Vacuum Micromanometer W. S. YOUNG AND R. C. TAYLOR, The Atlantic Rejining Company, Philadelphia, Pa.
4 vacuum gage operating on the manometric principle is particularly suited to the pressure range of lo-' to mm. of mercury. Readings are independent of both the physical properties of the gas and the presence of condensables in a gas mixture. At present it is finding application in the field of mass spectrometry and in rapid molecular weight determinations of volatile liquids.
A
VACUUM gage suitable for measuring pressure in the range of 10-1 to 10-3 mm. of mercury with an average accuracy of * l % is described. This pressure region has in the past been troublesome because of the unsuitability of available vacuum gages. Pressure readings with thermal diffusion, ionization, and radioactive gages (9) are dependent upon the physical properties of the gas, and hence separate calibration is necessary for each gas measured. Accurate pressure measurements of unknown gas mixtures, therefore, cannot be made with such gages. Optical lever manometers (Sj, on the other hand, while suitable in most respects, are so sensitive to external vibration that they are difficult to use. Finally, the Mcleod gage, ordinarily thought of as a primary standard in this pressure region, is limited in its application to noncondensable gases; the presence of condensables seriously impairs its accuracy. The present gage, utilizing the manometric principle, is not affected by any of the factors mentioned above and is &ding application in mass spectrometry for measuring gas pressures of the order of 10 to 100 microns and also for rapid molecular weight determination of volatile liquids (6). PRINCIPLE OF THE MANOMETER
The operation of the manometer is based upon the movement of a bubble of gas trapped in a capillary tube connecting two large reservoirs of liquid. Movement is caused by pressure acting upon the liquid in one reservoir while the other reservoir is maintained a t a constant reference vacuum. From the linear displacement of the gas bubble, the known dimensions of the reservoirs and capillary tube, and the density of the fluid, the actuating pressure may be calculated. The principle has previously ( 1 , 4 ) been suggested for measuring small pressure differences a t or near atmospheric pressure, using various liquids as the manometric fluid with air producing the bubble. So far as is known, however, this principle has not been extended to high-vacuum measurements. For such use a relatively nonvolatile fluid is required which will not absorb the gas whose pressure is to be measured. A t the same time the fluid must possess a sufficiently low viscosity and surface tension to permit it to flox rapidly and smoothly through a capillary tube. Inasmuch as mercury is unsatisfactory in this latter capacity, it is necessary to employ a second liquid such as n-pentane in the capillary, sealing it from the vacuum system by means of two barometric legs of mercury. Figure 1 shows the manometer with mercury filling part of the upper and lower reservoirs, and n-pentane filling the capillary tube and the upper portions of the lower reservoirs.
being denoted by subscripts 1 and the right half by subscripts 2 , the manometer a t equilibrium after evacuation satisfies the relation
where P o
residual pressure acting on the upper reservoirs after .. evacuation H = head of mercury above the datum plane h = head of pentane above the datum-plane p m = density of mercury and p p = density of n-pentane (all in consistent units) =
Let an unknown pressure, P,be applied to the left-hand reservoir; then
where the change in mercury and entane heads in each reservoir is identical and equal to M , a n a t h e change in pressure in the right-hand reference reservoir, due to compression caused by the head change, is equal to Ap. Subtracting Equation 1 from 2 and solving for the applied pressure,
Assuming incompressible fluids, the volume transferred from the reservoirs due to the change in head must equal the volume transferred through the capillary tube:
AHA = la where A = area of the large reservoirs a = area of the capillary tube 2nd 2 = linear movement of the bubhle also where D and
=
diameter of the large reservoirs
d = diameter of the capillary tube
Rearranging and substituting Equation 4 in 3 ld2
(
P = 2 -D 2 2 - -
z:)
+ A p
Solving for the sensitivity
DERIVATION OF MANOMETER CONSTANT AND SENSITIVITY
Defining the manometer constant, C, in terms of dimensions and physical properties
The sensitivity of the manometer as used here denotes the ratio of the linear displacement of the air bubble to the applied pressure: 1 Sensitivity, S, =
1
C = 2$(2
F
-
z)
Substituting in Equation 6 the values, d = 0.126 cm. D = 8.10 cni.
where 2 = bubble displacement in mm. and P = applied pressure in mm. of mercury. Setting up a datum plane a t A-A,Figure 1, and dividing the manometer into two halves by B-B, the left half 133
ANALYTICAL CHEMISTRY
134 13.534 grams per cc. a t 25" C. 0.6213 grams per cc. a t 25" C. C = 1056 pm = pp =
Substituting this constant in Equation 5
S = 1056 -
~
LENOIO
1056 A p P
ON UNGER
The negligible effect of the A p term on sensitivity can be shown by the following examples: REFERENCE VACUUM RESERVOIR
Assume pressure P to be measured is 50 microns, and that the residual reference reservoir pressure, Pp, amounts to 10 microns. Pg will change according to the relation
__
where V = original reference reservoir volume and
A V = change in the reference reservoir
volume caused by the applied pressure, P
MM.
rd2
A V = AHA = la = 1 -
But
4
and from Equations 5 and 6,
S = p1
AP = 1056 - 1056 -
P
1 = 1056 ( P - A p )
or, Therefore,
A V = 1056
nd2 4 (P -
Ap)
Substituting in Equation 7 and rearranging, Apt 1056
e + A p v + 1056 4
?rd2
(Pi - P ) ] -
Figure 1. Manometer
?rd2
1056 4P,"P = 0 Assuming a value for V of 100 cc. and inserting the numerical values in cm. of mercury for PX and P , Table I. Comparison of McLeod Gage and Micromanometer Pressure MoLeod" Microns
Pressure Manometer Microns
Difference
Microns +0.1 +0.6 +1.2 -0.6 +0.4
10.6 1-0.2 +0.4
-0.2 +0.1 $0.1 -0.5 +0.2 +0.8 0.0 -0.1 -0.2 +0.4
-0.6 -0.2 -2.1 0.0 +1.2 +0.2 1-0.2 +0.9 +0.6
+3.8 +0.1 0.0 -1.3 0.0 +0.1 -0.2 -0.4 -0.1 +1.5
Micromanometer sensitivity a
McLeod sensitivity, P t - reading in mm.
=
-
-0.6 f0.8
% 1.8 6.0 10.0 3.4 2.2 3.2 0.9 1.8 0.7 0.3 0.3 1.7 0.6 2.3 0.0 0.3 0.6 1.0 1.3 0.6 4.6 0.0 2.6 0.4 0.4 1.6 0.8 6.0 0.2 0.0 2.0 0.0 0.2 0.3 0.6 0.1 2.0 0.6 1.0 Av. 0.9
1015.
0.0063Lz, where P = pressure in microns and
A p is found to be 6.6 X lo-' cm.
and
S = 1056 - 1056 X 1.3 X 10-4
=
1056 - 0.13
Thus, less than 0.013% change in sensitivity would result from 10 microns' residual pressure in the reference reservoir. Similarly it can be shown that a reference reservoir pressure of 780 microns would be required to change the sensitivity by 1%. Hence, this factor can be neglected for practical purposes and the sensitivity regarded LS equal to the manometer constant:
S = 1056 and
p = - 1 1056 CONSTRUCTION
The essential construction of the manometer is shown in Figure 1. For compactness the upper reservoirs are actually located directly above the lower ones. The diameters of the reservoirs and capillary tube may be chosen to bring the sensitivity of the gage close t o 1O00, so that a millimeter scale will read directly in microns. Changing the capillary tube diameter from 1.26 to 0.92 mm. increased the time necessary to attain equilibrium from 0.5 to 2 minutes. Changing from n-pentane to n-heptane also increased the equilibrium time to several minutes. The length of the mercury legs is chosen so that a head of approximately 730 mm. is maintained on the pentane in the capillary tube when the upper reservoirs are evacuated. The assembly is mounted on a rigid angle-iron frame with the reservoirs held in place with plaster of Paris. A movable millimeter scale is attached to the capillary to measure the bubble travel and the reservoirs and mercury legs are enclosed in a shell of asbestos paper to minimize the effect of temperature fluctuations caused by drafts. Before being filled with fluid, the manometer is evacuated and
V O L U M E 19, NO. 2, F E B R U A R Y 1 9 4 7 degassed by thoroughly flaming the glass. Mercury is then distilled into the apparatus through tube a until the liquid just enters the upper reservoirs. Tube a is then sealed off and partially der d n-pentane is admitted to the lower reservoirs through .C. 1 (Figure 1) until the interface between the mercury and pentane stands halfway up the vertical sides of the reservoir. At this point the mercury half fills the upper reservoirs with the meniscus on the vertical sides. A bubble of air is next introduced into the capillary tube by opening S.C. 2, and applying gentle suction to the pentane reservoir with S.C. 1 turned in such a position that air is drawn into and partially fills the bore of S.C. 1. S.C. 1 is then turned to connect the pentane reservoir with the capillary, thus forcing the air bubble into the capillary tube by the flow of pentane. The bubble position is adjusted by either adding or withdrawing a small amount of pentane from the manometer reservoirs through S.C. l. The pressure on the pentane is slightly less than atmospheric, so that flow will normally take place into the manometer when S.C. 1 is opened. Gentle suction on the pentane reservoir is then sufficient to remove pentane from the system when necessary. Some degassing of the pentane usually occurs after the manometer is first filled. This ceases, however, after standing under vacuum for several hours, and the air bubbles resulting from this degassing must be removed through S.C. 1. Both S.C. 1 and S.C. 2 in contact with pentane are lubricated with hydrocarbon-insoluble starch-glycerol grease. The mercury cutoff between the upper reservoirs serves two purposes: i t acts as a safety valve t o prevent fluid from being blown into the reference reservoir should high pressure accidentally be admitted to the manometer, and it eliminates the need for a stopcock a t this point with the attendant difficulties of leakage and absorption-desorption of gas. CALIBRATION CHECK AND OPERATION
Because of the uncertainty involved in accurately determining the effective diameters of the reservoirs and capillary tube, it was considered desirable to check the calculated sensitivity against a McLeod gage. The manometer and McLeod gage were attached to a vacuum system and evacuated to 0.01 micron. The reference reservoir was shut off and the scale zero set to coincide with one end of the bubble. A controlled amount of air was then let into the system,
135
so that the resulting pressure came between 10 and 80 microns. The bubble travel was read from the scale after an equilibrium period of approximately 30 seconds had elapsed. The gas was then trapped in the compression bulb of the McLeod gage and the pressure read several times until checks were obtained within 0.1 micron, The average of 40 pressure readings made in this manner indicated a sensitivity of 1015. Compared to the calculated sensitivity of 1056, it seems that this represents satisfactory agrecment, in view of the uncertainties involved in measuring the capillary and reservoir diameters and in determining the constant of the McLeod gage. Using the measured average sensitivity of 1015, the manometer pressure was found to agree with the McLeod gage pressure to better than 1 micron in approximately 85% of the measurements. Table I shows these data and the agreement obtained. The differences found seem to be independent of pressure, and in the 20- to 50-micron range amount to an average error of 1%. I n most cases a slight zero shift occurs during a pressure reading. Normally this shift will amount to only a few tenths of a micron and may be neglected, but where rapid temperature fluctuations are occurring larger shifts have been found. I n these cases an arithmetic average of two zeros, one taken just before and another taken immediately following a reading, has been found to result in satisfactory accuracy. Where the manometer is to be used as a continuous indicating instrument, it is believed that proper thennostating will eliminate this zero shift. LITERATURE CITED
(1) Henry, A , , Compt. rend., 15, 1078-88 (1912). (2) Mellen, G.S., Electronics, 19,142(1946). (3) Reilly and Rae, “Physico-ChemicalMethods”,Vol. 1, New York, D. Van Nostrand Co.,1939. (4) Roberts, B. J. P., PTOC. Roy. Soc., A78,410(1906). (6) Young, W. S., and Taylor, R. C., ANAL.CHEY.19, 136 (1947).
Molecular Weight Determination with a Vacuum Micromanometer W. S . YOUNG
AND
R. C. TAYLOR, The Atlantic Rejining Company, Philadelphia, Pa.
A method for determining molecular weights of volatile liquids has been developed which is considerably more rapid than the conventional cryoscopic method. Results on a number of organic compounds in the vapor pressure range from 730 to 0.3 mm. of mercury at room temperature indicate that an average accuracy of approximately *2% may be realized in an elapsed time of 3 to 4 minutes per determination. Although the method was developed primarily for molecular weight determinations of hydrocarbon mixtures occurring in the gasoline boiling range, it is applicable to a variety of liquid substances. Liquids whose molecular weights cannot be determined by this method are those with vapor pressures below 0.1 mm. of mercury, which react with mercury, or which show association or dissociation in the vapor state. Acetic acid gave results which indicated considerable vapor phase association, as was expected (2). No other compounds tested showed such a phenomenon.
T
H E method is essentially a modification of the Gay-Lussac or Hoffman vapor density method (S),consisting of means for vaporizing a small accurately measured quantity of liquid into an evacuated vessel and measuring the resultant pressure. I n contrast to (S), however, operations are carried out a t room temperature and pressures are measured a t less than I mm. of mercury absolute. Results are calculated by means of the gas law rearranged to
M
= gRl’/PV. In practice the weight of liquid vaporized is calculated from the density and a measured liquid volume. Pressure is measured by means of a vacuum micromanometer reading pressures of 0.1 mm. with an accuracy of =t1%. APPARATUS
Figure 1 shows the general arrangement of apparatus.
