ANALYTICAL CHEMISTRY
414 Selson's Arsenoniolybdate Solution. One hundred grams of ammonium molybdate are dissolved with stirring in 1800 ml. of distilled mater. Then 84 ml. of concentrated sulfuric acid are slowly added with continued agitation and finally 12 grams of sodium arsenate heptahydrate are added. When the arsenate is dissolved, the solution is diluted to 2000 ml. with water and stored at 37' C. for 48 hours. At the end of this period, the solution is filtered and stored in a brown bottle. Procedure. A 2-ml. aliquot of the clarified extract (for\r:ducing sugars) or of the inverted extract (for total sugars) is placed in a Folin-\Tu blood sugar tube with an Ostwald pipet. Then, 2 ml. of Somogyi's copper reagent are added from a 26-ml. buret and the tube is placed in boiling water for 20 minutes. (When a number of samples are being analyzed, sufficient space must l i e provided around each tube to permit adequate circulation of the boiling water. \Tire test tube supports serve this purpose very well.) The sugar tubes are then cooled in water at room temperature and 2 ml. of Selson's arsenomolybdat,e soution are added from a 25-ml. buret. Because the copper reagent has a high specific gravity, the solutions are most effectively mixed by moderate vertical agitation with a small knob on the end of a glass rod. This rod is washed and the contents of the 6ugar tube are diluted t o the 26-ml. mark with rTater befort, shaking to ensure thorough mixing. It has been found atlvantageous to allow the tubes to stand for 16 minutes t,o permit, maximum color development before the solutions are read at 600 mu in a photoelectric colorimeter or spectrophotometer which has b t m adjusted to give 100% transmittance with distilled lratei,. With each series of unknown samples, tubrs containing
2 nil. of \$atel for a blank and 2 ml. of standard solutions having 0.10 and 0.20 mg. of glucose are treated in a similar manner to obtain a standard wference graph. The precision ot the analyses was deteimined 131th ten replicate samples of ground frozen lima beans where the reducing sugar content was found to be 0.068% and the standard deviation of a single determination was *0.003 After inversion of aliquots of the same extracts, the total sugar content n a s 2.43nc with i-0 07 its the qtandard deviation of a single determination. LITERATURE CITED
(1)
(2) (3) (4) (5)
Official Agi. Chem., Official and Tentative Method3 of dnalyses, 6th ed., p. 564, 1945. Davis, W. B., Ind. Eng. Chem., .Yc7cs Ed., 17, 752 (1939). F o h n , 0.. J . B i d . Chem., 67, 357 (1926). Lee, F..%., IXD.ENG.CHEM.,.IN.LL. ED.,17, 719 (1945). Leonard, 11. H., Meade, R.C . , and Dustman. R. B., Ihid., 15. 579 .~SZOC.
(1913).
(6) (7) (8) (9)
Telson, N.,J . B i d . Chem., 153, 375 (1944). Polis. B. D., and Sortwell, M., Arch. Biochem., 11, 229 (1946). Somogyi, M., J . B i d . Chem., 160, 6 1 (1945).
Ihid.,160, 69 (1945).
RECEIVED .June 6, 1947. Joiirnal Paper 715, S e w York State Agricdtriral Experiment Station. GrnPva, K.Y.
Simplified Absolute and Differential Manometer ROGER GILMONT T h e Emil Greiner C o m p a n y , \-eielC I b r k , S. 1'. A new manometer for either absolute or differential measurements based upon a combination of new and previously described design elements is presented. The closed end of the manometer is fabricated with a U-type loop and cut-off stopcock. This construction eliminates the difficult process of filling a closed-end manometer and still ensures a perfect seal by virtue of the manometric fluid trapped in the loop. It also permits rapid changeover from absolute to differential measurements. The ratio of the diameter of the manometer tube to the diameter of the reservoir is chosen so that a single reading on the manometer tube gives a direct pressure reading in millimeters of mercuq at 0' C. The theoretical basis of this design is discussed as well as the tolerances premitted in the
T
HE need for an absolute manometer which can be c a d \ -filled and cleaned has presented a constant problem for thts laboratory scientist and technician. Several schemes have been proposed for surmounting this problem, such ab sprcial devices and techniques for filling closed-end manometeis ( 1 , 2 , S, ?, 10, 12). To simplify filling and cleaning, some experimentel5 have used a stopcock to make the closed end (4, 11), but this unfortunately leads to uncertain readings because the stopcock cannot be relied upon to be absolutely leakproof. The use of a loop to cut off the closed end is the basis of the Zimmerli gaq> ( 1 3 , and more recently of a gage proposed by Robertson (9). If thejdea of a loop to cut off the closed end is combined with a stopcock to close off the loop, a simplified type of absolute manometer is possible; the loop forms a mercury seal which prevents any gas from entering the closed end even if the stopcock should fail to be leakproof. Moreover, the presence of the stopcock makes it possible to use the manometer for differential pressure measurements, and also permits any desired height of gage to b(, conveniently constructed. I n Figure 1, a working drawing is
above ratio to maintain a given precision; thus, high precision is obtainable with reasonably large tolerances. A plastic scale having a temperature coefficient of linear expansion of the same order of magnitude as the volumetric coefficient for mercury eliminates errors due to changes in ambient temperature. The permissible tolerances which give a desired precision are theoretically derived for the choice of plastic. Other factors, such as surface tension, are considered in order to establish tolerances in dimensions which preserve high precision. The manometer is easily filled and very convenient to qse, especially since a single reading gives, with high precision, the true corrected pressure, which normallj has to be obtained by suitable correction calculations.
shown for such a gage designed to read a maximum of about 200 mm. In the reading of the ordinary C-type manometer, two columns are observed, necessitating subtraction to obtain the pressure differential. Some investigators have employed a very large reservioii, so that its change in level could be neglected, and thereby have eliminated a double reading and subtraction. For precise work, as in barometers, the scale is adjusted to read from the level in the reservoir, but this again introduces an additional operation, which sometimes leads to more trouble than it is worth. Thus, for precise work, unless an impractically large reservoir is used, the change in level cannot be neglected. Nevertheless, it is still possible t o obtain precise results with a single reading by making us(' of a specially contracted scale which accounts for the change in level of the reservoir. The tolerances required in the bore of the tubing employed are not too critical to obtain precise results, if a reasonably large reservoir is used. In view of the fact that precise pressure readings mith a mercurial manometer must be.corrected to read a height of mercury
V O L U M E 20, NO. 5, M A Y 1 9 4 8
475
a t 0" C., it is possible to design a manometer using a regular scale and a suitably sized reservoir (the dimensions of which are determined below) which by means of a single reading gives the pressure reading in millimeters a t 0" C., directly. Furthermore, if a plastic scale having a coefficient of thermal e x p a n s i o n of the same order of magnitude as mercury is used, the single r e a d i n g c a n be automatically corrected for changes in the ambient temperature. The deFIGURE I sign in Figure l is ABSOLUTE AND for a manometer having these feaDlFFPR€NT/AL tures. The theoM 4NOM€ TCR retical basis for its design is described in the f o l l o w i n g section. THEORk
The basis for choosing the size of the manometer tube and reservoir is the fact that the contraction in the h e i g h t of t h e mercury column due to the change in level of the reserALL DIMENSIONSIN CM voir can be exactly sc4 L E neutralized by the c u * 5 + eypansion of the mcrcurv column due to the increase in temperature from 0' C. to the ambient room temperature. Thus, using the symbols of Figure 1: Equality of volume displacement yields
and
ho = above height reduced to mercury a t 0' C. exerting the same pressure D R = -! = ratio of diameters of manometer tube to reservoir Dz p = coefficient of volumetric thermal expansion of mercury for the interval 0" to t o C. The volumetric expansion coefficient of mercury is used, since this correctly accounts for the change in height of the column due to temperature as shown below. (The thermal expansion of the glass is not involved in so far as the change in length of the mercury column with temperature is concerned, since this is affected by density changes alone. The change in the diameters of the glass tubes with temperature would be proportional and not affect the value of R.)
h = PV where h = height of mercury of specific volume, v , exerting a pressure, P , a t its base For constant P, .
@ = p d v = -h -du dt
Therefore
dv p -1 x -dh= - 1x - = h
dt
v
+ hi
(I
+ pt). = (1 + R 2 )
or
R2 = Pt
The height of the mercury column reduced t o 0" C., which is the true pressure by definition, is expressed by (3) where hi = height of mercury column in manometer tube above zero pressure differential position h~ = depth of mercury column in reservoir below zero pressure differential position h = height of mercury column in manometer tube above level in reservoir a t temperature t o C. (corrected for capillarity)
(5)
Basing the calculations on a room temperature of 25" C. and using an average value of 18.2 x l0-6per C. for the volumetric coefficient of thermal expansion of mercury, taken from the Handbook of Chemistry and Physics (5),one obtains a value of: '
R
=
0.0675
(6)
If a 3-mrri. bore capillary tubing is used for the manometer tube, a reasonably sized reservoir 44.4 mm. in imide diameter is obtained from Equation 6, which corresponds to a standard wal1 Pyrex tubing 48 mm. in outside diameter. The permissible variation in R to obtain a given desired precision may be determined as follows: Since an ordinary scale can be read with the naked eye to no better than about 0.1 mm., a precision of 0.1 mm. in 200 mm. will be assumed-Le., Ah1 = 0.1 mm. and hl = 200 mm. From Equation 2, it follows by differentiation that for constant h:
-O.lo0 400
and substituting hz from Equation 1,
(4)
dt
Equation 4 demonstrates that the fractional change in mercury height of column with temperature is measured by the volumetric coefficient of expansion, which is the fractionel change of specific volume with temperature. The condition required to make hl = ho is obtained by combining Equation8 2 and 3 as follows:
The total height of mercury column is given by
h = hi
u dt
dt
x
221
x
100 = -5.5%
(7)
Thus, a deviation of as much as 5.57" can be made in the selection of the ratio of diameters and still maintain a precision of 0.1 mm. in 200 mm. Experience has shown that these tubes may be selected within a precision of 1% of their respective sizes, even for sizes as small as 3-mm. capillaries. When tubing of small diameter is used for manometric measurements, the effect of surface tension must be considered. 81though the capillary depression for a tubing 3 mm. in diameter may be as high as 4 mm., this is accounted for in setting the zero position of the scale a t zero pressure differential. However, the variation in this correction must be considered. For the 3-mm. capillary, the permissible variation in its diameter, to maintain a precision of 0.1 mm., may be calculated as follows from the surface tension and density of mercury:
476
A N.A L Y T I C A L C H E M I S T R Y Table'I. Data on Plastics
Property Thermal Expansion, l O - s / O C. Modulus, Ib. per sq. inch, X 103 Water absorption in 24 hours, l/g inch, 70 Commercial
Vinyl Chloride Flexible. Unfilled
7-25 3.5-4.1
j,
Vinylidene Chloride
Polyvinal Butyral, Rigid
19
8-22
18-23
18
8-16
5-15
3.54.0
0.4
0.15
1-3.5
4
