition is to place the assembly, after removing the capillary system, in a refrigerator for some 20 minutes. The chilled sealing composition becomes rather brittle and adheres less firmly to the glass, so that it is readily removed with a knife blade or spatula. Any remaining wax, and the'petrolatum around the top edge of the test gas chamber, may be removed easily with a cloth dipped in benzene o r naphtha, and the apparatus is ready for assembling with a new test specimen. For determinations a t zero relative humidity, the tissue paper and the test specimen are thoroughly dried in a low-temperature oven or a vacuum desiccator before assembling, and a small amount of desiccant, such as silica gel or calcium chloride, is placed in the test gas chamber. Positive maintenance of almost a n y desired higher relative humidity in the test gas chamber may also be ensured by introducing a suitable control solution into the chamber through one of the side arms after assembling. Tests a t temperatures either above or below room temperature are readily made by placing the entire apparatus, xhich is small and compact, in a temperature-controlled cabinet. The smaller the volume of the low-pressure chamber the greater the sensitivity of the instrument. It is for this reason that 1-mm. inside diameter capillary is specified. I n practice, the major portion of the low-pressure volume is due to the tissue paper which is used to ensure substantially unobstructed flow of permeated gas into the capillary system. The volume of the low-pressure chamber, which must be known fairly accurately, must be determined with the tissue paper in place and compressed by substantially 1 atmosphere of pressure. This volume is easily determined as follows: The instrument, is assembled exactly as described for a test 'specimen, but, an impermeable flexible sheet,, such as 0,001-inch aluminum foil free from any pinholes, is used as the test, specimen, with the t'issue paper t'horoughly dried. A small chamber of known volume is connected bct'ween the capillary system side arm and the vacuum pump, with another stopcock to shut it off from t'he pump. S o w the side-arm stopcock is left open and the pump stopcock is opened carefully until the pressure in both chambers falls enough to read it on the capillary system manom-
395 eter. The pump stopcock is closed and the manometer is read carefully. Kow the side-arm stopcock is closed and the known chamber vacuumized completely. Next, the pump stopcock is closed and the side-arm stopcock opened, whereupon the air in the low-pressure chamber of the instrument expands into the vacuumized chamber of known volume and the manometer is read again. Simple application of the gas law gives the volume of the low-pressure chamber under operating conditions. CALCULATIONS AND UNITS
Gas permeability is expressed in various units, generally interconvertible by suitable factors, but for sheet materials used in packaging the units are usually either N.T.P. cc. per sq. meter per 24 hours per atmosphere or S.T.P. cc. per 100 sq. inches per 24 hours per atmosphere, meaning the volume of gas in cubic 760-mm. pressure, permeating through 1 centimeters a t 0" square meter, or 100 square inches, respectively, of the sheet material in 24 hours when the partial pressure of the test gas on opposite sides of the sheet material differs by 1 atmosphere. Rate of permeation of any gas through a sheet material free from holes appears to be substantially directly proportional to the difference between the partial pressures of that particular gas on opposite sides of the sheet and independent of the total pressure of that gas or of the pressure of any other gas on either side. However, there is an important exception to the latter part of this statement, in that the presence of water vapor markedly affects the permeability of many sheet materials, especially hydrophyllic materials such as cellophane, to other gases. Therefore, it is generally necessary in giving gas permeability data t o state not only the temperature a t which they were taken but also the relative humidity. It is possible, also, that gases such as ammonia or carbon dioxide may affect the permeability of certain sheet materials to other gases, especially if the sheet materials absorb, dissolve, or react wit,h the foreign gas. This is a matter that merits investigation. For homogeneous sheet materials the gas permeability is inversely proportional to the thickness of the sheet, so that specific permeability is often given, also in various units which are interconvertible by suitable factors. A logical specific permeability unit might well be P, = X.T.P. cc. per cm. per second per mm., the volume permeating through a centimeter thickness per square centimeter of area per second per millimeter of mercury partial pressure difference, but this unit is far too large for practical use. Davis (1) has used the unit P , = N.T.P. CC. per sq. cm. per minute per cm. per atmosphere, which is 1/(60 X 760) of the above. However, since packaging material thickness is usually given in 0,001-inch units, a very convenient specific permeability unit is P , = S . T . P . cc. per sq. meter per 24 hours per atmosphere per 0.001 inch, which is 1/(10000 X 60 X 24 X 1000/2.54) = 1/5,670,000,000 of Davis' unit.
c.,
For the inst,rument shown in Figure 1, let A = test area in square centimeters, T7 = low-pressure chamber volume in cubic centimeters, P = pressure in test gas chamber in millimeters of mercury, p , = manometer reading at beginning of t'est period in millimet'ers of mercury, p2 = manometer reading a t end of test period, T = test t,eniperature in degrees absolute, and H = length of test period in hours. Then, for a test a t zero relative humidity, the gas permeability in S . T . P . cc. per sq. meter per 24 hours per atmosphere is given by
65,544,000 T'(pz--pi)
TAH (P-
'q)
For tests a t other than zero relative humidity, in which case substantial water vapor pressure equilibrium should be established on both sides of the test specimen before the test period is started, the water vapor pressure in millimeters of mercury should be subtracted from P, p,, and p , in each of the above equations.
V O L U M E 1 9 , NO. 6
396 Actually, because of uncontrollable variables, the probable error in gas permeability determinations is usually at least as large as 1 5 t o *IO%, so that for all determinations a t , say, 25" * 5' C'., 0 to 1007, relative humidity, with P = 760 * 20 mm., and manometer readings up to 50 or 60 mm., the calculation may be simplified t o
ments on hand, it is probably bimpler to increase the length of the test period to several days, or even weeks, if necessary. In this case, even the most minute leak in the system would become very significant, but with all ground-glass joints properly fitted and lubricated, the wax seal around the test specimen carefully made, and the test specimen free from any holes, several tests have been run for periods of 4 to 6 weeks without any evidence of leaks.
sq. meter per 24 hours per atmosphere
For a typical instrument of the type described, A = 70 sq. cm. and V = 0.58 cc.; therefore Po = 2.5 ( p z - p J / H . Thus, the senjitivity, as previously calculated for the other types of permeability testers discussed, is 0.052 N.T.P. cc. per sq. meter per 24 hours per atmosphere. This is about seven times the sensitivity of Shuman's instrument, six times that of Todd's instrument, and one third greater than that of the modified Todd apparatus described.
.
For testing materials of very low permeability it would be possible t o increase the sensitivity of this type of instrument thirteenfold by using dibutyl phthalate in the manometer instead of mercury, but because the simplicity and low cost of the instrument make it feasihle t o have a considerable number of initru-
iCKNOWLEDGMENT
The author wishes to express his appreciation to the Fisher Scientific Company for its cooperation in executing his design into a number of instruments of the type described. LITERATURE CITED
(1) Davis, Donald W.,Paper Trade J . , 123, No. 9, 33-40 (1946). ( 2 ) Doty, P. M., Aiken, W. H., and ,Mark, Hermann, ISD. h t 7 CHEY., ANAL.ED., 16, 686-90 (1944). (3) Elder, L. W., Modern Packaging, 16, No. 11, 69-72 (1943). ANAL,ED., 16, 58-60 (1944). (4) Shuman, A. C., IND.EKG.CHEM., ( 5 ) Smith, F. R., and Kleiber, Max, Ibid., 16, 586-7 (1944). (6) Todd, H. R., P a p e r Trade J . , 118, No. 10, 32-5 (1944).
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Determination of Gas Permeability of Saran Films T. W. SIRGE, Saran Development Laborcrtory, ?'ha Dow Chemical C o m p ~ nMidland, ~, Mich. A modified manometric apparatus for measuring gas pernieabilities of films having extremely low transmission characteristics is described. Experimental results of equilibrium transmission for Saran films measured by a variable pressure technique are reported. Oter-all results for Saran film gas transmissions are lower than those generally encountered in the literature for any organic film material. The self-consistency of results obserbed with the present apparatus, the relationships obsened, and the extended examination of several gases under sarioils pressure differentials appear to justify the present exposition.
T
H E extremely low water vapor transmission characteristic of Saran films was recognized early, as evidenced by widespread application t o packaging of metal parts ( 2 , 6). Detailed properties were given and extended application of the films to gas impervious packaging was suggested, following preliminary data on gas transmission (8). The present research was undertaken to obtain extended information on the permeability of Saran (trade mark, Dow Chemical Company, for polymers and copolymers of vinylidene chloride) films to the gases of the atmosphere, as well as to certain lower aliphatic hydrocarbon gases. A technique based on manometric methods was employed, and transmission rates were obtained for helium, hydrogen, oxygen, air, nitrogen, carbon dioxide, methane, ethane, propane, ethylene, and acetylene at 25 ' C. and several pressure differentials. . A P P ~ R A T UA S N D PROCEDURE
Several methods of measuring gas transmission through thin films are known. These methods involve a t least one of the following measurements: refractive index, thermal conductivity, and pressure or volume. The Sational Burkau of Standards general y employs the measurement of refractive index to obtain transmission, while the Shakespeare fabric permeameter (Cambridge Instrument Company) measures the thermal conductivity of gases. Neither the refractometer nor the permeameter has yet been extensively applied to the measurement of extremely low gas transmission as found among certain plastic films because of the time-consuming calibrations which are required. Techniques involving volume (11 ) and pressure (6, 10) have recently been
described. The two latter methods appear to be the most satisfactory for experimental determinations, in view of the difEculties mentioned previously, and it would seem that any lack of time sensitivity which may be attributed t o the methods is probably compensated by a closer approach t o true equilibrium transmission. The apparatus which was selected for the present work is an adaptation of the manometric instrument described briefly bg Elder (6) and in detail by Shuman (10). Only the essential differences will be pointed out here. 1. I n thc apparatus originally described, a drying agcrit (IlFhydrite with indicating Ilrierite) ability cell on the measuring side of t apparatus omits the dehydrating ag nating a volume correction for the d quant,ityof drying agent outside the whichare attached to t h e two holw provided for the entering :i11t1 emerging gas (Figure 1). 2. The original appitratus a-: described maintains an atmosphere of gas other than air above the sample by passing,@* through a glass tube inserted by means of a rubber st'opper into one of the holes mentioned above and allowing it to leave by thc other. The present apparatus maintains an atmosphere,of tht. test gas (including air) by a "static" method. The entire apparatus is transferred t o a tall bell jar on a polished metal plate, vacuum-sealed, fast,ened, evacuated, and then filled lr-ith the ga.\ t o be measured. The entire evacuated syst,em is enclosed in a wooden box having a safety glass observation window. I n addition, gas cylinders, a sulfuric acid gas drying bottle, a vacuuni pump, and a 1-meter mercury vacuum gage (not shown) complete the equipment necessary for the determinations (Figures 2 and 3). 3. The total volume on the manometer side of the ~1.11W W P reduced approximately fourfold (2 c r . to 0.5 cc.).
