1214
ANALYTICAL CHEMISTRY
successfully for many months and the operator has been relieved of any fear of losing Iiis capillary through breakage.
draws distilled water through the capillary, then a little acetone, and finally a little air.
The capillary is protected against mechanical shock by a shield of 7-mm. tubin Six holes, three on opposite sides, 11the shield near the tip of %e rapillary permit circulation of the solution. A hole in the shield near its upper end permits air to escape when the ca illary is immersed. During routine analysii a stream of distilkd water from a wash bottle directed through one of the ports in the shield sprves to wash the capillary free of any solution. Adhering water is removed readily by wiping the capillary and shield with a small piece of filter paper.
The hand-drawn capillary with the protective shield can be cleaned as easily as the same capillary without the shield or a capillary of marine barometer tubing, but it may be a little more difficult to determine whether or not liquid is passing up the capillary.
The following is a very efficient way to clean the capillary, either the hand-drawn model or one of marine barometer tubing.
Having removed all mercury from the capillary (by carefully jarring the rxipillary or by suction supplied by an aspirator), one first draws hot. concentrated nitric acid through the ca illary, using an aspirator. Whether or not the acid is passing tErou h the capillary can be determined by lifting the capillary out of t i e acid and draining any excess off the tip. If the passage is free, a column of liquid will be seen moving up the capillary. Next one
LITERATURE CITED (1) Kahan, G..J., IND. ENG. CHEM., ANAL.ED., 14, 549 (1942). (2) Kolthoff, I. M., and Lingane, J. J., Chem. Revs., 24, 1 (1939). ANAL.ED.,13, 794 (1941). (3) Langer, A.. IND. ENG.CHEM., (4) Lingane, J. J.,Zbid., 16, 329 (1944). (5) Lingane, J. J., and Laitinen, H. A., Ibid., 11, 504 (1939). (6) McReynoIds. R. C., Ibid., 14,586 (1942). (7) Mue1ler.E. F., Zbid., 12, 171 (1940). (8) Novak, J. V. A., Collection C w c h o s h . Chem. Commune., 12, 237 (1947). RlcrrvrD December 29. 1949.
Rate-Indicating Mariotte Bottle F. A. SCHWERTZ Koppers Company, Znc., Mellon Institute, Pittsburgh 13, Pa. MARIOTTE bottle is frequently employed in the laboratory If the liquid is used to displace a gas, this bottle serves also to meter the gas a t rates far below the threshold of the ordinary wet-test gas meter. Its utility suffers, however, from the fact that it is not an indicating instrument and must be set a t the required flow rate by a method of trial and error. The present note deals with some simple additions to the Mariotte bottle that transform it into a rate-indicating device. These additions are based on the approximate theory of the operation of the bottle.
Putting this value in Equation 4 gives
A to obtain low but constant rates of liquid flow.
THEORY OF MARIOTTE BOTTLE
ud
=
d2g(h, - hb)
or vc =
d2ghl
The velocity of discharge is therefore proportional to the square root of the hydrostatic head between the points of liquid discharge and air entry. The rate of discharge may accordingly be regulated by changing the distance between these points. An alternative way of controlling the ,rate is to insert a resistance in the air-intake .line.
A typical Mariotte bottle, shown in Figure 1, consists essentially of a jar provided with a liquid-exhaust line, A , and an airintake line, B A s the liquid flows out of the jar a t C it is relaced by air which enters a t B and bubbles up through the iquid level, D. The ratre of discharge of the liquid, considered as ideal and nonviscous, may be calculated from Bernoulli's equation, which requires that the energy per unit volume of liquid a t any two oints along a streamline must be constant. Its familiar form or an incompressible liquid is
P ' P
u2
+ P + dgz = constant
(1)
where d is the density of the liquid, u its velo'city a t any point, P the hydrostatic pressure a t the same point, and z the vertical distance of the point above some arbitrary datum line. If this datum line is taken a t level C , it is necessary that
tu2
+ Po = K
(2)
where us is the velocity of discharge, Po is atmospheric pressure, and K is a constant. Similarly, because the velocity a t liquid surface D is negligibly small,
_ _ _ _ _ _ - -I
I
+
Pi dgho = K (3) where Pi is the air pressure above the liquid surface. Hence, on combining Equations 2 and 3,
or
(4) I t is also necessary that P o = Pi
+ dgha
(5)
I
*Is
Figure 1. Typical Mariotte Bottle
V O L U M E 2 2 , NO. 9, S E P T E M B E R 1 9 5 0
1215 where k is a constant, provided the liquid is fldwing in a steady stream. If, however, the rate of flow is so small that dropleta are formed a t the exit point, C, surface tension will play a role and Equation 9 will no longer be valid. Nevertheless this equation serves as a guide for transforming the Mariotte bottle into a rate-indicating device.
air
MODIFIED MARIO’LTE BOlTLE
From Equation 9 it is apparent that the liquid rate, R, will be a function of h, alone if hz is held constant, or, conversely, of hz if h, is held constant., The problem of designing a satisfactory rate-indicating Mariotte bottle therefore consists of varying and measuring h, or hz in a simple manner. Two methods of effecting t>hisresult are illustrated in Figure 2. In one of them, hl is held constant and hz is varied; in the other, the reverse is true. To vary b,the air is allowed to leak into the Mariotte bottle through the liquid trap, A . This operation reduces the pressure in the air-int,ake line below atmospheric ressure by an amount indicated on the liquid manometer, B. n operating this device, the leveling bulb, C, is used to bring the liquid level in the trap above point D. Stopcock E is then opened and liquid is allowed to discharge from the Mariotte bdttle. This action draws the liquid from the leveling bulb up into the liquid trap until the discharge ceases. The pinchcock, F, is then closed and the leveling bulb dropped below level D. Immediately thereafter the pinchcock is reopened, air flows into the Mariotte bottle, and hz is adjusted to any desired value.
P
In this manner the calibration curve in Figure 3 was obtained. Here the rate of discharge of water, R, was plotted against 4 h T z in order to check the validity of Equation 9. When the liquid was discharged in a full stream, the rate of discharge was indeed proportional to d h l hz. When the discharge was dropwise, surface tension played a role, and the rate of discharge was considerably less than one would expect from the back-extrapolation of the straight-line calibration curve. Two additional features of the calibration curve are attributable to surface t,ension-the discharge rate does not fall to zero for ( h , - h2) = 0 &s would be expected from Equation 9, and the back-extrapolated straight line (dotted portion) does not pass through the origin of coordinates. The first feature can be quantitatively explained as follows:
-
liquid
Figure 2.
Development of Modified Mariotte Bottle
Without inquiring into the nature of this resistance, assume that it lowers the pressure of the intake air an amount equal to a hydrostatic head of height b. Then, in place of Equation 5, one has Pe - dghs = Pi -I- dghb (7) Combining this equation with Equation 4 yields v8 d 2 g ( h i - hz) (8) F~~ an actua],viscous fluid the velocity of discharge will be somewhat smaller than that given by Equation 8. The rate of liquid dicharge, R,should then follow the equation
R = k d ( h i - h)
(9)
The bubble formed a t the discharge tip, G, is capable of su porting a column of liquid, h, whose magnitude is defined by equation ‘hdg = 2 y / r (10)
tg
where y is the surface tension of the liquid.and .r is the radius of the discharge orifice. Because water was used, y = 7 2 dynes per cm. while r = r0.045 cm. Consequently h = 3.3 cm. At m = 1.7, so zero flow rate the calibra-tign urve gives d that (hl - hz) = 3 cm., a fi&e in rough agreement with the preceding one. (A more careful consideration of this point may show that the Mariotte bottle is adaptable to surface-tension measurements.) That the back-extrapolation of the straighb line portion of the calibration curve does not p a s through the origin is probably related t o the fact that the flowing liquid loses energy in forming fresh liquid surfaces around the intake air bubbles and a t the exhaust orifice, G. The method of calibrating the Mariotte bottle by varying hl and keeping hz constant is also illustrated in Figure 2.
Figure 3.
Calibration Curve for Hydrostatic Head
One need merely connect the dischar e tip, G, to the gooseneck, H by means of a rubter tube. If the gooseneck is h t e d above level I , the flow will !x entirely shut off. As it is lowered, the rate of discharge will increase in a manner similar to that depicted by the calibration Zurve in Figure 3. If these ia negligible flow resistance in the air-intake line, hz = 0, and consequently therate of discharge will be simply proportional to &.
1216
ANALYTICAL CHEMISTRY
Very accurately reproducible microflow rates may be obtained by inserting one or more pieces of glass capillary tubing in series with the air-intake line, using rubber tubing connections. Glass thermometer tubing serves well for this purpose.
:
80-
APPLICATION OF MARIOTTE BOTTLE
The M,ariotte bottle has been utilized to calibrate a fine capillary flow-rate indicator in the flow-rate range below 100 cc. of gas per minute. I n this range the usual laboratory instruments, such aa a webtest meter, will not serve, and the Mariotte bottle affords a simple but accurate means of doing the job. The technique of calibration may easily be understood with reference to Figure 4.
c
W 2
16 PRESSURE DROP ACROSS CAPILLARY
Figure 5 . FLUSHED GAS
FLOW RATE INDICATOR
Figure 4.
Setup for Calibration
The discharge tip of the Mariotte bottle is connected to tube A . Water is then run into the graduated cylinder a t a fixed,
invariable rate. The gas in the cylinder is thereby displaced and caused to pass through the capillary. To make the setu essy to handle, various refinements are incorporated. Stopcocf B is used to fill in the test gas a t the same time the foreign gas is being flushed out through stopcocks C and D. To prevent splashing and to smooth out the flow of water, the lip of the dis-
20
24
28
- CM B U T Y L PHTHALATE Two Calibration Curves
32
charge tube is provided with a very fine glass cat's-whisker which extends into the graduated cylinder. The drying bottle is used toapresent a moisture-free gas to the capillary. In Figure 5 are two calibration curves obtained with the arrangement shown ,in Figure 4. The upper curve refers t o hydrogen, the lower to air. The straight-line calibration holds good down to flow rates in the neighborhood of 5 cc. per minute and presumably lower. To test the accuracy of the work, the inverse ratio of the slopes of these two curves was compared to the ratio of the viscosities of the respective gases a t the experimental temperature of 25" C. The ratio of the viscosity of air to that of hydrogen at this temperature is 2.05, whereas the inverse ratio of the slopes is 2.06. There are several fine points to be considered if very high &ccuracy is required. In the first place, the solubility of the test gas in the water is of no importance, because the volume of the displaced gas alone is measured. But this displaced gas is watersaturated, so that the gas displacement rate of Figure 2 should strictly be corrected downward for the water vapor held up in the drying bottle. On the other hand, the gas is displaced at a pressure higher than atmospheric by the pressure drop across the capillary. The gas displacement rate of Figure 5 should accordingly be corrected upward if all gas volumes are to be referred to atmospheric pressure. These two effects therefore tend to cancel out and for most work' cdibration curves similar to those depicted in Figure 5 kill be adequately arcurate. RECXIVED December 22. 1949
Determination of Phosphorus in Alloys JA3IES I,. KASSNER &ND MARY ALICE OZIER, University of Alabama, University, Ala. REAGENTS AND STANDARD SOLUTIONS
HE analytical usefulness of the doublestrength citromolybT date solution which was used in the determination of phosphorus in iron ore (6)has been extended to include the determina-
The reagents for this method are essentially those used in t h e determination of phosphorus in iron ore (5).
tion of phosphorus in alloys. The analysis of several Bureau of Standards samples indicates that the accuracy and precision of this method are good, and average deviations in results are well within the range recommended for iron and steel analysis (3). Standard procedures other than those given may be used in dissolving the samples, provided that the volume of the solution before the addition of the citromolybdate solution is not over 80 to lo0 ml., and that the solution contains not more than 10 grams of ammonium nitrate or its equivalent in addition to not more than 6 ml. of concentrated nitric acid (specific gravity 1.42) or not more than 6 ml. of 60y0perchloric acid. The mixed indicator ( 4 ) used in the determination of phosphorus pentoxide in phosphate rock is used in determining the end point.
Steels Soluble in Nitric Acid. The procedure for dissolving the steel samples is essentially that adopted by the American Society for Testin Materials ( 1 ) and others ( 7 , 9). The volume of acid should be fetermined by the size of the sample, so that it will not be necessary to use more than 8 ml. of concentrated ammonium hydroxide (specific gravity 0.90) in adjusting the acidity. From this point, proceed as in the determination of phosphorus in iron ore ( 5 ) (Table I). Steels Insoluble in Nitric Acid. Weigh out a 0.5- to 2-gram sample of the steel into a 400-ml. beaker, add 30 ml. of hydrochloric-nitric acid (IO)mixture and 0.5 to 1.0 ml. of hydrofluoric acid, and heat on a hot plate until the sample is in solution and t h e silica is volatilized ( 1 ). Add 30 ml. of 60 to 70% perchloric acid, evaporate to fumes of perchloric acid, and fume for 5 to 10
DETERMMATION OF PHOSPHORUS IN STEEL
