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A SIMPLE, AUTOMATIC GAS BURET ROBERT D. GOODWIN Air Reduction Company, Inc., Research Laboratories, Murray Hill, New Jersey
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measurement of rate of evolution of a gas is a procedure of very general applicability. For low rates it is convenient to employ a buret. This requires continuous manual or automatic adjustment to preserve a I t is assumed that gas pressure, p, in the leveling bulb is constant pressure in the system under study. It is ac- constant. The variables then are eliminated by the cepted practice to employ manostatic devices involving condition dP/du = 0,noting that dv = -adH. The reelectric relays for control of the amount of confining sult is liquid in the buret.' aD/Q = 1 + 1/r (4) Upon inquiring whether such paraphernalia are necWe see that a leveling bulb of large cross section is deessary, it was found that automatic control could be sirable in that a minimum spring extension equal to obtained simvlv . . bv . sus~ending - a leveling- bulb from a the buret length will be obtained thereby. When an s~ring.~ It is the aim of this communication, therefore, to illus- approximately correct spring constant, k, has been obtrate for pedagogical purposes that the most simple equipment may be surprisingly versatile, and that in the design of experiments elementary laws of hydrostatics find repeated application. The physical system requiring analysis is illustrated by the figure, in which A represents a gas buret and R represents a leveling h u b suspended from a spring. It is the purpose of the analysis to find the relationship betmeen the parameters of the system imposed ky the condition that the pressure in the buret shall he illdependent of volume. Symbols employed have the following meaning: a,
cross-sectional area. of cylindrical gas buret, cm.'
h,
height of liquid in lev&ng bulb, cm.
D, density of confining li uid, g. em.-8
of liquid in buret, em. H, height mass per unit length of flexible connecting tube, g. cm.?
1,
spring constant, g. cm.? buret leneth. em. gas pressire'in leveling bulb, g. em.-' pi P, gas pressure in buret, g. om.? Q, k j / 2 , g. om.? ratio of area of cylindrical leveling bulb to buret ases. r, gas volume of buret, cm.8 u, z, downward displacement of leveling bulb, cm. For simplicity, assume H = L and h = 0 when z = 0.
k, L.
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The significant apparatus parameters are a, r, &, and D. Three variables of displacement, namely, x, h, and H must be eliminated. Only three relations obtain among the variables; their elimination is possible by a single differentiation, representing the required condition, since the equations are of the first degree. The three relationships are the following: (1) total volume of liquid is constant; ( 2 ) difference of liquid levels is determined by gas pressures; (3) forces on the leveling bulb a t rest are in balance.
' HODQINS, J. W., AND R. B. HARVEY, Can. J . Research, 24B,
81-2 (1946).
'WILSON, L. D., Ind. Eng. Ckam., Anal. Ed., 8, 488 (1036). 369
370
tained in practice, final adjustment of the system may be achieved by means of small variations in the diameters of the flexible tube and of the leveling bulb. Any small rod inserted in the leveling bulb will decrease the liquid surface area. For mercury in a 20-mm. diameter buret, the spring constant required will be about 40 g. cm.-' It would be instructive for students to discuss the condition for which P = p, namely, that the buret. pressure equal the external pressure upon the leveling
JOURNAL OF CHEMICAL EDUCATION
bulb. The reason why the mass of the empty bulb does not appear in these expressions involves an understanding of the behavior of an ideal spring. What information is necessary to determine the length of spring required? The question whether this system is in stable equilibrium; the dependence of sensitivity upon density of confining liquid; and the time of response to changes in the rate of gas evolution-these questions should afford material for stimulating interest in the practical applicability of this useful device.
