Single-Pan Balances, Buoyancy, and Gravity or "A Mass of Confusion" Rubin Battino Wright State University, Dayton, OH 45435 Arthur G. Williamson Department of Chemical Engineering, University of Canterbury, Christchurch, 1, New Zealand
The advertising literatun: on single-pan balanws (hoth mechanical and t ~ l t ~ c t n ~isn iaccommentary ~ on the pullihilits of consumers and the app&ently confusedideas many magufacturers have about weighing. , manufac.. . For e x a m ~ l eone turer uf single-pan electrunic balilncr lists ior a dun1 wt4ghing ranee ot 1500 1.51)e. "readsbilitir~"of 0.1,O.Ul p, "precii~tms" he readout of ~0510.007g, a i d "linearities" of 0.110.01 displays five digits which accounts for the readability. We certainly hope the linearity is of the same order. As to how they determine precisions which are better than the "readability" or "linearity" we can only guess. Most single-pan electronic balances display five digits, some show six, and one company even offers eight (0.1 mg for the l-kg range). The single-pan mechanical balances of the analytical type (load 160-200 g, "readability" of 0.1 mg and "precision" of 0.05 mg) generally deliver seven significant figures. This wealth of "readabilities. ~recisions.and linear"~ ities" is offered along with oodles of si'&ificant fibres despite the fact that (we fondlv hone) anv so~homoretaking auantitative analysis could'tell'the manufacturers tha'i due to buovancv c still discussed) . effects (if. . . indeed, this arcane t o ~ i is the accuracy is often of the order of one part per thousand or 0.1%. If an accuracy of 0.1 mg is required in a mass of 100 g then buoyancy corrections must be made to 0.1%! Beine- miehtilv . .and the manu- - intrigued - hv the foregoing facturers' literature, we sent out a brief questionnaire to all companies which we could identify as manufacturers of single-pan balances. We asked the following questions of their research directors ~
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A. Single-Pan Mechanical Balances 1. What are your "weights" made of and what is their den-
sity? 2. Do you have a set of instructions far calibrating the "weights", or must this cheek be done by you? 3. Do you have a set of instruetionsapplying to huoyancy eor-
rections? B. Single-Pan Electronic Balances 1. Do you have a set of instructions for calibrating the accuracy of your balance aver its full range? 2. Since your balances will only read correctly when weighing objects of a certain density, what is the density of the standard weights against which your balances were ealibrated? 3. Do you have a set of instructions applying to buoyancy corrections?
The responses to these queries were most disheartening since almost all of the manufacturers just sent us more literature in return. Moreover, it was quite evident from the responses that most manufacturers either do not understand the idea of huoyancy corrections or believe them to he irrelevant (which thev sometimes are). This ienorance of huovancv . . corrections is not limited to manufacturers-one of us recently heard a colleaeue com~laininethat the tor, loading sinnle-pan balance in hisiaboratbry hadhad a "systkmatic"~erro~ ofapproximately 1glkg ever since it had been bought. The manufacturers of single-pan mechanical balances expect you to accept their original calibrations indefinitely
(perhaps, because the weights are protected, i.e., untouched by human hands),or to consult them in case of trouble. None supplied directions for calibration. The calibration of the weights in such a balance is fullv described hv a vublication of tlhe American Society for ~ e s t i ~n e~t h o d (s l j .An alternative approach which examines the internal consistency of the weights but does it without checking their absolutevalues and which has been used as a laboratory exercise by one of us is described in the Appendix. Most manufacturers of single-van electronic balances included directions for csiihrar;m..~heprocedure was t o put a "stnndard" weight, usually unsperified as to density or NBS clnss (21,on t h ( I~almcrpan and then turn a ralibrating screw until the read-out gave the nominal weight. The Mettlrr Instrument Corpora& supplies a calibritor weight with its balances and also sells them. The Sartorius balance has a built-in calibration weight. To calibrate any electronic balance one needs to use a standard weight of adequate accuracy. For a 100-g weight (a typical calibration weight) the class S tolerance is 0.25 mg, the class S - l tolerance is 1.0 mg, and the class P tolerance is 2.0 me. Thus. strictlv from the view~oint of accuracy, it is difficultto understand the extra digits these balances disdav. . " How can an analvtical balance be accurate to 0.1 mg when a class S weight is only accurate to 0.25 mg? (The tolerance of a class M 100 me weieht is 0.50 me.) Let us now turn to the interesting problem of thedensity of the weiehts used inside sinnle-pan mechanical balances. A standard f o r weights used in analytical balances was promulgated in 1973 by the Organisation Internationale de Metrologie Legale. Their recommendation is to use weights ~ All of the Mettler balances built of density 8.0 g ~ m at- 20°C. since 1973 have weights made of stainless steel with a density of 7.96 g cm-"ut "adjusted" to 8.0 g ~ m for - a~standard air density of 1.2000 g cm-3. Earlier Mettler balances used stainless steel weights of 8.4 g ~ m - ~We . do not know how Mettler accomplishes this "adjustment". Ainsworth uses nickel-plated brass weights of density 8.4 g ~ m in- some ~ balances and stainless steel ones of densitv 7.8 e cm-3 in others. Sartorius balances use weights of 7 . ~ cmZ3 8 ~ density. Whatever the original reasons for this multiplicity of weights of different densities, there can be no real excuse for not standardizing on weights of a densitv of 8 e cm-3. Recently an entir;new technolob of weighing has been developed in the form of the all-electronic balance. (A transition period included mechanicallelectronic hybrid balances.) With these devices we have in effect returned to the spring balance. The object to be weighed is placed on a pan and downward force is given by mg
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3Lj "objec
where m is the mass of the object,g, the acceleration of gravity, and a is the density (uai, 0.0012 g cm-3). This downward force is automatically balanced exactly by the interaction of the magnetic field from a coil and that of a permanent magnet. The current in the coil is converted electronically to a weight reading and then displayed digi,@ly. I t is possible to make the
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Volume 61
Number 1 Januaw 1984
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scale much more linear than that of a mechanical spring balance, and precisions of a few parts per million or better are ~ossible.For measurements where onlv relative masses are important (and using the same balancein the same place for all weiahinps) no calibration ~ o i n ist necessarv (within the "linear~ty'";f tht*bi~lanw!).The apparent mais scale is obviousls a function of the Iocd rravitational held. .\lthourh portland, Oregon and ~ h a r l e s t o n South , Carolina have issentially the same altitude, g differs by 0.11%; between New York, New York and Denver, Colorado this difference is 0.07%. When one calibrates single-pan electronic balances one is, in effect, determining the force constant of the electromagnetic nulling system against a standard weight of a particular density. If one knows that density (or the one the manufacturer used,, then one can reasonably apply buoyancy corrections and also calibrate the balance for the density of weights the manufacturer designed it ior. Mrtrler supplies a standard weight of 8.0 g cm- 'density umith its instruments (and also s14lsthtm senaratelv~.Sartorius calibratvs all of t heir halances against weig'hts with a specific gravity of 7.88 g cm-3. All of the other manufacturers we contacted gave no information on this matter. Basically, they tell you ;here the calibration screw is and to use it in coniunction with a "standard" weight. Buovancv corrections for single-pan mechanical balances h a w bien &alt with before i n ~ ~. I~o ~l Ns , \ I(.I-5). . The most complete analysis was ziwn h\. \Vinward, M'uolley, and Rutler. ~ u t , - n omatter how one approaches it, if one weighs an object of density 10 g em-3, the buoyancy corrections are of the order of 0.1%or one part per thousand. Mettler gives charts on how to handle this for their mechanical balances, and Sartorius eives directions in their instruction manuals. Air buoyancy corrections for single-pan electronic balances are the same as for two-pan equal-arm mechanical balances
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where Wo is the in uacuo weight of the object, Ww is the w i g h t read on the read-out device, and p,;,, PO, and p,, are, respectidy, the d m s ~ t i e of s air, the object, and the weights used to calibrate the balance. The huoyanc\f . . correction fur weighing 1kg of water is about 1g! While the manufacturers of balances are to be congratulated on their achievements in providing both very high precision and great convenience in the use of their products, it is unfortunate that these advances have not been accompanied by corresponding advances in the education of balance users, particularly with respect to the precautions necessary to use these fine devices. A standard 100-9 weight is of such small cost relative to the cost of a balancethat they should be supplied with the balance. Beware of being bedazzled by all of those bright red digits. If all else fails, re-read the section in a good quantitative analvsis book on balances and their errors. or even choose to work with the slower equal-arm balances where one can easily calibrate the weights and tare with real obiects. Of course. if you never work Gyond precisious of 1ppt,"feel free to ignore this paper. But, then, why are you using such an expensive balance? LHerature Cited
Appendix: Intercalibration of Welghts on a Single-Pan Weight Loading Balance Using Dummy Welghts ol Approximately Known Mass Only 1) Set balance level 2) Release beam 3) Set optical scale zero (this is useful but not necessary) 4) Read optical scale: S, 5) Arrest beam 6) Dial up 1unit: MI I ) Release beam 8) Read optical scale: S, MI = IS1 -So) (optical scale units) 9) Arrest beam 10) Add external weight: W. (-MI) 11) Release beam 12) Read optical scale: S.
W.=S.-So 13) Arrest beam 14) Dial MI 15) Release beam 16) Read scale: S'. 17) W, = S,' - So Wa=M1+(S,'-S) 18) Arrest beam 19) Remove MI 20) Remove W, and add Wb (ZM,) 21) Release beam 22) Read Sb Wb = (Sb- So) 23) Arrest beam 24) AddM1 25) Release beam 26) Read S$ Wb = MI + (Sb' - So) 27) Arrest beam 28) Add W. 29) Dial up M2(.12M1) 30) Release beam 31) Read S,
It is always necessary to examine the way in whieh the removal of interval weights from the beam is related to the dial readings. For example the Mettler H5 balance has the weights: 1,1,2,5,10,20,40, 80 g. The Mettler HI0 has 1,2,3,6,10,10,20,40,80. It is important to order the measurements so that the proper intercomparisons are made. By the careful choice of dummy weights and their combinations all the weights can be expressed in terms of each other and same (small) term in optical scale units. This latter can,of wurse, in its turn he expressed in terms of MI if desired. Usually the error in the optical scale makes only a small contribution to the error in determining the relationship between the weights, but it can make a significant error
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A hyi~alerrenion uithe prwedure dr-erlhed in steps 1-32 is used todeal \ \ i ~ hall the other ~rlghL5.Finally all wpightscan thrn, ifdrsired, be exmessed as fractionsof the largest weight in the set whieh is the one likely to have the smallest percentage error. As has been pointed out in the text, if all weighing8 for a chemical
exneriment are done on the same balance there is usuallvnocase for rrquirln!:an)thing other than a linear mnisscalr brraui~~rawmrrric chcmtcal rxprrimenti arc soncrrned with the r a r m (81 marsrs at various stages of the experiment. .
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Journal of Chemical Education
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