April 15, 1943
ANALYTICAL EDITION
The hydroquinone has an equivalence of 2; therefore one mole of hydroquinone would take 2 faradays for complete oxidation. As only half the quantity of hydroquinone used is to be oxidized, half of the required faradays for complete oxidation should be used, or one faraday per mole of hydroquinone. The hydroquinone (20 rams) was dissolved in a suitable amount of water and pouref into the outer cup of the electrolytic apparatus. Two to 3 grams of sodium sulfate were added and the level of the liquid was raised to within 2.5 or 5 cm. (1 or 2 inches) of the top of the cup. The inner cup was half filled with distilled water, 5 ml. of glacial acetic acid were added, and the cup was filled with distilled water to within 1.9 cm. (0.75 inch) of the top. The current was then turned on at various amperages and
285
for various times (Table I). Sodium sulfate was added to the outer cup liquor in small amounts from time to time to maintain a constant ampera e. At the completion of the required oxidation period, the sofution in the inner cup was concentrated and cooled, and the quinhydrone was filtered off. The yield was about 75 per cent of the theoretical.
The purity of the quinhydrone in each experiment mas 98 per cent or better in each case. I n the opinion of the author a higher yield may be obtained by using the mother liquor repeatedly.
Accurate Low-Pressure Gage FRANK E . E . GERRIA” AND KENNETH A. GAGOS University of Colorado, Boulder, Colo.
LO”-
PRESSURE gages commonly found in physics and chemistry laboratories are either of the Bennert closed U-type, or one of the many modifications of the McLeod type. The Bennert type js satisfactory for pressures above 1 cm. of mercury, but is not very accurate for lower pressures. For the low-pressure range the McLeod gage is usually used, b u t its application is limited b y the fact that i t depends on increasing the pressure in one part of the system. This increase in pressure mill, in the case of vapors from liquids having high boiling points, lead t o a condensation of the vapors, which will make the measurements useless. Thus in the case of measuring the vapor pressure of water of crystalline hydrates, the pressure cannot be increased above that over pure water at the same temperature without bringing about dew formation. A number of methods have been used for increasing the accuracy of such measurements, one of which involves the replacement of mercury by a Iiquid of low density and negligible vapor pressure, always being certain t h a t the vapors being measured are not soluble in the confining liquid. The floating tube barometer described by Caswell (1) in 1704 and later adapted to use in what has been called t h e steelyard barometer (3) embodies the basic principles of a recent instrument known as the Dubrovin (2) gage, which may be purchased from scientific apparatus houses. Since there appears to be no published description of the theoretical background of the floating barometer, i t seemed worth while t o develop the equation for the magnification factor, and to give directions for making a gage which would be useful in vacuum distillation work, as well as around physical chemistry and physics laboratories. Figure 1 shows an inverted closed cylinder floating freely over mercury. Its lateral motion is controlled by three point guides at top and bottom lightly touching the inside walls of the containing vessel. The device is placed on its side and a high vacuum is created by means of a good oil or diffusion pump. This.removes all the air and adsorbed gases from the inside and outside of the floating tube. It is then set up on end and atmospheric pressure is slowly restored. If the density of the tube material is less than that of mercurv. the tube will float and the inside of the floating tube will be entirely filled with mercury. Now if the external pressure is gradually reduced, the tube remains stationary until the external pressure becomes equal to the height of the mercury column inside the tube above the outside level. (Capillary forces are for the moment neglected.) Reducing the pressure still further results in the condition shown in the figure. The height, N , measures the pressure in the
large cylinder. As the pressure is progressively reduced, the mercury column drops while the tube itself rises. Thus a dro of I-cm. pressure results in a drop of 1 cm. in height N , whiz H may increase 10 or 20 cm., corresponding to multiplying factors of 10 or 20.
-DI -D2
FIGURE 1 Regarding the tube as a freely floating body a t equilibrium, constrained by guides to move only in a vertical direction, and assuming the gas pressure inside the floating tube to be zero, we may equate the sum of the downward forces t o the sum of the u n-ard forces. Height N of the liquid inside the tube depends OI& on the external pressure, P. The pressure in the liquid at the base of the floating tube is made up of the sum of the gas pressure, P = Ngp, and the pressure of the liquid column, K , which is Kgp = (L - H)gp, in which g and p represent the force of gravity and the density of the liquid. This total pressure gp(N + L - H ) over the annular ring area of
Vol. 15, No. 4
INDUSTRIAL AND ENGINEERING CHEMISTRY
286
+
the tube 9 ( D ; - D:) exerts an upward force 2 ( D ; - D:)(.V 4 4 L - H ) . To this we add F, the algebraic sum of all other constant forces exerted by surface tension, floats, etc. Hence: Total upn-ard force
=
2 (D; 4
D:)(S
+ L - H) + F
The downward force is made up of W , the weight of the tube, and the pressure, P = iVgp, over the sectional area of the tube
Total downward force
=
rrNgpD; 4
+ IV
For such a body in equilibrium we may equate the upward to the downward forces and obtain
4 (D;- D:)(N
W P
+ L - H) + F
=@ ?!r% .
4
+W
Simplifying and grouping the constant terms as C, this becomes
Differentiating, we obtain
This equation states that as S increases, I€ decreases and vice versa. It also states that the rate of change of H with respect to N is constant, since it depends only on the constant tube dimensions. The numerical value of this rate of change for a given instrument n-ith constant tube diameter and constant wall thickness is accordingly the same for infinitesimal and for finite changes in H and N . Since the weight of the tube, the density of the liquid, surface tension forces, etc., included in the constant term, C, do not appear in the final equation, the rate of change of H with respect to N is independent of all such constant terms. The absolute value of N depends on the pressure, P , in the outer tube and on capillary forces. The absolute value of H depends on the densities of the tube and the liquid, pressure P , and surface forces. In view of these facts it is evident that the ratio of the absolute value of H to N is meaningless. On the other hand, a decrease in the pressure, P , of 1 mm. of mercury is accompanied by a decrease in N of 1 mm. if the confining liquid is mercury. If simultaneously the tube rises 10 mm., then H has increased by 10 mm. and the change of H with respect to W is 10. This is then the true value of the multiplying factor or magnification. As indicated in the equation for the rate of change of H with respect to S , it can be calculated from the internal and external diameter of the floating tube, and is independent of all other factors. Both theory and experiment show that as the liquid inside the tube falls and the tube rises, the level of the outside liquid does not change. This means that the volume of the cylinder that comes out of the liquid equals the volume of the liquid that drops into the body of the fluid. The instrument has the very distinct advantage over other mechanical and optical magnifying devices of not magnifying the error, if any, due to capillarity, adhesion to the tube, etc. The apparent density of the tube may be changed either by making the lower submerged part qf tube itself of a doublewalled sealed cylinder or by attaching a separate float made of glass at its base. In this way even a platinum tube can be made to have the absolute value of H greater than the barometric height of 76 cm. of mercury, using mercury as the confining liquid. We then have a direct-reading magnifying barometer. The guides serving to hold the tube erect make only slight contact with the outer tube, some clearance being allowed. When a
reading is t o be made, a light tap on the side of the outer tube momentarily releases contact, permitting the floating tube t o rise or fall freely about its equilibrium position, which is easily reproducible to less than 0.2 mm. If we have a tube with a magnification factor of 20, a barometric change of 1 mm. of mercury is accompanied by a 20-mm. change of H . An error of 0.2 mm. in reading the height of H is an error of 1 per cent. Stated another way, a 0.01-mm. change in barometric pressure is the minimum change which can be observed directly without the use of a vernier. Since the accuracy of reading is independent of H , lo-* mm. of mercury is the lowest pressure that can be read on an instrument whose magnification factor is 20 when the liquid used is mercury. If in place of mercury we use Apiezon B oil, whose density at 28" C. is 0.861 gram per cc., the accuracy is greatly increased. With the above instrument having a magnifying factor of 20, and a minimum observable pressure change of 0.01 mm., the minimum observable pressure change becomes 0.01/15.7 = 0.00064 mm. of mercury, in which 1!.7 is the ratio of the densities of mercury and Apiezon B oil at 25 . The above considerations show that for mercury as a confining liquid the useful range of the gage lies between 10-2 and 103 mm. of mercury, whereas with dpiezon B oil the lower range is extended to 6.4 X inm. A relatively high accuracy is achieved over w T-ery large pressure range without the use of a vernier. Readings are made directly and are instantly observable. S o operation such as changing volumes as in the case of the bIcLeod gage is necessary. Mercury as a confining liquid has the great advantage of dissolving very fem vapors of either organic or inorganic substances. It has the disadvantage of high density and accompanying inaccuracy in reading small pressure changes. It is this latter difficulty which the floating tube overcomes. 4 concrete illustration of its use in the authors' laboratory of physical chemistry: In the determination of gas densities by direct weighing, the student is instructed to evacuate the bulb to 0.1 mm. or less and then weigh. This involves the use of a gage of the McLeod type. However, by including the floating gage in t'he system the pressure can be read directly. Although the equation enables the calculation of the dimensions of the tube for any specific multiplying factor, the following have been found practical. D1
0 2
Inch 0.1225 0.3576
Inch 0.1260 0.375
Wall Thickness Inch 0,00125 0.0087
L Inches 10 12
Magnification 24.25 10.03
Stainless steel, nickel, platinum, and glass tubes may be used with mercury. Since a uniform bore and wall thickness are essential to a uniform pressure scale and the thin-walled tubes which are necessary are stronger when made of metal, metal tubing is especially satisfactory. Strength is often necessary, since a rapid restoration of pressure in the outside container may cause the resulting mercury hammer effect to break out the top of the floating tube. To obviate this, the lower part of the tube may be made with a rather small opening, and thus avoid a rapid entry of the mercury.
Acknowledgment The authors wish to thank the Superior Tube Company, Norristown, Penna., and the Summerill Tubing Company, Bridgeport, Penna., for their kindness in making up special tube sizes for use in the above studies.
Literature Cited (1) Caswell, Phil. Trans.,24,No.290, 1597 (1704).
(2) Dubrovin, John, Instruments, 6,194 (1933). (3) Hutton's Mathematical Dictionary, Vol. 1, p. 208, 1815.
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