Microeffusiometry of Gaseous Mixtures FRANK E. HARRIS
LEONARD K. NASH
AND
Harvard University, Cambridge, Mass. 'I'he true molecular etfusioll of pure gases is very accurately described hy Graham's law, However, the analjsis of gaseous mixtures in terms of their relative rates of molecular effusion is seriouslj hindered by the partial separation of components that characterizes such effusion. The progressive alterations in composition that are so produced vitiate the direct application of Graham's law to the bulk of the mixture. This difficulty can be overcome by the separate application of Graham's law to each of the com-
T
H E most refined forms of the conventional (Bunsen-Schilling) effusiometer yield values of gas density that are uncertain Iiy at least 2% (3, 4). If an effusiometric density determination is used as the basis for a calculation of the percentage composition of a binary mixture of gases, it is plain that there will be gross uncertainties in the results-the errors in the primary density datum are greatly magnified in the course of the indirect calculation. t,hat -must be emn ployed. The uncertainties in the effusiometric determination of density arise from t.he fact t h a t t h e measured tdlusion rate depends not only on the gas density but also on secondary factors, such as the viscosit'y (2). A recent atB tempt ( 1 ) to diminish the secondary effects, by conducting the effusion at critical velocities, has been so little successful t.hat in favorable cases the density dat'a could not be depended on to better than 4%. The fact t>hat in these nieasurements rather elaborate equipment was used, to est,ablish the effusion times with an accuracy of O.lY0, serves to emphasize the essential futility of at,tempting to improve effusiometric determinations by merely increasFigure 1. 1Microeffiisiometer ing the accuracy with which t h e p r i m a r y measurements ran be made. The real need is for M I unambiguous method of 111terpreting the results of such measurements. Such an unequivocal method is potmtially available in Gritham's law. Although this law does n o t provide a satisfactorily precise correlation of the rates of hydrodynamic efflux measured by conventional effusiometers, it does applv rigorously to true molecular effusion ( 5 ) . The effusion ot pure gases undei such conditions that the mean free path M t i s grwter than 10 times the orifice diameter yielded data that were satisfactorily construed in terms of Graham's law ( 6 ) . In ptinciple, then, Graham's law can be used to determine the average molecular weight of a gaseous mixture undergoing molecular effusion; but its practical application is hampered by the unavoidable separation of the components of the mixture. The observed rates of effusion are then no longer a simple function of the nipan density of the original sample; and the direct application of Graham's law does not yield satisfactory results ( 6 ) . If, on the other hand, t h e convrn-
ponents of the effusing mixture. In effect, such a course makes a virtue of necessity, and creates the new p o s d d i t y of securing from effusiometric work the complete quantitative analysis of mixtures contiliuing more than two constituents. Some qualitatibe data can also be obtained. i Fery simple apparatus and technique for the microeffusiometric exaniination of mixtures of gases are described, and the hroad capabilities of this method are illustrated h j a number of experimental results.
tional h j drodynamic flow effusiometer is used, no separation ( 1 1 the componmts takes place; but Graham's law does not providr a sufficiently accurate interpretation of the observed flow rates. To date this double difficulty in the practical application ot thib law has severely restricted the use of the effusiometer in the iinaI\ sis of gaseous mixtures. Although the substantial corrections required when Grahani'h law is applied to nonseparative hydrodynamic efflux are extreme]) difficult to evaluate in practice, an explicit form of the Ian can b(s rigorously applied to the individual components of a gaseous mixture undergoing molecular effusion. The uncomplicated state of true molecular effusion can then be maintained, and the separation of the components that is characteristic of such effusion is qerifically accommodated by the modv of calculation. GENERAL TREATMENT OF MOLECULAR EFFUSION OF 4 GASEOUS MIXTURE
It hits been shown (6) that the molecular effusion of a pure K:L\ expressed in terms of the following formula:
r:w be
hric I T 15 the volume of the rh:tmhc~rin nhich SOmolecules ( J f the gas are confined a t zero tiinc, :inti in which A'l molecules will remain a t time tl. It i.; a s s u m d , in the derivation of this iormula, that V is invariant throughout the cs\periment. The molecules, moving with averagr velocity ?, ew:tpc from the ch:imtwi through an orifice of area , I , into a zone that is maintained : I [ negligibly low pressure. A% factor, K , which is indqwnitviit 01 the nature ot the g ~ < , tlefincd as: M
Substituting K and recalling that, because the effusion is con= Po/PI, Equation 1 can be ducted at constant volume, trritten in the form:
where -11 is the molecular weight of the gas concerned. Using Kquation 2, K can be determined empirically from the rate oi pressure decay observed during the effusion of a pure gas of known molecular weight. Turning now to gaseous mixtures, it is plain that Equation 2 van be separately applied to the individual components, if it can be assumed that each gas effuses independently. The substitution of the appropriate partial pressures in Equation 2 then gives for each component an equation similar to
1552
V O L U M E 2 2 , NO. 1 2 , D E C E M B E R 1 9 5 0 where ~ p represents = the partial pressure of component A (molecular weight M A ) at time t,. SOKfor the total pressure, P,, a t time L,, we may write:
P” =
.4pn
+
Bpn
+ . .. . ..
and on substituting the rspwssioris typified by Equation 3 we find :
PO
= APO f BPO
+
If we are dealing with a mixture of n + l components, measurement of the extent of the effusion a t n different times will yield n + l equations, from which the original partial pressure of each component can be solved by means of determinants. We then find that AX^, the mole fraction of component A in the original mixture, is given by:
1553 The proposed method of analysis is, perforce, an indirert one, so that any errors in the primary measurements are considerably multiplied in the calculation of the results. The method should not be applied to mixtures of components whose molecular weights are too nearly alike. The assumptions involved in the proposed determination, and the deductions drawn from them, now provide a fairly clear characterization of the apparatus to be employed: 1. The working gas pressure must be so low that the mean free path of the specimen is a t least 10 times the orifice diameter. If a pinhole orifice in glass is used, a gas pressure of the order of 1 mm. of mercury will genera!ly be suitable. The ratio of the initial and final pressures of the effusing specimen should be determinable with an accuracy of ca. 0.2%. 2. There must be no back-diffusion through the orifice, so that the back-pressure must be maintained at a negligibly low level. 3. The volume of the chamber from which the gas effuses must remain constant throughout the determination. This volume should be about 25 cc. if an average effusion time of 5 minutes is to be employed. 4. The effusion must be timed from its very beginning if the formulas given above are to be employed. One cannot, as with most existing effusiometers, start with a slight ewess of the gas sample, and begin the clocking only when the residual sample corresponds t o some fiducial value of the pressure and/or volume. 5 . I t must be assumed that the relation between the diameter of the effusion chamber and the mean free path of the specimen is such that the noneffused portion of the gtm is maintained in a substantially homogeneous condition. A s in point 1, work at low pressures is indicated. Furthermore, the design of the effusion chamber must not imply the presence of any long narrow sections of substantial volume, in which case significant concentration gradients would almost certainly exist.
An apparatus designed to meet these specifications is shown in Figure 1. APPARATUS AND PROCEDURE
:tnd similar expressions will be found for the mole fractions of the other components. The right side of this equation contains only known or measurable quantities. K is evaluated by standardization with a pure gas of known molecular weight, and the values of \I are known if the qualitative composition of the analytical sample is given. I t is only necessary, then, to measure the time inttlrvals at which the various fractional diminutions of the total ~ i r t w u r care ~ observed. I I I priuviple, multicoiiipoiient iiiistures can he treated by this nic:thotl: liut in practice sufficiently accurate analysis of more than tww- or three-component, mixtures is not generally feasible. 111 the case of a two-component mixture the ratio of the initial and final pressures need he measured at only one time interval, :tnd Equation 4 r d u w s to the following simple form:
P
The glass pinhole orifice, 0 (67projects , into s chamber, C, to which it is attached through a ground joint. C and the orifice may be separately connected, through stopcock 11, with a sampling and pumping line, SP. C, whose effective volume approuimates 25 cc., also communicates, through stopcock I, with the bZcLeod gage chamber, M , which has a capacity of ca. 250 cc. The short length of 1.5-mm. capillary tubing a t the head of .Wis ground internally to minimize “sticking” of the mercury ( 7 ) . This capillary bears a fiducial mark, a,and the volume between this mark and the bottom of stopcock I is ca. 0.25 cc. ill is connected with mercury reservoir R, and the rise and fall of the mercury in M is controlled by adjustment of the air pressure in Ii. Into R there also dips the mercury barometer, B, the upper portion of which consists of another section of internally ground 1.5mm. capillary tubing. A millimeter scale is placed behind B, and the position of the scale is adjusted until the mercury meniscus in B stands a t zero when the meniscus in M stands a t a and the whole system is evacuated. In making a determination the system is first evacuated, and the mercury in M is brought somewhat below a, t o a position which is varied in accordance with the espected pressure of the prospective sample. Tap I is opened, and tap I1 is turned to connrct C with SP. The sample is admitted through SP and, by closing t’apI, a specimen is a t once shut off in M . Chamber C and the line to the orifice are then evacuated through SP, the mercury in -11 is lowered to level b, tap I1 is turned to connect 0 with c‘, and tap I is opened momentarily. As long as C and 0 are connected through stopcock 11, the same gas exerts the same pressure on both sides of the orifice, so that no effusive processes can occur. When tap I is opened, pressure equilibrium is rapidly estahlished between chambers C and M , after which the tap may be closed. The mercury level is then raised to mark a,the pressure in the gage is read from the scale behind B , and the value is recorded. The mercury is then lowered slightly until its level in R is just below the base of tap I. Then, in rapid succession, t,ap I1 is turned to connect orifice 0 with the pumps, through line S P , and tap I is opened. A stop watch is started a t the moment that the mercury in X “jumps” upward, as the gas passes from M into C. LIinor adjustments are made until the mercury in M is just even with the bot,tom of tap I, and the effusion is allowed to proceed.
ANALYTICAL CHEMISTRY
1554
Some seconds before the close of the allotted period for the effusion, tap I is closed, and the mercury is rapidly drained from M until the meniscus stands a t mark b. At the moment corresponding to the termination of the experiment tap I is opened wide. Thereby the pressure in C is cut by a factor of ca. 1/11 and, because the rate of effusion is diminished by the same factor, a few seconds may be allowed for the establishment of pressure equilibrium between C and M . Tap I is then closed, the gas in M is compressed into the volume above mark a, and the pressure is read from the scale behind B , and recorded. This completes the determination. Both before and after the effusion, pressure equilibrium is established between C and M while the mercury level in the latter stands a t b. Consequently, when the gas in M is compressed into the volume above a, the ratio of the initial and find pressures read from B may be taken to indicate the ratio of the corresponding pressures in C. Inasmuch as the equilibrium distribution of gas between C and M finds 10/11 of the sample in M , and the volume of C stands to the volume between mark a and stopcock I in the ratio of ca. 100 to 1, a gas sample filling C to a pressure of 1.1 mm. of mercury will correspond to a scale reading of ca. 100 mm. Pressures of this order of magnitude are easily read with adequate accuracy.
Table I. Ga8
01 C Hd
Ht OY
COY
Nt
Pure Gases
(Effusion time, 300 seconds in all cases) P Q ,Mm. H g (Approx.) K x 10' 1.8 9.27 0.9 9.27 1.5 9.27 1.9 9.24 1.3 9.25 1.6 1.6
0.5 1.5
9.78 9.96 9.84 9.79
Any systematic errors or lags in the crude timing technique employed will tend to cancel out between standardization and use, because the procedures involved are identical. The apparatus was operated in a room whose temperature did not vary by more than 0.5"C. Close temperature control is unnecessary; the rate of effusion varies by less than 0.1% for a temperature change of 0.5"C. and the pressure readings are taken within a few minutes of each other and enter the final calculation only as a ratio. C.P. tanked gases were used throughout this work. Gaseous mixtures were prepared by successively introducing the components into a constant-volume buret, measuring the increase of pressure after each addition. If repeated measurements, a t different stages of the effusion, are required, as in the analysis of complex mixtures, a fresh portion of the sample may be taken for each trial. No attempt has been made to secure maximum sample economy in the present work, but 0.1 cc. (N.T.P.) of the specimen is ample for a single trial. DISCUSSION OF RESULTS
The results secured in a number of experiments are shown in Tables I, 11, and 111. Each experimental value cited represents the average of two (or more) duplicate trials. Standardization and Behavior of Pure Gases. Oxygen was used for the primary standardization, and the instrumental constant, K , was calculated by substituting the empirical data for oxygen in Equation 2. A representative series of six standardizations, with initial pressures of oxygen varying from 0.9 to 1.8 mm. of mercury, yielded values of K varying from 9.22 to 9.31 X with an average of 9.27 X and a mean deviation of 0.30/,. The uncertainty of K thus amounted to no more than a few parts per thousand. The corresponding uncertainty in the determination of the molecular weight of an unknown gas does not exceed 0.5%. From the examination of a few other pure gases, several independent evaluations of K were secured. These results, shown in
Table I, were collected over a period of 3 months, using one orifice throughout. The day-to-day constancy of the standardization was excellent ( ~ 0 . 2 %and ) thcre was no perceptible "drifting" of the instrumental constant. The value of K did undergo one abrupt alteration of close to 5%, indicated by the horizontal line in Table I. This change may signify the disappearance of some minute obstruction in the orifice. It appears that only relatively infrequent checks of the standardization are required and that, should there be any change in the standardization, it will probably be sudden and unmistakably large. If, for the moment, we leave aside the carbon dioxide results, the experimentally determined values of K are seen to be free of any significant dependence on the nature-i.e., viscosity, etc.and pressure of the test gas. An exception is carbon dioxide which, when studied a t normal operating pressures, yielded a conspicuously divergent value of K. However, when the working pressure of this gas was diminished the divergence wm sharply reduced; and the residual deviation from the norm can probablv be attributed to the inadequacy of the present equipment as a p plied to the measurement of very low working pressures. The anomalous behavior of carbon dioxide is easily understood when it is recalled that, of all the materials studied, this gas has by far the largest molecular diameter. At a given pressure, the larger the diameter of the molecules involved the shorter will be the mean free path; but, if ideal molecular effusion is to occur, the mean free path must substantially exceed the orifice diameter. Consequently, the larger the molecular diameter of a gas, the smaller must be its working pressure if ideal molecular effusion is to be obtained through an orifice of given diameter; and, indeed, reduction of the working pressure goes far toward bringing the carbon dioxide results into line. It appears that, in general, the gases used in these experiments underwent ideal molecular effusion. If gases of larger niolecular diameter were to be handled it would only be necessary to employ lower operating pressures. This could be done without significant loss of accuracy-e.g., simply by reducing the volume between mark a and stopcock I, to provide for a higher multiplication of the pressure readings.
Table 11.
Binary Mixtures
t,
7 of % Li hter component Deviation talculated from of Results Equation Equation Based on 2 5 Equation 5 (76.3) 67.8 +0.2 (78.2) 67.1 -0.5 (75.4) 67.8 +0.2 (74.7) 67.9 f0.3 -0.8 (73.4) 66.8
Mixture
Log P Q / P
CHd 67.6Y0 0% 3 2 . 4 %
0.2711 0.3241 0.3782 0.4851 0.5361
Sec. 300 360 420 540 600
CHI 38.170 02 6 1 . 9 %
0.2444
300
CHI 18.7Y0 81.3%
0.2283
300
Hz 8 2 . 7 % COP 1 7 . 3 %
0.6379 0.7397 0.8218 0.9076 0.9787 1.0386
300 360 420 480 540 600
Hz 5 7 . 3 7 COS 4 2 . 7 %
0.4427 0.7117
300 600
57.4 57.6
+0.1
Hz
18,170 COz 8 1 . 9 %
0.2578
300
20.3
+2.3
S n 35.7% COz 6 4 . 3 %
0.2087
300
36.1
+0.4
..
Oz
(97.2) (95.7) (94.8) (94.1) (93.1) (91.9)
37.8
-0.3
18.4
-0.3
82.7 82.9 82.4 82.9 82.9 82.6
0.0 +0.2 -0.3
f0.2 f0.2 -0.1
+0.3
Binary Mixtures of Known Qualitative Composition. The results obtained in the examination of several binary mixtures are shown in Table 11. The proportion of efflux need be determined a t only one time interval, but some of these samples have been run a t srvwal intervals.
1SS5
V O L U M E 2 2 , NO. 12, D E C E M B E R 1950
,
The bracketed results entered in the fourth column of Table I1 were calculated on the very dubious assumption that the effusive separation of the components might be ignored. The use of Equation 2 then yields a value for the apparent mean molecular weight of the original sample, from which the composition of a binary mixture is calculable. The results so obtained are as grossly inexact as might have been expected. A previous attempt (6) to ignore the effusive separation was not so unsuccessful because, in that work, a first fraction (enriched in the light component) and a last fraction (enriched in the heavy component) were both discarded. In the present investigation only the final fraction wm discarded, so that there was not even approximate compensation for the effects of the effusive separation. It is plain, however, that the application of Graham’s law to the bulk of a gaseous mixture undergoing molecular effusion is apt to be productive of highly erroneous results. The fifth column of Table I1 contains the results secured by the use of Equation 5, which realistically allows for the effusive separation of the gaseous components. The differences between the known percentages of the lighter components and the percentages cdculated from Equation 5 are entered in the sixth column. The errors are no greater than those to be anticipated from the experimental inaccuracies in these relatively crude measurements ; and, as is to be expected, this indirect analysis is a t its best when the ratio of the molecular weights of the gases involved is largest. There is one conspicuously poor value, obtained in the analysis of a hydrogen-carbon dioxide mixture rich in the latter component. The deviation is in the right direction, to be explained in terms of a failure to use a working pressure sufficiently low to permit molecular effusion of a mixture rich in carbon dioxide. Polycomponent Mixtures of Known Qualitative Composition. Table 111 contains the results of the analyses made on a few polycomponent mixtures, the calculations for which were carried out with expanded forms of Equations 4. As is to be expected from the character of this n-ork, the proportion of the heaviest component of the mixture is the most poorly defined. The errors in the results are no greater than those that would result from the inevitable multiplication of the experimental inaccuracies in the cdculations of this highly indirect analysis. In the common case o f mixtures of hydrogen and methane that may also contain some ethane, the effwiometric method should provide much more reliable analyses than could normally be obtained from simple volumetric combustion techniques. The significance of the Iirwketed figures in the fourth column of Table I11 is discussed I )f, low . Binary Mixtures in Which Qualitative Identity of Only One Component Is Known. With measurements of the proportion of effusion a t two time intervals, an indication of the identity (molecular weight) of the second component and a quantitative analysis of the mixture can be secured. The calculations are greatly simplified if the two periods of effusion are such that h = 2tl. Equation 5 can then be written in the form:
whence:
L is defined in terms of, and can be evaluated from, the left side of the equation, which involves only the measured pressure ratios
and times, the instrumental constant, K , and the known molecular weight of the first component. The molecular weight of the
second component can thcn be calculated from the following expression:
Table 111. Polycomponent Mixtures
Mixture
t,
% of Hydrogen Calculated as Binary .Mixture
So.
Log Pn/P
1
0.4716 0 7970
Sec. 300 600
2
0.533’7 0.7214 0.9139
300 420 600
(57.i)
3
0.4746 0.8127 1.0370
300 600 900
...
(45 2 ) (39.2)
161.9) (55 6)
.. ..
% Composition of
Sample Known Found 53.2 HI 6 2 . 1 2 0 . 2 20 7 CHI 26.1 On 27.4
c.
Er&r
+O S +O 3 -1
3
Hn 60.1 CH4 2 7 . 0 Nt 12.9
60.6 27.5 12.0
+0.5
FIn 3 4 . 1 CHI 2 2 . 0 COz 6 . 9 SFs 3 7 . 0
32.9 22.4
-1.2
5.9
38.8
f0.4 --O
!I
+O 4 -1.0
fl.8
Among the data collected with binary mixtures there are both 5- and 10-minute runs for the first methane-oxygen and for first and second hydrogen-carbon dioxide mixtures. If in each case only the identity of the major (lighter) component had been known, the use of Equation 6 would have provided values of 32.9 (instead of 32) for the molecular weight of oxygen, and 43.6 and 44.5 (instead of 44) for the molecular weight of carbon dioxide. Such indications will usually constitute a sufficient clue to the identity of the second component. Then, using the accurate molecular weight of that component, the quantitative composition of the mixture can be derived from either one of the measurements of effusion rate, as interpreted by Equation 5. Detection of Third Component in Supposedly Binary Mixture. If, in working with a supposedly binary mixture, the proportion of effusion is determined a t several time intervals, sufficient data are available for several independent calculations of the composition of the mixture. The results of these calculations should all agree within the experimental error, and the percentages secured from extensive measurements on two binary mixtures (see Table 11) bear out this prediction. However, if we attempt to treat as a binary mixture a sample that actually contains an unsuspected third component, the percentage compositions calculated from the effusion proportions a t different time intervals will not be concordant. Such a lack of agreement provides an unmistakable indication of the presence of an appreciable amount of a third component. This method of detection is obviously limited to cases in which the third component has a molecular weight significantly different from those of the two major components. The smaller this difference the less sensitive will be the indication of the presence of the third component. Despite this limitation, however, the method presents real possibilities. The bracketed results for hydrogen in the fourth column of Table I11 were calculated from Equation 5 on the assumption that the samples were binary mi\tures of the two major components. The internal variations of these sets considerably exceed the fluctuations produced by cxperimental errors; and it appears that, even with the crude equipment now available, 5% of ethane can be detected in a mixture supposed to contain nothing but hydrogen and methane. The usual combustion procedures provide no indication of the presence of ethane, and yield grossly erroneous findings when that substance is present in substantial proportions. Similarly, a number of fractional distillation and desorption procedures-applied to mixtures of hydrocarbons and to inert gas mixtures-&ult in cuts that are usually assumed to be binary
1556
ANALYTICAL CHEMISTRY
mixtures. The phyaical methods-e.g., thermal conductivit L , refractometry, et?.-ordinarily applied to the analysis of these fractions do not distinguish the possible presence of a third constituent and the analytical values may contain large and completely unsuspected errors when such a contaminant orcurs. Even when it does not allon total analysis of the mixture involved, the effusiometric examination can still shed some light on the degree of complexity of the sample. Other Applications. If a specimen of a completely unknown g x i is a t hand, it is advisable to determine the proportion of effusion a t a minimum of two time intervals. Using Equation 2 iii the interpretation of these data, we secure two or more independent cvsluations of the apparent molecular weight of the original specimen. If the vwlues 10 obtained are all concordant, the molecular weight ot the g:ts, and thence a valuable clue to its identity, is derived. (Thi?, of course, does not exclude the possihility that the sample is a mixture of two gases of nearly identical molecular weight.) On the other hand, a systematic variation in the value9 of the apparent molecular weight of the gas provides a definitive indication of the complexity of the sample. The divergence of the bracketed results in the fourth column of Tiihle I1 suggests the magnitude of the corresponding variation in thc apparent molecular weights calculated by the application of Equation 2 to a mixture containing molecular species of divcme we i ghtm . When incomplete analytical data are available from some other hource(s) there ensues a noteworthy simplification, and siniultaneous increase in power, of the effusiometric methods.
-4s a concrete example, consider the problem of identifying a minor component that is not absorbable in volumetric gas analytical procedures. From such procedures the complete quantitative make-up of the sample, and the qualitative character of all but the unabsorbed component, would be known. The determination of the molecular weight of the unknown constituent can then be based on a single measurement of the effusion rate. The "identification" of the argon in air provides an exemplification of this possibility. Assume that it has been found that air consists of the following components in the indicated proportions: ovygen 21.0; nitrogen 78.0; component X 0.9. A single effusion trial made with air that had been passed over Ascarite gave PI!Pc a q 0.5811 after 5 minutes For a ternary mivture n e may write:
of the molecular weights of the various components is not very large. COlVCLUSION
The method that has been described brings reasonably accurate analysis of binary mixtures within the compass of effusiometric work. Rather more important, it is one of very few purely physical methods (other than those based on spectrometry and spectrophotometry) that permits of even approximate quantitative analysis of polycomponent mixtures and is also capable of furnishing some indication of the qualitative make-up of such mixtures. The proposed method of analysis should be particularly valuable for the examination of any group of gases that are not readily separated from one another and that show suhstantial gradations in their niolecular weights. Two such groups are the paraffin hydrocarbons and the inert gases. This exploratory investigation has been conducted with relatively crude equipment, and the experimental techniques could be cwnsiderably refined. Thus, x n increase in the size of the effusion vessel, the size of the sample, and the duration of the experiment should greatly improve the accuracy of all the measurements, with a corresponding improvement in the quality of the analytical resultq. Furthermore, i t appears possible to replaw the present method of measuring the proportion of effusion, in terms of the residual quantity of gas in the effusion chamber, by an alternative technique that would not require a separate trial for the determination of each individual proportion. Thus, one might use an indirect hut semicontinuous method of assaying the proportion of effusion, measuring the quantities of gas that pass through to the low-prcssure side of the orifice. The authors hope to investigate the effect of these improvements. However, the effusiometer described will do practically everything (except handle condensable vapors) that can he done by any previously described effusiometer, and it is capable of many other determinations that no previous effusiomrter has brought even remotely within the range of possibility ,iCKYOWLEI)C;MIE\IT
The authors are indebted to E. H. deButts and It. E. Lundin for a number of helpful suggestions. LITEK4TURE CITED
ill1 the mole fractions, and two of the three molecular weights, are known. Solution for the third molecular weight then gives
from which the molecular weight of component X is calculated as 39.3. The closeness of this approximation to 40, the molecular weight of argon, is rather striking when it is recalled that less than 1 of the unknown constituent was present, and that the spread
(1)
Benson, S. W., and C'aswell, S.,J . Phys. Colloid.
