TN295 .U4 No. 9031 "O. AT ^^VrMTk*" «*> «i *ft^^i,*„ 'TIS /SkT .* .V ./x :.' .*^'*-, • V ■'*.^* ,^ '- "L ' ' ♦' -^^d^ .^^°- • >^"V. '• .^°- O. * , , < o ,0"' ^^ '* ,^^ ^^. *' .♦''♦. '?^^ ^J* o^t •' '=^..*^ .- **"*« ■•.' .,. ^^v --^ .J' "#. •.?^^.' *' ■'* hi" 'V / ." '.•i;;^-\ 0°*.^^^.% ,**.C^.\ <.°*.i^^.'\ /.-i.;^.*-?, /.i^^Jl."^ \ >•' V ;-• ,e.°-n..J-^;^,.^°-, -.« ^»^^^"^^ ^^^^" ^^^% °-w^*" /\ '.^K*" ^^'V • .o-n*. '. >"'^^. \ <<•. c*^ ^V- . . "^ * o « o ■■ <; -i-*^ c^k^feC!. -^ 'e^ A^" *>^^/):^„ %. j^^ - ° ^^^^ "'JiR': '^^'^^ «^W%t -^^^ » '. -t. ^v^o^ " V^ •'.»<'..,. .v°'" -"*"-•. ■'■^' r* A /X *' °^ .'^^ /! 'bV "oV" -X ".o^V.-.^o r* A *. .« .-^wv. ^^^^' •^^ ^° '^i:-. °^ a^^ ...., ^^ .•*' »! • X.^* •'^■- *W* .-^te": %.<*^ ." I': *W* /°- 0^ oo""*^^© %, v.^^^ ^^-n^. •^v^^^ c^^. ;•' ^0^ ^^ 'I .^*^°- .,% ^* r^0 .^^\ > V x/ **^% 3' *, I,'-. ■%.,^'' ' •o "Pa a"* ft? ^A <^ . ■'/> \ *bv" *^'. V ^ >. c-^' ^^^9^^ .^^'V V ^ -^^0^ 0^ .r^% ^^ -01.-' m^ , N o « '0/ **'% •j^ & ♦J i^r-^ """ v^" •- ^' ^'-^.^ nV V r *i ' .*' =ef>. ^<5' •n^-o* o V * .^' ^^-n^ ,*^% V -^^0^ '-> '- v^* .....\ ^V" ^v^' J^ 9031 Bureau of Mines Information Circular/1985 Computer Program for Calculating Gravimetric Primary Standard Gas Mixtures By Ernest W. Loya UNITED STATES DEPARTMENT OF THE INTERIOR ,T5J 'V/NES 75TH AV*^ Information Circular 9031 Computer Program for Calculating Gravimetric Primary Standard Gas Mixtures By Ernest W. Loya UNITED STATES DEPARTMENT OF THE INTERIOR Donald Paul Hodel, Secretary BUREAU OF MINES Robert C. Norton, Director TV! 0.^9 Library of Congress Cataloging in Publication Data: Loya, Ernest W Computer program for calculating gravimet ric primary standard gas mixtures. (Information circular /United States Department of the Interior, Bu- reau of Mines ; 9031) Bibliography: p. 7-8. Supt. of Docs, no.: I 28.27:9031, 1. Gases— Analysis— Computer programs. I. Title. 11. Series: Infor- mation circular (United States. Bureau of Mines) ; 9031. TN295.U4 [QD121] 622s [544'. 4] 85-600064 4 O CONTENTS ^ Page 1 ""■v^ Abstract 1 /^introduction 2 r^ Acknowledgments 2 VJ Method of calculation 2 Buoyancy correction 2 Final composition 3 Standard error 4 Program description 6 Input 6 Output 7 References 7 Appendix A. — Computer program listing for PRISTD 9 Appendix B. — Flow chart for computer program PRISTD 17 Appendix C, — Sample calculation of gravimetric primary standard mixture 30 Appendix D. — Nomenclature 34 UNIT OF MEASURE ABBREVIATIONS USED IN THIS REPORT °c degree Celsius kg kilogram g gram mg milligram g/mL gram per milliliter mL milliliter g mol gram mole mm Hg millimeter of mercury K kelvin % percent COMPUTER PROGRAM FOR CALCULATING GRAVIMETRIC PRIMARY STANDARD GAS MIXTURES By Ernest W. Loya ^ ABSTRACT The Bureau of Mines has developed a computer program for calculating the composition of gravimetric primary standard gas mixtures. The For- tran IV program applies corrections due to buoyancy variations of the cylinder and inaccuracies of the balance weights. The program also de- termines the statistical error due to the sensitivity and precision of the balance and applies the analytical error of the weighed gases. Chemist, Helium Field Operations, Bureau of Mines, Amarillo, TX. INTRODUCTION This report describes a computer pro- gram developed to determine the content and associated statistical error of grav- imetric gaseous mixtures prepared by the Bureau of Mines. In the production of helium, the Bureau uses the primary stan- dard mixtures to calibrate analytical in- struments, determine their accuracy and verify their precision. Previous reports have dealt primarily with mixture preparation techniques and descriptions of the calculation procedure (1-2). 2 Subsequently, computer technol- ogy has permitted the performance of com- putations with higher efficiency and ac- curacy. The algorithm was developed to improve the quality and accuracy of the standard mixtures and to relieve the ana- lyst from the tedious mathematical mani- pulations required. The program is written in Fortran IV for a computer with 64,000 bytes of core and auxiliary disk storage. A cathode ray tube (CRT) terminal is used to enter the input data. The output is printed on a 600-line-per-minute printer. ACKNOWLEDGMENTS The author extends his appreciation to Betty A, Lowe, chemist. Helium Field Op- erations, for her invaluable assistance and suggestions in modifying and prepar- ing the computer program. Recognition is also given to Marvin L. Burfield, a form- er employee, for developing the algorithm and writing the original program. METHOD OF CALCULATION The following equations are utilized in the program to determine the buoyancy correction, final composition of the mix- ture, and standard error (standard devia- tion of the mean) (3^). BUOYANCY CORRECTION The buoyancy correction is calculated for each cylinder weighing. Buoyancy is the product of ambient air density and volume of the cylinder. The correction is determined from the difference of the buoyancies due to the cylinder and the utilized weights, as shown by the following: B = D^V, DwVw, (1) where B = buoyancy correction, g. density of air in balance weighing chamber chamber), g/mL, cylinder volume, mL, (upper ^Underlined numbers in parentheses re- fer to items in the list of references preceding the appendixes. and D^ = density of air in balance weight chamber, (lower cham- ber), g/mL, V^ = volume of utilized weights, mL. Air density is the sum of the densities of ambient dry air and water vapor. Den- sity, as given below, is determined from temperature, relative humidity, and baro- metric pressure measurements obtained from bimetal centigrade thermometers, direct-reading hygrometers, and a mercu- rial barometer, respectively. D = (M^/Vj„)(Tg/T)[(F - RVp)/Pg] + (M„/V^)(Tg/T)(RVp/Pg), (2) where D = density of ambient air, g/mL, M^ = molecular weight^ of air, g, P = barometric pressure, ram Hg, ^Reference to molecular weight, atomic weight, and moles in this report are in gram units, i.e., molecular weight refers to gram-molecular weight, etc. R = relative humidity, Vp = vapor pressure of water, mm Hg. Tg = Standard absolute tempera- ture, K, M^ = molecular weight of water, g, Vj^ = molar volume of ideal gas at standard conditions, mL, and N = total number of added gases. Moles of each component are the quo- tient of the mass added of component i from each gas j and the molecular or atomic weight of component i, as given by the following: Mi,j = Gi^j/Y, (5) where G^^ ^ = mass of component i in gas J, g, Pg = standard barometric pressure, mm Hg, and T = absolute temperature, K, Vapor pressure of water is determined from an empirical approximation of the Clausius-Clapeyron equation, which cor- relates the variation of vapor pressure with temperature (4-5). and T (3) where Vp = vapor pressure of water, mm Hg, A = -5305.041903, K, C = 20.96094276, constant of integration, and T = absolute temperature, K. FINAL COMPOSITION Yj^ = molecular or atomic weight of component i, g. Mass of added component i in gas j is the product of the weight fraction for component i and mass of added gas j, as given by the following: • = F- W- (6) where F^ = weight fraction of component and W^ = mass of gas j , g. Weight fraction of component i per gas j is determined from the following equations: 12 Fi = ^i/.Z^Zi, Zi = XiYi (7) (8) where Xj^ = mole fraction of component i in gas j , The final composition in mole fraction of each component is the quotient of the total moles of a component and the total moles of att components in alt added gases. N N 12 Ci =.E M. j/_E E Mi j, 3 = 1 '-■ j = li=l '-" (4) where C^ = mole fraction of compo- nent i, M^ • = moles of component i in gas j , g mol. and YjL = molecular weight or atomic weight of component i, g. Mass of gas j is the difference of the average mass determinations of the cylin- der in the applicable weighing sessions k and k + 1, as given by the following: ^1 - %+1 ~ hi (9) where R-^ = average mass of cylinder for weighing session k, g. and k + 1 average raass of cylinder for weighing session k + 1, g. Average mass of the cylinder for a weighing session is the quotient of the sum of the mass determinations and the number of determinations as given by the following: N N i^l^i' (10) and mass determination i for weighing session k, g, total number of mass deter- minations of cylinder for weighing session k. Each mass determination is the algebra- ic sum of the average balance zero value, the determined buoyancy correction, and the corresponding correction factor due to the inaccuracies of the balance weights with the nominal mass measurement of the cylinder, as shown below: standard error of each weighing session. The following description begins with the equation for mole fraction standard error. The variables and data required for each equation are presented. Mole fraction standard error for each component is calculated from propagation of error combinations of the standard errors due to the precision variance of the balance and analysis error of the gases. Standard error is the square root of the standard error variance, as given by the following: where ^c. -''V' (12) 12 12 S2 = (1/.^ M. )^{S2 [(.^ M. ) - M. ]2 i=l i i=l 1 12 -"fi^iSiSi>-=iiJ. (13) mole fraction standard er- ror of component i. Ri = R^ - [(Zj. + Z^+i)/2] + B + F, (11) where R^. = nominal mass measurement of the cylinder, g, Zj. = balance zero measurement, g, B = buoyancy correction, g, and F = balance weights inaccuracy correction factor, g, STANDARD ERROR The following describes the statistical error determination (mole fraction stan- dard error) for each component. Final error variations are calculated from two sources: the precision variation (stan- dard error) of the balance and the ana- lytical error determined for each compo- nent of the gases. The program calcu- lates the mean, standard deviation, and standard error for each weighing session. Analytical errors are entered and statis- tically combined with the calculated and Mi = total moles of component i, g mol. >j^j = standard error of Mi , g i mol. The standard error of the total moles of component i is the error propagation combination of the standard error of the total mass added of component i and the molecular or atomic weight standard er- ror. However, the standard error for the molecular or atomic weight is compara- tively small and is considered zero, the expression for s2 is simplified as shown Mi in equation 16 below. S2 = (S2 /y2) + (g2s2 /YJ) , d^) 1 Y-i 1 Mi ^ Gi i since \ = 0. then ^^i = VI (15) (16) and 1 mass of component i, g, = standard error for the mo- lecular or atomic weight of component i, g, of component i, g. Standard error for total mass of compo- nent i is a summation of the standard er- rors determined for the mass added of component i per gas j , as given by the following: 'I (17) Zi = XiYi (20) where X^ = mole fraction of component i in gas j . Yj^ = molecular or atomic weight of component i, g, and S2 = standard error of Z^ , i The standard error of Z^ is determined from the error propagation combination of the standard error of the mole fraction of component i in gas j and the molecular or atomic weight standard error. How- ever, since S^ =0 (see equation 15), then S2 is reduced to equation 22 as ^i shown below: where Sq = standard' error for mass i'j of component i in gas j. The standard error for mass of conq)0- nent i in gas j is determined by the fol- lowing expression: S2 = s2 W? + f2s2 , (18) i/D where Sp = weight fraction standard i error for component i, S2 = y2s2 + X2s2 , (21) ^ , X A . 1 I . Ill 'I'^W' (22) ^ fraction of component i in gas j, and Sy = standard error for the mo- i lecular or atomic weight of component i, g. W^ = mass of gas j, g, F^ = weight fraction of compo- nent i. and St.7 = standard error for mass of ^ gas j, g. The standard error for the mass of gas j is calculated from the error propaga- tion of the average mass of the cylinder determined in weighing sessions k and k+1, as given by the following: S2 = si + s2 (23) Weight fraction standard error for com- ponent i is calculated from the following equations (6): where S^ = standard error for average ^ mass of cylinder for weighing session k, g. 12 12 S2 = (1/ Z Z.)4(s2 [( z z.) - Z.]2 F i=i 1 Z i=i 1 1 + Z2[( E%2 ) _ s2 )]}, (19) 1 1=1 \ \ and S^ = standard error for aver- ^"•"^ age mass of cylinder for weighing session k+1, g. Standard error for the mass of the cyl- inder is calculated from the following: S2 = .^(R - R.)2/N(N - 1) R^ 1=1 k X (24) Rj^ = mass determination i of cyl- inder for weighing session k, g. where R^^ = average mass of cylinder for and N = total number of mass deter- weighing session k, g, minations of cylinder for weighing session k. PROGRAM DESCRIPTION Item 3a-3g: Item 4a-4c: The program, labeled PRISTD, is written Item 1: to use double precision floating-point arithmetic to perform all calculations. Dimension statements limit the number of gas additions to six and the number of Item 2: weighing sessions and weighings per ses- sion to seven. The computation deter- mines the mole fraction for a maximum of 12 components. Atomic and molecular weights for the nine normally utilized components appear in the program. A max- imum of three additional components and their associated atomic or molecular weights may be entered as required. The input data is coded on specifically pre- pared data sheets and entered by use of a CRT terminal. Requisite computation data are recorded from instrumentation used in the prepara- tion of the standard mixtures. All the II. weight determination data are acquired from a high-capacity, substitution-type balance. Buoyancy variations are deter- mined by computing air density and the external volumes of the cylinder and uti- lized weights. Air density is computed from data gathered by measuring the following ambi- ent conditions: temperature, relative humidity, and barometric pressure. The external cylinder volume is determined by a gravimetric measurement of water dis- placement. The volume of the weights is calculated from density data supplied by the manufacturer. The computer program listing for PRISTD is given in appendix A and flow chart is illustrated in appendix B. Identifying information, maximum of 66 alphanu- meric characters, 66A1 format. Number of weighing ses- sions specified in in- teger numbers, II format. Number of weighings per session specified in integer numbers, II format. Chemical symbol and mo- lecular weights of ad- ditional optional com- ponents specified in alphanumeric and real numbers, A4 and FIG.G format, respectively. Mass and buoyancy determination data recorded for each weighing. Item 1 Item 2; Item 3: Item 4; Item 5: INPUT The following describes the tered using a CRT terminal. I. Program identification and parameters. input en- control Item 6: Weight readings, speci- fied in real numbers, FIG.G format. Zero balance readings specified in real num- bers, F1G,G format. Temperature readings re- quired for correction of mercurial barometer readings specified in real numbers, F1G,G format. Barometric pressure readings specified in real numbers, F1G,G format. Relative humidity read- ing of balance upper chamber specified in real numbers, F10,G format. Relative humidity read- ing in balance lower chamber specified in real numbers, FIO.O format. Item 7: Temperature reading in balance upper chamber specified in real num- bers, FIO.O format. Item 8: Temperature reading in balance lower chamber specified in real num- bers, FIO.O format. Item 9: Displacement volume measurement of cylin- der specified in inte- ger numbers, 110 format. Item 10: Counterbalance weight of cylinder specified in integer numbers, 110 format. III. Composition data of the gases in mole fraction and respective error deviation are entered for the following components: helium, hydrogen, neon, nitrogen, methane, oxygen, argon, carbon dioxide, helium-3, and a maximum of three additional optional components. Each of these data items are specified in real numbers, D20.10 format, OUTPUT A previously composed heading (INPUT, I, Item 1:, see page 6) is printed at the top of the initial and final output pages. Subsequent to the initial head- ing, all the entered input is printed al- lowing for verification and reference. The printed calculated results are listed in the next column. I, Computation of interim values and buoyancy correction A, Barometric pressure in real num- bers, 8F10.3 format. B, Vapor pressure of water in bal- ance upper chamber in real num- bers, 8F10.3 format. C, Vapor pressure of water in bal- ance lower chamber in real num- bers, 8F10.3 format, D, Air density upper chamber in real numbers, 3E12,5 format, E, Air density lower chamber in real numbers, 3E12,5 format, F, Buoyancy of cylinder in real numbers, 3E12,5 format, II, Computation of cylinder mass A, Mass of cylinder (after applic- ation of all corrections and zero value subtraction) in real numbers, 8F10,4 format, B, Average mass of cylinder for weighing session in real num- bers, F10,4 format, III, Computation of final results A. Previously composed heading (INPUT, I, Item 1:, see page 6) printed in alphanumeric char- acters, 66A1 format, B, The final calculated results are printed in five columns labeled "CONCENTRATION, STANDARD ERROR, RELATIVE ERROR, MOLE FRACTION, and STANDARD ERROR" for each component. All the values are in real numbers with formats of F15,5, F15,5, F15,5, E16,10, and E16,10, Sample output data are demonstrated in appendix C of this report. REFERENCES 1, Loya, E, W, , C, A, Seitz, and D, E, Emerson, Gravimetric Preparation of Pri- mary Standard Gas Mixtures in the Parts Per Trillion Range. BuMines RI 8643, 1982, 4 pp. 2. Miller, J. E., A. J. Carroll, and D. E. Emerson. Preparation of Primary Standard Gas Mixtures for Analytical In- struments, BuMines RI 6674, 1965, 10 pp. 3, Barford, N, C, Experimental Mea- surements: Precision, Error, and Truth, Addis on-Wes ley (London), 1967, pp, 35- 37, 4. National Research Council of the United States of America, International Critical Tables of Numerical Data, Phys- ics, Chemistry and Technology, McGraw- Hill, V, III, Isted,, 1928, pp, 210- 212, 5. Prutton, C. F., and S. H. Maron, Fundamental Principles of Physical Chem- istry. Macraillan, 1951, pp. 91-95. 6. Meyer, S. L. Data Analysis for Scientists and Engineers. Wiley, 1975, pp. 39-48. 7. Brombacher, W. G. , D. P. Johnson, and J. L. Cross. Mercury Barometers and Manometers, U.S. Dep. Commerce, NBS Mono- graph 8, May 20, 1960, pp. 4, 27-28, 33. 8. Dalton, B. J. Local Value of Ac- celeration of Gravity at the Helium Research Center (Potsdam System). Helium 43, April Res. Center Memorandum Rep, 1964, 13 pp.; available from Helium Field Operations library, Amarillo, TX. 9. CRC Press. CRC Handbook of Chem- istry and Physics, Cleveland, OH, 57th ed., 1976, 2390 pp. 10. McCracken, D. D. A Guide to For- tran IV Programing. Wiley, 2d ed. , 1972, 288 pp. APPENDIX A. —COMPUTER PROGRAM LISTING FOR PRISTD. PROGRAM CALCULATES COMPOSITION AND ERROR OF GRAVIMETRIC PRIMARY STANDARD GAS MIXTURES c* * C* PRISTD ♦ C* * (;**♦♦♦*♦**♦♦****♦*♦♦*♦*******♦**************♦**************♦********** C C *** THIS PROGRAM CALCULATES THE MOLE FRACTION, STAMDi\RD ERROR, AMP C *** RELATIVE ERROR FOR NINE COMPONENTS - He H2 Nf N? CH'+ 02 C *** AR C02 HE3 - OF GRAVIMETRIC STANDARD MIXTURES PREPARED C *** BY SECTION OF TECHNICAL AND ANALYTICAL SERVICES. OPTION TO C *** DETEpyilNE THE RESULTS FOR THREE ADDITIONAL COMPONEMTS IS C *** PROVIDED. C C****************************** SECTION A it*************************** c C *** SECTION A SPECIFIES AND ASSIGNS VARIABLES AND MOST OF THE C *** CONSTANTS USED IN THE PROGRAM. C REAL M INTEGER COMPID,DaTaOK,WW,VC DOUBLE PRECISION A »C ♦ M , S ,CA iCB »CC ,CD ,CG tCT, Z , RELERR , * AIJtWY,XfXY,Y,ZCfCON»TO,RHWtAWC»BY,TB, * DC«DWtDWS«FM,H,RHC«S2Fl>'fS2W,S2WF»S2WGtS2WK» * S2WY,S2XY,SLIMWY,SUMXY,SUSPWK,SUS2WY,SUS2XY»SX,Tc» * TW»VPC«\/PW,Kl«WC,WF,WG,WK«WSlfWS2»WS.^,WS^ DIMENSION WSl(ll) ,WS2(10) ,US3(10) tWStdO) , IHF AD ( 66 ) » JJ ( 8 ) , * H(7) ,RHC(7) ,PHW(7) tTCC?) fTW(7) ,VPC(7) » VPW ( 7 ) , WC( 7 ) » * ZC(8) »S2WG{8) fWY(l?),AWC(e),DWS(3)tW(8) ,S^'-I(8) , * WG(8) »y(8»l2) ,SX(e,l2) ,FM(12) ,Y(l2) »TB{^) » * S2WY(12),S2FM{12) ,SUS2WK(12) ,C0MplD(l2) ,RELERR(12) DATA A,C,S/-530 5.0m90 3,20,g609t276,1.8'+E-5/» * CA,CB,CC,CD/1.81tm01E-4,7.0l6E-9,2.8625E-ll,2,617E-m/, * WSl, WS2, WS3,WS4/0... 0185 t. 017 i.OSMt.O^lt, . 0636 ,. 0707, . 0802 » * .1042,. 1185,. 1 318,. 0,. 0021,, 0016,. 00^7,. 00 76,. 0099,. OlOf, * .0121, .0108, .0131, .0,-. 0001, -. 0002 ,-, OOOl ,-. 0002 ,-. 0005 , * . 0007, -.0008,, 0019,. 00 2?,. 0,-. 0001, -.000«|,-. 0007, -.0002, * -.0004, -,0004,. 0003,. 0007,. 000 3/, * COhPID/'HE* , •H2» ,»NE* , •N2' ,»CH4« , •02',«AR« ,*C02» ,'HE3» , * » » , » ♦ , » ♦ / Yd) = 4,0026 Y(2) = 2,01594 Y{?) = 20.183 Y(4) = 28.0134 Y(5) = 16.04303 Y(6) = 31.9908 Y{7) = 39.948 Y(8) = 44.00995 Y(9) = 3,0160 T0=273.15 C0N = 273 .15/(22413, 83*760 . ) c *** THEAD c *** MAXI c *** JJ c *** CnMPID c **♦ Y c 10 ion CONTINUE c C*****************************NOTE ***♦*****♦♦*♦******♦*********♦**♦*♦ C *♦* ALL CONSOLE ENTERED INPUT DATA MUST BE PrEcEDED BY TWO BLANK C *** SPACES, THIS IS NEEDED FOR THE DATA TO COINCIDE WITH THE FIELD C *♦* DESCRIPTOR INSTRUCTIONS OF THE READ FORMAT STATEMENTS. THIS C **♦ REQUIREMENT WAS ESTABLISHED TO ADAPT THE PROGRAM FOR USE WITH THE C *♦♦ PERKIN-ELMER DATA SYSTEMS MODEL llOO TERMINAL, C C****************************** SECTION B **************************** c C *** SECTION B REQUESTS INPUT DATA FOR THE FOLLOWING! COMPOSED HEADING NUMBER OF WEIGHING SESSIONS NUMBER OF WEIGHINGS PER SESSION CHEMICAL SYMBOL FOR ADDITIONAL COmPONENT(S) ATOMIC OR MOLECULAR WEIGHT FOR ADDITIONAL COMPONENT(S) WRITE(2»3000) READ(2t3001) (IHEaD(I) f 1=1 ♦66) 200 WRITE(2«3002) READ(2.3039)MAXI IF(MAXI.LE,7,AND.MAXI,GE.l) GO TO 101 WRITE(2»3003) GO TO 200 101 CONTINUE DO 102 I=1,MAXI WRITE(2t300H) READ(2«3039) JJ(I) 102 CONTINUE 103 CONTINUE DO lot J=10tl2 WRITE(2»3005) RFAD(2t30 37)COMPTD( J) WRITE(2«3006) READ(2»3012)Y(J) lOU CONTINUE WRITE(2.3007) READ(2»300a)DATAoK IF(DATAOK.GT,0) GO TO 103 DO 105 J=l,12 SUS2WK{ J)=0 S2WY(J)=0. WY(J)=0 105 CONTINUE SnMWY=0 WG(1)=0 S?WG(1)=0 WRITE(3,3038) WRITE(3t30 0l) (IHEAD(I) .1=1*66) WRITE (3*3018) MAX It ( JJ(I) » 1 = 1 « MAX I) WRITE (3* 30 09) (COMPID(J) ,J=10tl2) WRITE(3»3010) (Y( J) .J=10,12) 11 c *** **♦ *** *** *** *** *** *** *** *** »** *♦* *** ♦ ♦4c *** **♦ *** *** *** *♦* *** *** *** *** *** *** *** *** »♦♦ *** ***************************************************************** ************************* SECTION C ***************************** 10 201 20? 203 SECTION EACH WEI WC - ZC - TB - H - RHC - RHW - TC - TW - VC - WW - VPC - VPW - X - sx - DWS DC DU BY AWC S2W WG S2WG XY S2XY SIIS2XY SUMXY WF WK WY SUMWY S2WF S2WK SIIS2WK C REQUESTS iNPuT DATA AIMQ/OR CALCULATES THE FOLLOWING FOR GHING session; - BALANCE WEIGHT MEASUREMENTS S CaLC. MaSS OF CYLINDER - BALANCE ZERO READINGS - BAROMETER TEMPERATURES - BAROMETER READINGS X CALC BAROMETRIC PRESSURES - RELATIVE HUMIDITIES OF BALANCE UPPER CHAMBER - RELATIVE HUMIDITIES OF BALANCE lOwEP CHAMBER - TEMPERATURES OF BALANCE UPPER CHAMBER - TEMPERATURES OF BALANCE LOWER CHAMBER - WEIGHING CYLINDER DISPLACEMENT VOLUME - COUNTER BALANCE WEIGHT - CaLC. H20 VAPOR PRESSURES OF BALANCE UPPER CHAMBER - CALC. H20 VAPOR PRESSURES OF BALANCE LOWER CHAMBER - MOLE FRACTION OF COMPONENT J - ERROR DEVIATION OF X - CALC. CORRECTION FOR INACCURACY OF BALANCE WEIGHTS - CALC. AIR DENSITIES OF BALANCE UPPER CHAMBER - CALC. AIR DENSITIES OF BALANCE LOwER CHAMBER BUOYANCY CORRECTIONS AVERAGE MASS OF CYLINDER VARIANCE OF AWC CALC CALC CALC CALC CALC CALC CALC CALC CALC CALC CALC MASS OF GAS VARIANCE OF WG WEIGHT OF COMPONENT J VARIANCE OF XY SUMMATION OF S2XY»S SUMMATION OF XY»S WEIGHT FRACTION Op COMPONENT J MASS OF COMPONENT J CALC. MOLES OF COMPONENT J CALC. SUMMATION OF WY'S CALC. VARIANCE OF WF FOR COMPONENT J CALC. VARIANCE OF WK FOR COMPONENT J CALC. SUMMATION OF S2WK»s DO 113 I=1»MAXI IJ=JJ(I) IJ1=IJ+1 AIJ=IJ WRTTE(2,3020) WRITE(2»3011) READ(2»3012) (WC( J) f J=ltIJ) WRITE(2»3007) RFAD(2»3008)DATAOK IF(DATAOK.GT,0) GO TO 201 WRITE(2»3021) WRITE{2»3011) READ(2t3012) ( ZC ( J ) « J=l » I Jl ) WRITE(2»3007) RFAD(2«3008)DATAOK IF(DATAOK.GT,0) GO TO 202 WRITE(2»3031) 12 WRITE(2.3011) RE'AD(2»30l2)(TB(J)»J=liIJ) WRITE(2»3007) RFAD(2f3008)DATAOK IF(DATAOK.GT,0) GO TO 203 20U WRITE(2t3022) WRITE(2»3011) RE AD (2. 30 12) (H(J)»J=1«IJ) WRITE(2»3007) READ<2i3008)DATAOK irCDATAOK.GT.O) GO TO 20«f 205 WRITE(2.3025) U'RITE(2»3011) READ (2 t 3012) (RHC( J) ♦J=1«IJ) WRITE(2«3007) READ(2»3008)DATAOK IF(DATAOK.GT,0) GO TO 205 20A WRITE(2«3026) WRITE(2»3011) READ(2i3012) (RHW(J) «J=1«IJ) WRITE(2»3007) READ(2t3008)DATAOK IF(DATAOK.GT,0) GO TO 206 207 WRITE(2t3023) WRITE(2»3011) READ (2*30 12) (TC ( J ) » J=l t I J ) WRITE(2t3007) READ(2»3008)DATAOK IF(DATAOK.GT,0) GO TO 207 20fl WRITE(2»302H) WRITE(2t3011) READ (2*3012) ( TW ( J ) » J=l » I J ) WRITE(2f3007) READ(2t3008)DATAoK IF(DATAOK.GT,0) GO TO 208 209 WRTTE(2»3013) READ(2»30«+0)VC WRITE{2f3007) RFAD(2i3008)DATAOK IF(DATAOK.GT,0) GO TO 209 2in WRITE(2»301H) READ(2»30^0)WW IF(WW,GE,1) GO TO 106 WRITE(2»3035) GO TO 210 106 CONTINUE WRITE(2»3007) READ(2«3008)DATAOK IF(DATAOK.GT.O) GO TO 210 WRITE(3»3019)I WRITE (3 ♦3020) (WC(J) »J=1»IJ) WRITE(3.3n2l) (ZC( J) »J=l»IJl) WRITE(3«3022) (H( J) tJ=l»IJ) DO 107 J=1«IJ M=CA+CB*TB(J)+CC*TB(J)**2+CD*TB{J)**3 CG=,001280764*H( J) 13 CTr( (M-S)*TB(J) ) / ( 1+ ( M*TB ( J ) ) )*H{J) H(J)=H(J)-CT-CG 2=A/(TC(J)+T0)+C VPC(J)=DEXP(Z) Z=A/(TW(J)+TO)+C VPW(J)=DEXP{Z) 107 CONTINUE WRITE(3»3031) (TB(J) »J=1«IJ) WRITE(3.3032) (H(J)«J=1«IJ) WRITE(3»3023) (TC(J) »J=1«IJ) WRITE(3t302H) (TW(J) tJslf IJ) WRITE(3»3025) (RHC(J) »J=1»IJ) WRITE (3f 3026) (RHW(J) »J=1»IJ) WRITE{3»3027) (VPC{J) tJ=l»IJ) WRITE {3» 3028) (VPW(J) «J=ltIJ) WRITE(3t3029)VCtWW IF(I-I) 11,11,211 211 WRITE(2»3015) WRITE(2«3016) READ (2. 3012) ( X (I t J ) ♦ J=l « 12 ) WPITE(2t3007) READ(2f3008)DATAOK IF(DATAOK.GT,0) GO TO 211 212 WRITE<2«3017) WRITE{2f30l6) READ (2*30*^2) (SX(I»J)»J=1«12) WRITE(2»3007) READ(2»3008)DATAOK IF(DATAOK.GT,0) GO TO 212 11 AWC(I)=0 I5 = WW 11=15/1000 I2=(I5-I1*1000)/100 13= ( 15-11*1000-12*100 )/l0 14= (15-11*1000-12*100-13*10) DWS(I)=WSl(Il+l)+WS2(I2+l)+WS3(l3+l)+WSH{Tm-l) DO 108 J=1,IJ DC=(CON/(TC(J)-»-TO) )*( {28,9646*H(J) ) - ( 10 .S'^gS* ( V/PC ( J ) *RHC ( J) ) ) ) DW=(CON/(TW(J)+TO) )*( (28.96'*6*H(J) ) - (10 .9^93* ( VPW ( J ) ♦RHW( J) ) ) ) BY=DC*VC-DW*WW/7.93 WRITE(3f3034)DC»DW»BY WC(J)=(WC( J)-(ZC( J)+ZC( J+1) )/2.0D0+BY)+DwS(I) AWC(I)=AWC(I)+WC(J)/AIJ lOfl CONTINUE WRITE(3f5033) (WC(J) «J=1,IJ) W(I)=AWC(I) WRITE(3»3036)W(I) IF(I.GT.l) *WRITE(3«3030) (C0|«1PID(J) « X ( I » J) «SX ( I « J ) « J=l » 12) S2W(I)=0 DO 109 J=1,IJ S2W(I)=S2W(I) + (AUIC(I)-WC(J) )**2/(AlJ*(AlJ-1.0D0) ) 109 CONTINUE IF(I-I) 112»112»12 12 WG(I)=W(I)-W(I-1) S2WG(I)=S2W(I)+S2W(I-1) 14 1.1 SIJS2XY=0 SllMXY = DO 110 J=l,12 S?yY=(Y(J)*SX(I»J) )**2 S1JS2XY=SUS2XY + S2XY SUMXY=SUMXY+X(I«J)*Y( J) lin COMTINUE DO ill J=lfl2 XY=X(I.J)*Y(J) WF=XY/SUMXY S2XY={Y(J)*SX(I«J))**2 WK=WF*WG( I) IF(Y(J)) m»15,l4 m WY(J)=WY(J)+WK/Y(J) SUMWY = SUMWY + WK/Y(sJ) Ifi S?WF=(S2XY*(SUMXY-XY)**2+XY**2*(SUS2XY.S2XY) )/SUMXY**H S2WK=S2WF*WG(I)**2+S2WG(I)*WF**2 SUS2WK(J)=SUS2WK(J)+S2WK 111 CONTINUE IIP CONTINUE 11.1 CONTINUE C C********************************* ***************************** ******* C*»*4c**********************«*** SECTION D **************************** C C *** SECTION D CALCULATES AND INSTRUCTS PRINTER TO wRiTE THE FOLLOWING: C *** FM - MOLE FRACTION OF COMPONENT J C *** S2FM - VARIANCE AND STANDARD ERROR OF FM FOR COMPONENT J C *** RELERR - RELATIVE ERROR OF FM FOR COMPONENT J C WRITE(3i3038) WRITE(3«300l)IHEAD SUS2WY=0 DO ll*t J=l,12 IF(Y(J)) I6»im»16 16 S2WY(J)=SUS2WK(J)/Y(J)**2 SIJS2WY=SUS2WY + S2WY(d) 114 CONTINUE DO 115 J=1,12 FM(J)=WY(J)/SUMWY S?FM(J) = (.S2WY(J)*(SUMWY-WY(J) ) **2+WY ( J ) **2* ( SUS2WY-S2WY ( J ) ) )/SuMWY S?FM(J)=DSQRT(S2FM(J) ) llfi CONTINUE WRITE(3»30U1) DO 116 J=l,12 IF(FM(J),LE.O.ODO) GO TO 116 RFLERR(J)=S2FM(J)/FM(J) IF{FM(J).GE.1.0D-03) *WRITE(3»30H3)COMPIO(J) »FM{J) ♦S2FM(J) »ReLeRR ( J ) .FM ( J ) .S2FM(J) IF(FM(J).LT.1.0D-03.AND.FM(J),GE.1.0D-06) *WRITE(3»304'+)C0MPID(J).FM(J)»S2FM(J) .RELeRR ( J ) .FM ( J ) , S2FM ( J ) IF(FM(J).LT.1.0D-06.AND.FM(J).GE.1.0D-09) *WRITE(3»30if5)COMPlD(J) ,FM(J) .S2FM(J) fRELERR(J) . FM ( J ) . S2FW ( J ) IF(FM( J) .LT.1.0D-09.AND.FM(J) •G£,1.0D-12) *WRITE(3.30H6)COMPID( J) .FM( J) ♦S2FM( J) «RpLeRp{J) .FM(J) .S2FM(J) 15 IF(FM(J).LT.1.0D-12) *WRITE:(3»30U7)C0MPID(J) .FM(J) fS2FM(J) «RFLFRR(J) «FH(J) ,S2FM(J) lift CONTINUE 3000 FORMATdX,* ENTER HEADING OF STANDARD 66 CHARACTERS ARE ALLOWED* ) 3001 FnRMAT(66Al) 300? FORMATdX.'O/ ENTER NUMBER OF WEIGHING SESSIONS') 3003 FORMAT( 'O'tTC »** ERROR •) //»T10 • t LIMITS FOR "NUMBER 0F»» *♦ WEIGHING SESSIONS" EXCEEDED* »//♦ IX . 7 (• ** ERRoR •)) 3004 FORMAT(1X,»0/ ENTER NUMBER OF WEIGHINGS') 300^ FORMATdXi '0000/ ENTER SYMBOL OF ADDITIONAL COMPONENT') 300A FORMATdXt '0000000000,/ ENTER COMPONENT MnLECuLAR WFIGHT') 3007 F0RMAT('7?IS DATA OK ?? YES/RETURN--NO ENtER 1') 300fl F0RMAT(I3) 3009 FORMAK/' SYMBOL OF ADDITIONAL COMPONENTS ' «flX f 3 ( llX » fltf ) ) 3010 FORMAT(/' MOLECULAR WEIGHTS OF ADDITIONAL COMPONENTS ', 3( 5X»F10,6 ) ) 3011 FORMAT(1X,»00000000./ ENTER DATA REQUESTED AT CRT') 301? FORMAT<2X,F10,0) 3013 FORMATdX.'OOOO/ ENTER VOLUME OF CYLINDER') 3014 FORMATdX.'OOOO/ ENTER WEIGHT OF COUNTER BALANCE') 301R FORMATC ENTER MOLE FRACTION OF K') 3016 FORMATdX, '0000000000,000000000/ ENTER DaTa REQUESTED ♦) 3017 FORMATC ENTER ERROR IN MOLE FRACTION') 301fl FORMAT( 'ONUMBER OF WEIGHING SESSIONS = ',I3/' NUMBER OF WEIGHINGS *PER SESSION = ' tl0l3) 3019 FORMATCOFOR WEIGHING SESSION NUMBER ',12*' !') 3020 FORMATC CYLINDER WEIGHT READINGS 'tSFlCa) 3021 FORMATC ZERO READINGS »,8F10,3) 302? FORMATC BAROMETER READINGS •f8FlO,3) 3023 FORMATC TEMPERATURES OF UPPER CHAMBER ♦t8Fl0,2) 302U FORMATC TEMPERATURES OF LOWER CHAMBER »,8F10,2) 3025 FORMATC HUMIDITIES OF UPPER CHAMBER '.SFlO.S) 3026 FORMATC HUMIDITIES OF LOWER CHAMBER '.8F10.3) 3027 FORMATC VAPOR PRESSURES OF UPPER CHAMBER »»8F10.3) 302fl FORMATC VAPOR PRESSURES OF LOWER CHAMBER 'tSFlCS) 3029 FORMATC VOLUME OF CYLINDER X WEIGHT Op COUNTER BALANCE '♦ I9» HO ) 3030 FORMATC MOLE FRACTION AND STD. DEV. OF COMPONENTS IN ADDED GASV *3X.2(A*f.'= 'iE15.9C SD= '.E15.9C 2 ')/, *3X.2(A4«'= '.ElS.g.' SD= '»E15.9C 1 ')/» *3X.?(AH»'= ',E15.9.' SD= 'fE15.9C 3 ')/, *3X,2(A4C= 'fElS.g.' SD= 'iE15.9C 3 ')/, *3X,2(A4.'= ',E15.9,' SD= '»E15.9C 1 •)/» *3X.2(A4»'= '«E15.9C SD= 'fE15.9,' 3 ')) 3031 FORMATC BAROMETER TEMPERATURES '»8F10,2) 303? FORMATC CORRECTED PRESSURES •♦8F10,3) 3033 FORMATC MASS OF CYLINDER ♦♦SFlCH) 3034 FORMAT ( ' DC DW BY » t 3E3 2.5) 303«> FORMAT( '0' .7C**FRR0R ')//T20.' WW-NOT GlVpN • , // » IX » 7 C **ERR0R ')) 3036 FORMATC AVERAGE OF CYLINDER MASSES •♦F10.<+) 3037 F0RMAT(2X»A*t) 303fl FORMATdHl/) 3039 F0RMAT{2X.I1) 3040 F0RMAT(2Xd't) 3041 FORMAT (//.35X» • STANDARD ' dOX » ' RELATIVE • dOX » 'MOLE' . lAXC STANDARD ' / *1?X» 'CONCENTRATION' d IX. 'ERROR' »13X. 'ERROR' » lOX t 'FRACTION' . *17X« 'ERROR' ) 3042 FORMAT(2X.D20,10) 16 SO'*.-^ FORMAK 'O' ,3X,A^, 2PF15.5»' % *, 2PF15.5.' % S 2PF15,5»» « <• * ,0PE16.10» • ) • »«SX» M • fOPEie.lO* • ) • ) 30tft| FDRMAK •0» ♦3X»A'+. 6PF15.5»» PPM», 6PF15.5»» PP^lN 2PF15.5»» SB (• * ,0PE16.10»M»»f5Xt»'(» ♦0PE16.10f ♦ ) • ) 30tt«S FORMAK 'O* ,3X.A4, 9PF15.5»» PPB», 9PF15,5»» PPR'» 2PFl5.5.» 55 (• * .0PE16.10* • ) ♦ »5X» M • »0PE16,10» » ) • ) 304^ FnRMAK 'O* ,3X«A*+,12PF15,5»» PPT • , 12PF15 .5 ♦ • PPtS 2PF15.5t» % (• * ,0PE16.10» ♦ ) • »5Xt • ( • »0PE16.10» • ) • ) 3047 FnRMAK 'O' ,3X,A1,5Xf lPEl5.9f5X«lPEl5,9,2pFl3.5,» % (• *.0PE16.10t» ) • t5X, M ♦tOPE16.10f • )♦) WRITE(2.30'+8) 304ft FORMAT(lXt«0/ ?7 ANOTHER CALCULATION ?? YES/ENTER 1--N0/RETURN* ) READ(2«3039) LOOP IF(L00P,GE,1) GO TO 100 999 STOP END /* 17 APPENDIX B.— FLOW CHART FOR COMPUTER PROGRAM PRISTD Program calculates compositions and error of gravimetric primary standard gas mixtures. Section A: Specifies and assigns variables and most of the constants used in the program. ( START J I REAL; I^f^EGER; DOUBLE PRECISION variables specified: M; COMPID, DATAOK, WW, VC; A, C, M, S, CA, CB, CC, CD, CO, CT, Z, RELERR, AI J , WY, X, XY , Y, ZC, CON, TO, RHW, AWC, BY, TB, DC, DW, DWS , FM, H, RHC , S2FM, S2W, S2WF, S2WG, S2WK, S2WY, S2XY, SUMWY, SUMXY , SUS2WK, SUS2WY, SUS2XY, SX, TC, TW, VPC, VPW, W, WC, WF, WG, WK, WSl, WS2, WS3, WS4 I DIMENSION of arrays specified: WSl(ll), WS2(10), WS3(10), WS4(10), IHEAD(66), JJ(8), H(7), RHC(7), RHW(7), TC(7), TW(7), VPC(7), VPW(7), WC(7), ZC(8), S2WG(8), WY(12), AWC(8), DWS(8), W(8), S2W(8), WG(8), X(8,12), SX(8,12), FM(12), Y(12), TB(8), S2WY(12), S2FM(12), SUS2WK(12), C0MPID(.12), RELERR(12) I Data for following constants specified: A, C, S, CA, CB, CC, CD, WSl, WS2, WS3, WS4, COMPID I DATA FOR yd) thru y(9) assigned I TO AND CON ASSIGNED 18 Section B: Requests input data for the following; IHEAD, MAXI, JJ, COMPID, Y. /^ ^ / Read com- N 100 j W posed head- V y \ ing (IHEAD) 'Read maxi- mum number of weighing sessions (MAXI) I Read number of weighings per / / session (JJ) / V Read symbol (s) and molecular weight(s) of additional component (s) s Assign; SUS2WK(J)=0 S2WY(J)=0 WY(J)=0 for J- 1.2. . 12 s Assign: SUMWY=0 WG(1)=0 S2WG(1)=0 5 Write: IHEAD, MAXI, symbol (s) and molecular weight(s) of additional com- ponent (s)j. W Section) 19 Section C: Requests input data and/or calculates the following for each weighing session: WC , ZC, TB , H, RHC , RJ-IVJ, TC , TW VC, WW, VPC, VPW, X, SX, DVJS, DC, DW, BY, AWC , S2W, WG, S2v^G, XY, S2XY, SUS2XY, SUMXY, WF , \K, WY, SUtWY, S2WF, S2WK, and SUS2WK. Read data for weighing session: WC - Balance weight measurements ZC - Balance zero readings TB - Barometer temperature readings H Barometer readings RHC - Relative humidities, balance upper chamber RHW - Relative humidities, balance lower chamber TC - Temperature upper chamber TW - Temperature lower chamber VC - Weighing cylinder displacement volume WW - Counterbalance weight Read WW - counterbalance weight -[> Write error statement — C/210J SL Write input data: weighing session I, WC(J) ZG(J), H(J) 20 Section C, continued; ± J - 1,2, ...,IJ (IJ = JJ(I)) I Calculate Barometric Pressure, H(J): M = CA + CB * TB(J) + CC * TB(J)**2 + CD * TB(J)**3 CO = 0.001280764 * H(J) CT = ((M-S) * TB(J))/(H-(M * TB(J))) * H(J) H(J) = H(J) - CT - CG I Calculate Vapor Pressure of Water for upper chamber, VPC (J); and lower chamber VPW(J) Z = A/(TC(J) + TO) + C VPC(J) = DEXP(Z) Z = A/(TW(J) + TO) + C VPW(J) = DEXP(Z) I J = J+1 £^ No Write input data, TB(J), TC(J), TW(J), RHC(J), RHW(J). For J =- 1,2, ...,JJ Write calculated values H(J), VPC(J) VPW(J), For J - 1.2, .JJ 1 Write input data VC and WW. 21 Section C, continued: 'Read mole fraction of components in weighed gas, X(I,.J); for J = 1.2 12 I 'Read error deviation of X, SX (I, J) for J - 1,2, ...,12 I Assign average mass of cylinder AWC(I) = 0, and 15 = WW I Calculate error propagation of WF(J) for component J, S2WF: S2WF = (S2XY * (SUMXY - XY)**2+XY**2 * (SUS2XY - S2XY))/SUMXY**4 I 26 Section C, continued i Calculate error propagation of product WF * WG(I), S2WK: S2WK = S2WF * WG(I)**2 + S2WG(I) * WF**2 5 Calculate summation of error of grams of component J,SUS2WK(J): SUS2WK(J)= SUS2WK(J) + S2WK 27 Section D: Calculates and instructs printer to write the following: inole fraction of each component (FM) , standard error, and relative error for each FM. Write IHEAD at top of page. ^ Assign: SUSWY = 5 I J - 1.2,...,12| Calculate summation of error of coraponent J, S2WY(J): S2l^(J) =SUS2WK(J)/Y(J)**2 5: Calculate summation of error of all components, SUS2l^rY: SUS2WY = SUS2WY + S2^^rY(J) 28 Section D, continued; i J =« 1.2 12 5 Calculate total mole fraction of component J, FM(J): FM(J) = WY(J)/SUm/Y I ^^M> S2FM(J) RELERR(J), _ V >» Mu^ 1/ p„(j)^ S2FM(J), Write: COMPID(J), FM(J), S2FM(J), RELERR(J), FM(J), S2FM(J), % range -^ Write: COMPID(J), FM(J) ppm range ^> Write: COMPID(J), FM(J) jvJS2FM(J), RELERR(J),L_r>^ "^ FM(J), S2FM(J), ■'^ ppb range ^ Write: COMPID(J), FM(J), S2FM(J), RELERR(J) FM(J), S2FM(J), ppt range -> Write: COMPID(J), FM(J), S2FM(J), JxJ RELERR(J), FM(J), Ijv, ^S2FM(J), ' '^ Exponential Notation 30 APPENDIX C. —SAMPLE CALCULATION OF GRAVIMETRIC PRIMARY STANDARD MIXTURE The following data were obtained for a methane-in-nitrogen mixture blended to contain approximately 3% methane. Three weighing sessions consisting of three weighings each were conducted. Inclusion of the chemical symbols and molecular weights for three additional components, ethane, propane, and isopentane, was nec- essary. The external cylinder volume was previously determined gravimetrically by a water displacement procedure. Purity of the gases was determined by analyses of the 12 listed components. Requisite computation data for the gravimetric mixture were obtained and recorded from various instruments. The weight and mass determination data were acquired from a high-capacity (12-kg) substitution balance sensitive to ±1 mg. Temperature, relative humidity, and bar- ometric pressure data were obtained from bimetal centigrade thermometers accurate to ±0.3° C, direct-reading hygrometers accurate to ±1.5%, and a mercurial ba- rometer accurate to ±0,05 mm Hg, respectively. Sample Input I, Program identification and control parameters. Item 1 (composed heading, IHEAD) : S-374, CYL, No, H-84846, 3% CH4 IN N2, 12/14/1979 Item 2 (No. of weighing sessions, MAXI): 3 Item 3 (No, of weighings per ses- sion, JJ(I)): 3 3 3 Item 4 (additional component chem- ical symbol and molecular or atomic weight, COMPID and (Y(J)): C2H6 30,07012 C3H8 44,09721 I-C5 72.15139 II, Mass and buoyancy determination data for each weighing. Session 1 Session 2 Session 3 ITEM 1 (WEIGHT READINGS, WC(J) , g) 4333,484 4342,566 4779,617 4333,486 4342,578 4779,629 4333,487 4342,592 4779,635 ITEM 2 (ZERO BALANCE READINGS, ZC(J), g) 0,355 0,416 0.487 ,359 ,428 .500 .363 .435 .504 .367 .447 .508 ITEM 3 (BAROMETER TEMPERATURE READINGS, TB(J), °C) 20.5 22.3 22.8 20.5 22.5 23.0 20.6 22.7 23.1 ITEM 4 (BAROMETRIC PRESSURE READINGS, H(J), mm Hg) 676.95 675.85 674.80 676.90 675.80 674.70 676.85 675.85 674.60 ITEM 5 (RELATIVE HUMIDITY READINGS OF BALANCE UPPER CHAMBER, RHC(J)) 0.190 0.175 0,185 .195 .185 .195 .200 ,195 .200 ITEM 6 (RELATIVE HUMIDITY READINGS OF BALANCE LOWER CHAMBER, RHW(J)) 0.125 0.130 0.130 ,125 .130 .135 .125 .130 .135 ITEM 7 (TEMPERATURE READINGS IN BALANCE UPPER CHAMBER, TC(J), °C) 21.6 22.6 23.7 21.6 22.7 23,7 21.6 22.8 23,8 ITEM 8 (TEMPERATURE READING IN BALANCE LOWER CHAMBER, TW(J), °C) 20,5 20.5 20.6 21.3 21.4 21.4 21.9 22.0 22.0 ITEM 9 (DISPLACEMENT VOLUME MEASUREMENT OF CYLINDER, VC, mL) 4220 J 4220 1 4220 ITEM 10 (COUNTERBALANCE CYLINDER, WW, g) WEIGHT OF 4333 1 4342 1 4779 III. Composition data of gases, 31 Mole fraction | Standard error Mole fraction | Standard error Methane Nitrogen He 0.00005 .00005 .00005 .00080 .995550 .00005 .00010 .00005 .0 .002300 .00080 .00020 0.00005 .00005 .00005 .00005 .000165 .00005 .00005 .00005 .0 .000069 .00005 .00005 0.000002 .0000012 .0000047 .99952 .00005 .000026 .00020 .00005 .0 .00005 .00005 .00005 0.000002 H2 .0000012 NE .0000047 N2 .00013 CH4 .00005 02 .000026 AR .00005 C02 .00005 He3 .0 C2H6 .00005 C3H8 I-C5 .00005 .00005 32 NO. H-84ei|6. 358 CHH IM N2, 12/14/1979 numrer of weighing sessions = 3 niimrer of ijeighings per session = 3 symrol of additional components molfciilar weights pf additional components CPH6 30.n70l?0 C3H8 141*, 097210 I-C5 72.l5i390 FOR WEIGHING SESSION MUMBER 1 : CYLINDER WEIGHT READIriGS il333.'»fi'+ 4333. Hfl6 4333. H87 ZERO RFAPTNGS 0.3 = 5 0.359 0.363 0.367 BAROMETER READINGS 676.950 676.900 676,850 BAROMETER TEMPERATURES 20.50 20.50 20.60 CORRECTED PRESSURES 673.8?7 673.777 673.716 TEMPERATURES OF UPPER CHAMBER 21.60 21.60 21.60 TEMPERATURES OF LOWER CHAMBER 20.50 20.50 20.60 HUMIDITIES OF UPPER CHAMBER 0.190 0,195 0.200 HUMIDITIES OF LOWER CHAMBER 0.125 0.125 0.125 VAPOR PRESSURES OF UPPER CHAMBER 19.346 19.3*16 19.3H6 VAPOR PRESSURES OF LOWER CHAMBER IS.OflS 18.085 18.196 VOLUME OF CYLINDER X WEIGHT OF COUNTER BALANCE tjSPO U333 DC DW RY 0.105q6F-02 0.106H«tE-02 0.38a99E + 01 DC nw RY 0.10595F-02 0.106t3E-02 0.38893E + 01 DC DW BY 0.10593E-02 0.10639E-02 0.388fl9E + 01 MASS OF CYLINDER t337.0722 "+337.0696 '♦337.0662 Average of cylinder masses 4337.0693 FOR weighing session NUMBER 2 : CYLINDER WEIGHT READINGS 4342.566 4342.578 4342.592 ZERO READINGS 0.416 0.428 0.435 0.447 BAROMETER REAniNGS 675.650 675.800 675.850 BARnMETER TEMPERATURES 22.30 22.50 22.70 CORRECTED PRESSURES 672.534 672.463 672.491 TEMPERATURES OF UPPER CHAMBER 22.60 22.70 22.80 TEMPERATURES OF LOWER CHAMBER 21.30 21.40 21.40 HUMIDITIES OF UPPER CHAMBER 0.175 0.185 0.195 HUMIDITIES OF LOWER CHAMBER 0.130 0.130 0.130 VAPnR PRESSURES OF UPPER CHAMBER 20.560 20.685 20.811 VAPnR PRESSURES OF LOwER CHAMBER 18.994 19.111 19.111 VOLUME OF CYLINDER X WEIGHT OF COUNTER BALANCE 4220 4342 DC DW RY 0.10540F-02 0.10593E-02 0.38679E + 01 DC.....DW BY 0.10534F-02 0.10589E-02 0.38656E + 01 DC nw BY 0.10530E-n2 0.10589E-02 0.38637E + 01 MASS OF CYLINDER 4?546.o674 4^46.0676 4346.0702 AVERAGE OF CYLINDER MASSES 4346.0684 MOLE FRACTION AND STD. DEV. OF COMPONENTS I^: aDDED GAS HE = 0.500000000E-04 SD= . 500000000E-04 D H? = . 500000000E-04 S0= . 500000000E-04 IMF = 0.500000000E-P4 SD= . 500000000E-04 3 N? = .flOOOOOOOOE-03 SD= . 500000000E-04 CH4 = 0.995550000E+00 SD= . 165000000E-03 D 0? = . 500n00000E-04 SD= .500000000E-04 AR = O.lOOOOOOOOE-03 SD= . 500000000E-04 D Co2 = . 5n0O0000OE-04 SD= . 500000000E-04 HE3 = O.OOOOOOOOOE+00 SD= . OOOOOOOOOE+00 ] C?H6= . 230000000E-02 SD= .690000000E-04 C3Hfl= 0.80000nOOOE-03 SD= . 500000000E-04 3 I-C5= . 2O0n00000E-03 Sn= 0.500000000E-04 FOR WEIGHING SESSION NUMBER 3 ! CYLINDER WEIGHT READINGS 4779.617 4779.629 4 ZERO READINGS 0.4«7 0.500 BAROMETER READINGS 674.800 674.700 BAROMETER TEMPERATURES 2?.fl0 23.00 CORRECTED PRESSURES 671.435 671.314 TEMPERATURES OF UPPER CHAMBER 23.70 23.70 TEMPERATURES OF LOWER CHAMBER 21.90 22.00 HUMIDITIES OF UPPER CHAMBER 0.1fl5 0.195 HUMIDITIES OF LOWER CHAMBER 0.130 0.135 VAPOR PRESSURES OF UPPER CHAMBER..,.. 21.973 21.973 VAPOR PRESSURES OF LOwER CHAMBER 19.703 19.824 VOLUME OF CYLINDER S, WEIGHT OF COUNTER BALANCE 4220 4779 DC DW BY 0.104fllE-02 0.10554E-n DC nw RY 0.1 0478*- -02 0.1054 8E-0 DC nw RY 0.10472t-02 0.10546E-0 MASS OF CYLINDER 4782.97^5 47fl2.9760 47 AVERAGE OF CYLINDER MASSES 4782. 97$1 MOLE FRACTION AND STD. DEV. OF COMPONENTS IN ADnED GAS HF = n.20000000nE-05 SD= 0.200POOOOOE-05 D H9 = . 1?OOOOOOOE-05 NF = n.47000nOOOE-05 SD= n.470000000E-05 3 N? = . 999520000E+00 Ch4 = 0.5n0000000E-04 SD= . 5O0nO00OOE-04 : 0? = 0.260000000E-04 AR = 0.200000000E-n3 SD= . 500000000E-04 3 Co2 = .500000000E-04 HE3 = O.OOOOOnOOOE+nO SD= O.OOOnOOOOnE+00 3 C2H6= 0.5nOOOOOOOE-04 C3Hfi= 0.500000000E-P4 SD= . 500000000E-04 3 I-C5= . 5nOOOOOOOE-04 779.635 0.504 0. 674.600 23.10 671.203 23.80 22.00 0.200 0,135 22.106 19.824 2 0.37870E+01 2 0.37860E+01 2 0.37836E+01 82,9756 SD= 0,120000000E-05 SD= 0.130000000E-03 SD= 0.260000000E-04 SD= 0.500000000E-04 SD= 0.500000000E-04 SD= 0.500000000^-04 S-S?"*. CYL. NO. H-84846. 3!S CH4 IN N2, 12/14/1979 33 COMCENTRflTlON STANDARD ERROR relative: ERROR HOLE FRACTION STANDARD ERROR HE 3.65886 PPM 2.59115 PPM 70.91865 % (0.3658857826E-05) (0.2591153849E-05) H2 2.88651 PPH 2.08040 PPM 75.07309 % (0.?886508594E-05) (0.20a0395965E-05) NE 6.26554 PPM 4.85536 PPM 77.49309 « (0.6265536484E-05) (0.4855358091E-05) m2 96.50008 % 0.01179 % n.01?22 % (0.9650007781E+00) (0.1179197625E-03) rHu 3.tt5t? % 0.00494 % 0.14325 % (0.3t454l761lE-01) (0.4935671702E-04) n2 26.82933 PPM 25.15933 PPM 93.77?45 X (0.?68293347aE-04) (0.2515932828E-04) flR 196.54328 PPM 48.27952 PPM 24.56432 56 (0.)965432775E-03) (0.4e27552233E-04) r02 1+9.99981 PPM 48.29654 PPM 96.59344 % (0.4999981174E-04) (0.4e29653585E-04) C2Hf, 127.75913 PPM 48.32145 PPH 37.82231 % (0.1277591253E-03) (0.4832144626E-04) r3Hfl 75.91958 PPM 48.29515 PPH 63.61356 % (0.7591958294E-04) (0.4829515294E-04) i-cs 55.1P377 PPM 48.29382 PPH 87.51454 % (0,5518376598E-04) (0.4829381626E-04) 34 APPENDIX D. —NOMENCLATURE AWC(I) Definition Constant In the vapor pressure of water determination. Program control parameter, equal to number of weighing measurements per weighing session. Average mass of cylinder for a weighing session, equa- tion 10. BY C CA OB CC CD CG COMPID(J) CON CT DATAOK Buoyancy correction factor, equation 1. Constant In the vapor pressure of water determination. Constant In the mean coefficient of cubical expansion of mercury determination (7). Constant In the mean coefficient of cubical expansion of mercury determination (7^). Constant In the mean coefficient of cubical expansion of mercury determination (_7 ) . Constant In the mean coefficient of cubical expansion of mercury determination (_7 ) , Acceleration of gravity correction factor (8^), Program alphanumeric array of chemical symbols for nine normally used components. Factor to correct density of air to standard conditions. Factor to correct barometric pressure measurement for temperature variations. General expression for determination of air density, equation 2, Program control parameter to correct data entry errors DC DW DWS(I) FM(J) Density of air determination In balance upper chamber. Density of air determination In balance lower chamber. Factor to correct cylinder mass measurements for Inac- curacies of utilized balance weights. Mole fraction determination for a component In the final mixture, equation 4, 35 Fortran Symbol Text Symbol Definition H(J) P Barometric pressure measurement. 11 Program parameter equal to quantity of utilized kilo- gram balance weights in a mass measurement. 12 Program parameter equal to quantity of utilized hecto- gram balance weights in a mass measurement. 13 Program parameter equal to quantity of utilized deka- gram balance weights in a mass measurement. 14 15 Program parameter equal to quantity of utilized gram balance weights in a mass measurement. Program parameter equal to nominal mass measurement of cylinder. IHEAD(I) Program parameter equal to composed alphanumeric head- ing of program composed by user. IJl Program parameter equal to quantity of balance zero measurements per a weighing session. IJ JJ(I) LOOP Program parameter equal to quantity of cylinder mass measurements per a weighing session. Program parameter equal to quantity of cylinder mass measurements per a weighing session. Program control parameter required to initiate a sub- sequent calculation. Mean coefficient of cubic thermal expansion of mercury determination (2^). Molecular weight of air. MAXI Program parameter equal to quantity of weighing sessions. Molecular weight of water. Barometric pressure at standard conditions, RELERR(J) RHC(J) RHW(J) Mole fraction relative error determination of a component. Relative humidity measurement in balance upper chamber. Relative humidity measurement in balance lower chamber. 36 Fortran Sjonbol Text Symbol Definition S Linear coefficient of thermal expansion of the barom- eter scale. S2FM(J) 'I Mole fraction standard error variance determination of a component in the final mixture, equation 13. SUMWY N 12 E IK 3=1 1=1 -' i»3 Summation of moles for all components in all weighed gases. SUMXY 12 Summation of products of mole fraction content and re- spective atomic or molecular weight of all components in a weighed gas. SUS2WK(J) % Total mass standard error variance determination of component in the final mixture, equation 17. SUS2WY i=l Mi Summation of standard error variance of total moles for all components in the final mixture. SUS2XY E S2 1=1 Zi Summation of standard error variance of products of mole fraction content and respective atomic or molec- ular weight of all components in the weighed gas. S2WF Si Weight fraction standard error variance determination of a component in the weighed gas, equation 19. S2WG(I) S2 S2W(I) %+1 S2W(I-1) % S2WK %. S2WY(J) % Mass standard error variance determination of a weigh- ed gas, equation 23. Mass standard error variance determination of the cyl- inder for next weighing session, equation 24. Mass standard error variance determination of the cyl- inder for a weighing session, equation 24. Mass standard error variance determination of a compo- nent in the weighed gas, equation 18. Total moles standard error variance determination of a component in the final mixture, equation 16. SX(I,J) Sx. Analytical standard error of a component in the weigh- ed gas. S2XY Product of mole fraction content and respective atomic or molecular weight standard error variance determin- ation of a component in the weighed gas, equation 22. 37 Fortran Symbol Text Symbol TB(J) TC(J) T TW(J) T TO T. VC V, VPC(J) Vp VPW(J) Vp Vw WC(J) % WC(J) \ WF Fi WG(I) Wj W(I) ^+1 W(I-l) \ WK WS1(I1+1) WS2(12+1) WS3(I3+1) 'lO Definition Atomic or molecular weight standard error variance of a component in the weighed gas. Ambient room temperature measurement. Temperature measurement in balance upper chamber. Temperature measurement in balance lower chamber. Temperature conversion factor, "C to K. Cylinder displacement volume measurement. Molar volume of ideal gas at standard conditions. Vapor pressure of water determination for balance upper chamber, equation 3. Vapor pressure of water determination for balance lower chamber, equation 3. Volume of utilized weights determination. Mass determination of cylinder, equation 11. Nominal mass measurement of the cylinder. Weight fraction determination of a component in the weighed gas, equation 7. Mass determination of the weighed gas, equation 9. Average mass determination of the cylinder for a weighing session, equation 10. Average mass determination of the cylinder for a previous weighing session, equation 10. Mass determination for a component in the weighed gas, equation 6. Program parameter equal to accumulated correction fac- tors of utilized kilogram balance weights in a mass measurement . Program parameter equal to accumulated correction fac- tors of utilized hectogram balance weights in a mass measurement . Program parameter equal to accumulated correction fac- tors of utilized dekagram balance weights in a mass measurement . 38 Fortran S3aabol WS4(I4+1) WW Text Symbol WY(J) ^i,j WY(J) Mi X(I,J) Xi Definition Program parameter equal to accumulated correction fac- tors of utilized gram balance weights in a mass measurement . Nominal mass measurement value truncated to the near- est gram. Moles of a component in the weighed gas, equation 5. Total moles of a component in the final mixture. Mole fraction content of a component in the weighed XY Yd) Y(2) Y(3) Y(4) Y(5) Y(6) Y(7) Y(8) Y(9) Y(J) Z ZC(J) ZC(J+1) 'r+1 Product of mole fraction content and atomic or molec- ular weight of a component in the weighed gas , equa- tion 8 and 20. Atomic weight of helium. Molecular weight of hydrogen. Atomic weight of neon. Molecular weight of nitrogen. Molecular weight of methane. Molecular weight of oxygen. Atomic weight of argon. Molecular weight of carbon dioxide. Atomic weight of helium-3. Atomic or molecular weight of additional components. Natural logrithm determination of vapor pressure of water calculation. Balance zero measurement. Next balance zero measurement. T!rU.S. GPO: 1985-505-019/20,082 IT.-BU.OF MINES,PGH.,PA. 28032 D DD 2 Q- O Q O O sr^i." f Q 5 - — O «i n in - 2" 3 -^ ^ ;c 3 Q Q — -I- « !±: to — Q -1 O- n (t> 3 t/i (I H -I 2 ± O o 5> m o X o ^0" ': -^^^^ ^ .>V^\ \^' ;a^-/ %,.*■ •■ V /\ • ■^^. : ^^^'^^^ ^^le; A'^^^ \ 4;-' vV^^* ^ ^ '^V' '^> "ir %?< "; ^*^°- o V "^Mr.*\-^i«i^X./ /Mfe^ ><..*^ .-^^C^". V^** /Jfe-v %/ 4 r^.'* '^ «^c 5"^. ••/'-..-•. "oV Ao^ ^^ ^-^..^^' ;aK^ ^^..^^ .«i^^o -^.^/^ /^g. \/ ; ,/% >;- '.- .-!••' °-. ^^^^. ,v V. 'i.> '«. v^^ ;* .o'5 ^"-"cK ,4q ^^-n^. Ao, ^,* -^^ ^* %/^^' ^^^>. °; .^ <^^^ >*"^'s:^.....V"^'^^.^.>:' / aK ^\ "^-^..^^ *^^ V •>,^<>' %, «^ q. ,% 'e^ A^ ' /^Va". '\ J" ♦^^^iK'. 'e. A^ ' ^'^ ^j^«b^ •^^^^ rZ:^s'^:€.y,><^-y.^^:^:/.^^^^ \,^^ .1>\ •7* ^^-n.. .^^"o, ^. '.mm, ^^'\ o, V.>* :^i£', *v.s*' ••• ^rfX * o - o ' O. V ^^\ ^ .% '^ ^ " ^^ ^^-^. ^Mr.'i o > ^ ^0 ^^'% ^^^^v :, ■3^. 'bV" ,^^ > V ^^-n^. . .*^"*. 5- Vk '.^ili^" .^^^'^