The Mariotte Bottle and Automation of a Potentiometric Titration John A. Lynch and Jimmle D. Narramore University of Tennessee at Chattanooga, Chattanooga, TN 37403 Titrations are a fundamental approach t o quantitative use of reaction chemistry. They often yield accuracies surpassing those obtained by any other common technique. A significant amount of the undergraduate chemistry curriculum is, therefore, devoted t o instruction in and application of titration methodologies ( I ) . Unfortunately the nature of this experience all too often conditions students to associate titrations with tedium. Indeed titrations are fairly complex compared to many other analytical measurements. Experimental implementation of titrations can, however, be simplified through the use of instrumentati&. ~ r o p e k i e ssuch as potential, absorbance, and temperature can all he recorded simultaneously with titrant addition using stripchart or microcomputer technology. Some form of constant rate del i v e r ~svstems is. with the exce~tiouof coulometric titration;, aiso needed for this automated approach to titrations. Mechanical burets are, however, not often available in anywhere near sufficient quantities in the shoestring world of the typical undergraduate chemistry laboratory (2). The subject of this paper is avery old, effective, and, most importantly, an inexpensive way of providing constant rate titrant delivery--the Mariotte bottle. Hislory and Theory In the 17th century the French physicist Edm6 Mariotte first documented the behavior of the bottle that now bears his name (3). The wonderful simplicity of this device is illustrated in Figure 1. For our purpose its salient feature is that once the tube fills with air the liauid discharee rate remains constant until the fluid level drops below the'tube. Mariotte explained this beautifullv bv citing that atmos~hericDressure, as in a harometer, can-susta& a column bf water of about 30 feet. Therefore, as long as the liquid height above the air inlet does not exceed a pressure equivalent to about 30 ft of water, fluid exits the bottle a t a rate determined by the distance between its air entrance and liquid discharge. The Mariotte bottle has been rediscovered many times since 1686. A theory published for i t in 1950 (4) stated that: where u is discharge velocity, g the gravitational constant, and h the distance hetween air inlet and fluid outlet. This equation agrees with Galileo's theorem linking the speed of free-falling bodies t o the height from which they fall a t rest and his assertion that objects falling from the same height fall a t the same rate regardless of their masses (5).Thus, the averaee velocitv of molecular discharee is inde~endentof liquiidensity. For ideal liquids multiolvina the velocitv obtained from eq 1by the area of the outiet orifice yields the discharge rate, R, in cm3/s. For real liquids Poiseuille's law ( 6 ) allows us to formulate:
-
A
Air
Buret
Pressure head due to height "h- in cm Figure 1. Design features of the Mariohe bottle.
where r a n d L are radius and length of the narrow discharge orifice, and D and 11 are the density and viscosity coefficient of the liquid. Calibrating the discharge rate, R, with water allows empirical reformulation of eq 2 to: R'
=
Rn, (1/%/'to)'l~
(3)
where R' is the discharge rate for a liquid having a relative viscosity ratio to water of 7/17., VT is the viscosity coefficient for water a t the liquid's temperature, and 7, is the viscosity coefficient of water a t the temperature of calibration. Extensive tables are readily available that allow calculation of R' for most common titrants (7). Application lo Automated Tkrallons In some early studies on titration automation, use was made of the Mariotte bottle as a constant delivery rate buret (8,9). BuckRogers, one of the authorsof the landmark paper later commented to us: "We on thermometric titrations (9), were trying to use the technology of the time; the stripchart recorder". Indeed the availability of the mechanical link provided by these recorders meant that the technology for mechanized burets had also come into being and other researchers soon began using them for automated titrations (10,ll)~ . o d a yth; , commekial availability ofseveral varieties of motor-driven burets bas left this use of the versatile Mariotte bottle to antiquity. In taking a page from the past we have, nonetheless, used the Mariotte bottle as an automatic buret for potentiometric titrations in an undergraduVolume 67
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Magnetic Stirrer Figure 2. A 500.0 potentiometer functions as a voltage divlder to allow adjustment of recorder span to the corresponding pH span of the titration.
ate analytical chemistry laboratory. Our reasons for doing this were: the economy afforded, the fundamental principles illustrated, and the fact thnt students can obtain reasonable results in t h e course of a 3-h laboratory.
Ftgure 3 T lration of o phthalate #onwith 0 1002 M NaOH exhtbiting an end polm slope of I ph unll Increase for 4 moll e q u w snfs aodad
Experimental Construction and Calibration of a Mariotte Bottle A simple Mariotte bottle, as shown in Figure 1, was constructed usingan ordinary 50-mL buret. Insertion of a 6-mm open-bore glass tuhe though a #00 one-hole rubber stopper made a suitable air inlet. Slow discharge was achieved by cutting the tube to come to within a few centimeters of the buret's stopcock. The buret was filled with distilled water and the tube tightly sealed into its top. A constant-pressure head was obtained by opening the stopcock until the tube filled with air. For calibration a thin layer of mineral oil was added to a 100-mL beaker to eliminate evaporation of the distilled water collected. The Mariotte bottle was then aligned vertically and allowed to discharge into the beaker. The weight increase of the beaker, the time period of discharge, and the density of water at the temperature of measurement yielded the discharge rate in cm"/s. Visual inspection indicated that tightly sealing the stopper into the buret returned the glass tuhe to the same distance from the bottom of the buret for each replicate calibration. All measurements were started after the tube filled with air and ended before the water level drained below the air inlet. Potmtiometric Titration of Potassium Acid Phthalate Standard with 0. lOOOM NaOH For use as the titrant an NaOH solution was standardized to 0.1002 0.0001M by titration of primary standard potassium acid phthalate to a phenolphthalein end point. A comhination glass/ reference electrode was connected to a Corning model 7 pH meter. The output from the pH meter was wired to the stripchart recorder and buffers used to set the recorder's resoonse . to a full-scale soan ranging from about pH 3 to 12. Since the Cornrng model 7 pH meter "sea had an output of 10 mV for full-scale deflection, n 500-!I purentwmeter was used as a voltage divid~r,ay illusrrared in Figure 2, to help achieve the desired recorder display. This allowed use ofa convenient 1-mV recorder scale for obtaining titration curves that encompassed, hut did not exceed, the recorder span. Samples of 0.6 to 0.8 g of primary standard potasaium acid ohthalate were weiehed to *0.1 me and dissolved in 25 mL of freshiv , distilled-deionized water. The eomhination electrode was rinsed wirh distilled-deronized water and inserted into a magnetrcally stirred solurion. The hlariotte bottle rrar rinred with the NaOH tmant, loaded, and allowed todrain until air filled the tube. It was positioned above the sample solution with care being taken to insure its proper vertieal alignment. Equation 3 was used to calculate a discharge rate of 0.1831 cm3/s for 0.40% NaOH at 23.9 'C versus 23.0 OC for water calibration. Recorder speed was selected so that 30 to 40 cm of Daoer would oass from the start of the titration and the aatieipated~q;ivalenrt. point. Calibration ofrhr uharr drive of the rerorder at this setting was checked. Simultanwus wirh the opening ot the stopcock, the rhnrt was marked. Titration and re~~
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Table 1. Callbratlon Results ol the Marlone Bottle
a
At
mean cm31s = 0.1828. % relative 0 = 0.19 23.0 'C the densiw of water is 0.99754 g1mL.
Table 2.
Results ol 0.1002 M NaOH Tltratlan of Potasslum Acld Phthlate Standarda
mmol of reactant used
mmoi of reactant determined
n,= 0.9132poirest 23.9 "C. and n.
% Enor
= 0.9325 poiseat 23.0 'C,
cordine " were continued until the eauivalence ooint had been oassed . hy at least 10cm. Theequivalence point wasobtained by locationof the inflrccion point on the symmetrical titration curve produced. ~~~~~
Results and Dlscusslon Table 1shows t h e results of t h e calibration of t h e Mariotte bottle used. T h e percent relative standard deviation of 0.19 for these data is comparable to the hevt calibration results reported in the literature (9)for this t w e o f device, and in also similar to t h e precision we have attained with mechanical burets. It is important t o note that, on other occasions, when discharge occurred in a dropwise fashion, t h e precision of the calibration degenerated by a factor of about fourfold t h a t cited here. Whether this was due ta effects of surface tension (4)or collection error caused by lack of a steady stream is not known. Table 2 gives the titration results. T h e average accuracy of 50.28%is a s good a result as is typically expected from titration methodologies. All of the determined values for these titrations contained errors witb~~~~
in the limit, fO.70%, calculated based on error propagation. Figure 3 shows a representative titration curve. Inspection of the curve yields no sign of distortion due to inconstant titration rate or any other factor. The appearance of these curves was of a quality equal to those displayed recently in the literature for similar titrations obtained with the aid of a mechanical buret (12). The overall performance assessment of our crude Mariotte bottle is very good, especially when one considers that it was assembled in a few minutes with readily available materials. Apparently the Mariotte hottle works quite well as a constant rate delivery device when eq 3 is used to obviate the need for frequent recalibration noted by other workers (8).
Literature Cned 1. Lakc,D. C.,Gmsarnan, W . E . A m I . Chem. 1387,59,829A-g?SA. 2. Gawkay, R. E.; Csrlron, A. F. J. Cham. E d u c 1986,67,554. 3. Mariotte, E. The Motion of Water and Orher Fluids Being o Treatise of Hydrostoricks: De8sguliers.J. T.. Translater: Amo: Near York, 1978. 4. Schwe*, F. A. A n d . Chem. 1950,22,121~1216,withcorroctiomootad: Scbwe*, F. A. Anol. Chem 1950.22.1511. 6. Galilei. G. Diolneuea ~" Concernine ' h o New Sciowes:. Crew. H.: DeSalvio. A,: Northwestern University: Evsniiton, 1939. 6. Shoemaker, D . P.; Garland, C. W.; Steinfeld. J. I.: Nibler, J. W . Erpotimenu in Physical Chemi*fry,4th ed.: MeGraw-Hill: New York. 1981: pp 328-361. 7. CRC H o d b o o k of Chemistry and Phydcs, 62nd ed.: Wesat. R. C., Ed.; CRC: B o a Raton, FL, 1981-1982: pp D-198to 0-257 & F-42. 8. Barredo, J. M. G.; Taylor,J. K. Trans. Elm. Cham'.Soe 1941.92.437444. 9. Lindc, H,W . ;Rogers, L. B.; Hurne, D.N. Anol. Cham. 1953,25.404407. 10. Lingane, J. J. Anol. Chem. 1948.20.285-292. 11. Jordan,J.:AUernan,T. G.Anol. Chom. 1957.29.9-13. 12. Selig. W . A m . Lob. 1384, IK(41.3643. ~
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