Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1980 The precision measurement of mass James Steven Gibson Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Analytical Chemistry Commons Recommended Citation Gibson, James Steven, "The precision measurement of mass " (1980). Retrospective Theses and Dissertations. 7372. https://lib.dr.iastate.edu/rtd/7372 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. INFORMATION TO USERS This was produced from a copy of a document sent to us for microfilming. 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ANN ARBOR, Ml 48106 18 BEDFORD ROW, LONDON WCl R 4EJ, ENGLAND 8019630 GIBSON, JAMES STEVEN THE PRECISION MEASUREMENT OF MASS lov/a State University PH.D. 1980 University Microfilms In t©rn Qtionsi 300 N. Zeeb Road, Ann Arbor, MI 48106 18 Bedford Row, London WCIR 4EJ, England The precision measurement of mass by James Steven Gibson A Dissertation Submitted to the Graduate Faculty in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY Department: Chemistry Major: Analytical Chemistry Approved : Signature was redacted for privacy. In Charge of Major Work Signature was redacted for privacy. For the Maj^r Dep^tment Signature was redacted for privacy. For the Gradùfete College Iowa State University AmesJ Iowa 1980 il TABLE OF CONTENTS Page I. INTRODUCTION 1 II. MEASURING THE DENSITY OF A SOLID. THE DENSITY OP 4-AMINOPYRIDINE A, Measuring the Density of a Solid 14 B. Density of 4-Aminopyridine 17 III. MEASURING THE DENSITY OF AIR 24 A. Introduction 24 B. Relative Effects of the Prevailing Conditions on the Density of Air 32 C. Preliminary Experience with the Measurement of Temperature 35 D. Preliminary Experience with Barometers 37 E. Preliminary Experience with Measurements of Relative Humidity 40 IV. CONSTANT TEMPERATURE BOX 42 A. Construction of the Constant Temperature Box 42 B. Piers to Carry the Balances, Barometer, and Cathetometer 51 C. Control and Measurement of Temperature 53 D. Measurement of Barometric Pressure Within the Constant Temperature Box 66 E. Vacuum System in the Box 72 P. Gas Pipet 7^ G. Determination of the Acceleration of Gravity 84 til H. Determination of the Elevation of Room 137A and of the Balance Pier 86 V. MODIFICATION OP THE METTLER, SINGLE-PAN BALANCE 89 A. Introduction 89 B. Increasing the Capacity of the Kilogram Balance 90 C. Increasing the Sensitivity of the Mettler Kilogram Balance and of the Mettler Semimicrobalance 95 D. Removal of the Taring Mechanism 97 E. Eliminating the Effects of Static Electricity 98 P. Partial Arrest Stop 107 G. Thermal Insulation of Balances 108 VI. ABSOLUTE DENSITY CYLINDER FOR THE DETERMINATION OF THE DENSITY OF AIR 112 A. Introduction 112 B. The Construction and Measurement of an "Absolute Density" Cylinder ll4 C. Adjustable Lapping Block for Cylinders 120 D. Additional Measurement of the Dimensions of Absolute Density Cylinder Number 1 124 E. Determination of the Volume of Cylinder Number 1 by Hydrostatic Weighing in Water 126 F. Determination of the Volume of Cylinder Number 1 by Hydrostatic Weighing in FC-75 132 G. Comparison of the Results Obtained for the Volume of Cylinder Number 1 137 iv H. Construction and Determination of the Volume of Tubular Counterweight for Cylinder Number 1 l4l I. Comparison of the Results Obtained for the Volume of the Tubular Counterweight 150 VII. VACUUM WEIGHING BOTTLE FOR THE DETERMINATION OF MASS 154 A. Introduction 154 B. Design of the Weighing Bottles 157 C. Measurement of the Mass (in an Actual Vacuum) of Cylinder Number 1 and of Its Counterweight I63 VIII. DETERMINATION OF THE DENSITY OF AIR USING CYLINDER NUMBER 1 16? A. Equation Used to Calculate Results 16? B. Apparatus and Procedure I69 C. Results and Discussion I70 IX. SURVEY OF THE LITERATURE ON THE CONTENT AND THE DETERMINATION OF OXYGEN IN THE ATMOSPHERE I8I A. Survey of the Literature I8I B. Proposal of a Method for the High-Precision Determination of the Oxygen Content of the Atmosphere 193 X. THE DISSEMINATION OF MASS, THE CONSTRUCTION OF A SET OF STAINLESS STEEL WEIGHTS I96 A. General Considerations 196 B. Selection of Stainless Steel Carpenter 20CB3 for Weights 203 C. Density of Various Lots of Carpenter 20CB3 206 D. Fabrication of Weights 211 V XI. THEORY OF THE CALIBRATION OF A SET OF WEIGHTS BASED ON THE FIBONACCI SEQUENCE 226 A. The Composition of a Set of Weights 226 B. Fibonacci Mathematics. General Survey, Nomenclature5 and Symbolism 231 0. Fibonacci Mathematics. Representation 235 D. Fibonacci Mathematics. Summation Formulas 239 E. Use of Representation and Summation in the Calibration of a Set of Fibonacci Weights. A New Symbolism to Facilitate Comprehension and the Handling of the Numerous Terms Involved 243 F. Use of the Single-Pan Balance in the Calibration of a Set of Weights 248 G. Further Development of the New Nomenclature and Symbolism 254 H. Schedule for Calibrating a Set of Fibonacci Weights 256 1. Calculation of Departure from Experimental Data Using Only the Next Two Lighter Weights (Simplest Case) 260 J. Calculation of Departure from Experimental Data Using Only the Next Two Lighter Weights But Including F_-, in the Set ~ 265 K. Calculation of Departure from Experimental Data. Horizontal Approach. Combined Treatment of All Representations of Each Weight in Succession 272 XII. SUMMARY 282 A. Chapter I 282 B. Chapter II 283 vi c. Chapter III 284 D. Chapter IV 286 E. Chapter V 290 F. Chapter VI 292 G. Chapter VII 296 H. Chapter VIII 297 I. Chapter IX 299 J. Chapter X 301 K. Chapter XI 303 XIII. BIBLIOGRAPHY 306 XIV. ACKNOWLEDGEMENTS 315 I. INTRODUCTION During 1975 and 1976, Koch and Diehl (66) and Koch e;fc al. (68) reported the results of high-precision, coulometric titrations of highly purified A-aminopyridine, results which enabled them to calculate a new value for the faraday, the fundamental constant interrelating chemistry and electricity. Somewhat earlier, physicists (28) had rejected the then current value for the faraday, a value obtained by Craig, Hoffman, Law and Kamer (31) at the National Bureau of Standards by the anodic dissolution of silver, in favor of a value calculated from other physical data. The Craig experi­ mental value was presumably "subject to some serious error". The new value of Diehl and co-workers (see table on next page) was identical to that of Craig as successively recalcu­ lated (41) for the change in the basis of the atomic weight scale, for two changes in the definition of the volt, for a determination of the isotope ratio of the silver used by Craig, and for a more generous statistical treatment of his data than was given by Craig. The experimental, electro­ chemical value of Craig and of Diehl was reinstated by the physicists (97) but there remains a discrepancy of 20 parts per million (p.p.m.) between the experimental and the calcu­ lated values, disturbing because the discrepancy is some five times the uncertainty estimated for the experimental value and ten times that estimated for the calculated value. 2 Table j--l. Recent values for the faraday F Worker. Location. 1972 NBS coulombs Year. Method. per g.-eq.-wt. (Uncertainty )®' 96,486.72 Craig, Hoffman, Law and Earner (31). (a = 6.8 p.p.m.) NBS. i960. Anodic dissolution of silver, as recalculated (41). 96,486.57 Koch and Diehl (66), Koch e^ aJ. (68). (a = 4.9 p.p.m.) Iowa State University. 1975, 1976. Titration of 4-aminopyridine. 96,484.56 Cohen and Taylor (28). NBS. 1973. (a = 2.8 p.p.m.) Calculation involving least squares treatment of other physical data.