Precision of Mass Spectrometer Analyses of Carbureted Water Gas WILLIAM VOLK Hydrocarbon Research Inc., Trenton,
N. J.
Data on mass spectronieter analyses obtained b) the National Bureau of Standards in 1950 habe been analjzed statistically for the components of withinlaborator) precisions. About 5Oqc of the within-laborator) \arialice conies froni the spectrometer, the calculators contribute an insignificant amount, operators contribute about 3070, and the balance of the variance is unaccounted for. The within-laboratory mass spectrometer precisions are better than similar precisions by chemical analysis, while between-laboratory checks by mass spectrometer are not as good as similar checks by chemical analysis. The analysis of variance technique used for the precision calculations can be used for other stepwise analj tical procedures to find the different components of the variance.
T
HE Sat,ional Bureau of Standards has published ( 5 ) the
results of cooperative mass spectrometer analyses by 27 laboratories of a standard sample of carbureted water gas. These result,s were obtained prior to May 1080; thus improvements in precision of mass spectrometer analysis which have occurred in the past 4 years are not reflected in this statistical Btudy. However, it, is felt that. a statistical study of these data is of value in providing an indication of the precisions then obtained, and of indicating a method of analyzing similar data. h recent publication ( 1 ) of a similar cooperative study of mass spectromet'er analyses of C1-C4 hydrocarbons made in Great Britain showed precisions similar to those reported here. This paper undert,akes to review the Bureau of St,andards data for the purposes of: determining the wit,hin-laboratory precision of mass spectromet,er analyses; determining the between-laboratory precisions; determining the principal sources of imprecision in the mass spectrometer operation; and presenting an example which a laboratory can readily follow to check its own mass spectrometer analysis precisione. h description of the gas sample together with a complete summary of the analgses is given in the original report ( 5 ) . An earlier report (4)by the same organization describes the procedure followed in making u p the sample and the bureau's recommendations and instructions to the cooperating la,boratories. Briefly, the laboratories cooperating in the mass spectrometer analysis checks were asked to have two operators each make tvio spectrograms of the gas sample and then to have two calculators each compute the gas analyses from the four spectrograms. The design of the analytical procedure provides a basis for determining not only the precision with which a laboratory checks itself, but the contribution of the calculators, the operators, and the mass spectrometer to t,he imprecision.
.z = the arithmetic mean = the number of observation of r The square of the estimated standard deviation is the estimated variance :
n
~ ( 0 . 0 5x, )
- .Ep
- n-1
=
=t2s(z)
hlt,hough rigorouslg t,he coefficient of the standard deviation for establishing the precision varies with t'he quant.ity of data involved, for the work reported here, twice the standard deviation errs only on the side of optimism. The precision is t'he range within d i c h the true value can be espected to be a t the probahilit,y level selected (95%) when t,he same factors are operating as applied during the collection of the data analyzed. The precisions in all cases refer to a single determination and are the ranges x-ithin which these data indicate a single mass spectrometer determination probably lies. I n ot,her words, a laboratory obtaining a carbon dioxide concentration of 4.5y0for one analysis of carbureted water gas can reliably stat.e that the true value lies within 4.5 i 0.270, when thc precision is reported as P(0.05) r ) = 1 0 . 2 . The between-laboratory precisions have been computed in the same manner a s t'he within-laboratory precisions, with the assumption that the different laboratories represent random saniples whose averages are normally and independently distributed. This figure would have real meaning if a chemist had to deal with component analyses made up from unidentified laboratories. However the beheen-laboratory variances present, an inkresting if only hypothetically useful figure. The probability level selected for all tests in this work is the 95% level. The Significance of variance differences and the criteria for pooling variances arc taken as established if statistical tests indicate that surh values could be expect,ed to occur by chance less than 5 % of t,he time. An example of the calculat'ion of the variance components is given at, the end of thip paper. ANALYTICAL RESULTS
The principal components of the gas analyzed were carbon dioxide, nitrogen, hydrogen, carbon monoxide, methane, ethane, arid ethylene. Several laboratories reported small amounts of other components as follom: Components CzH2
STATISTICAL METHODS
The measure of dispersion of the data is the estimated standard deviation, s(z), where
Z(z
-
It is t,he variance of a system that can be analyzed for component contributions, and can be subjected to tests for statistical significance. The analysis of variance, as illustrated below, provides a method for det,ermining est.imates of the different contributions to the observed variance of the data. The total variance has been estimated from the sum of the individual component variances, and this variance was used to estimate the precision of the measurements. The precisions are taken as twice the st,andard deviations:
0 2
This paper is not intended as a contribution to statistical theory, but is rather offered as an example of the application of statistical analysis to available data in order to understand better the precision of laboratory measurements. Detailed discussion of statistics can be found in several good tests on the sub,ject. Snedecor (6) and Brov-nlee ( 2 ) were employed by the author.
*
I).(.[
s*(x) =
c3+
CiHa CaHa CaH3 ClHlO
N o . of Laboratories Reporting
Range of Composition,
12 1 4 4
0.03-0,80 0.10 0.04-0.30 0.01-0.25 0.10-0.50 0.01-0.03 Trace
ii
2
1
70
One laboratory did not report any carbon monoxide in the gas, but obviously ( ? ) included the carbon monoxide as nitrogen in its analysis. This confusion of carbon monoxide and nitrogen was not included in the calculation of the between-laboratory precisions, but was included in the calculation of ivithin-laboratory precision, where the inaccuracy would not affect the statistical calculation. The minor constituents were not included in t!ie statistical study. 1771
ANALYTICAL CHEMISTRY
1772
-
a tenth of the total variance while the operators and/or con CH' CiH6 CzHi spectrograms account for the Over-all mean, z, % 4.5 6.2 34.8 30.4 7.8 3.3 12.8 balance. The data of all the Total precision, p ( 0 . 0 5 , z ) i 0.54 3.46 3.88 5.20 1.54 0.32 1.00 laboratories do not permit a Within-laboratory precision, 0.37 0.20 0.34 ~ ( 0 . 0 5z,) k 0.26 0.99 0.34 0.80 clear differentiation between S e t between-laboratory pre1.14 cision. ~ ( 0 . 0 5I)+ , 0.64 4.02 4.46 5.98 1.78 0.36 the variance due to operators and that due to spectrograms. Analysis of Within-Laboratory Variance 0.0010 0,0001 0,0006 Seven Selected LaboraContribution of calculators 0.0010 0.0196 0,0017 0.0251 Contribution of spectrograms 0,0067 0.0925 0.0494 0.0831 0.0027 0.0058 0.0124 tories. Seven of the cooperat0.0068 0.1110 0.0792 Contribution of operators 0.0425 0.0278 0.0009 0.0118 0.0022 0.0236 0,0055 Residual variance 0.0080 0.0027 0.0033 0.0037 ing laboratories followed the recommended test program and Number of replicate analyses = 138. Number of laboratories = 27. also reported their results in wch a manner that a complete Table 11. Seven Laboratory Results with Eight Analyses Each CHI CzHe CaHi analysis of variance could be cot Nt Hz co 8.0 3.1 13.1 calculated. (An example calOver-all mean, 2 , % 4.6 6.0 34.1 29.8 Total precision, p ( 0 . 0 5 . 2) I 0.29 1.74 1.18 1.97 0.98 0.25 0.58 d a t i o n from this group is Within-laboratory precision, 0.48 0.49 0.53 ~ ( 0 . 0 5z),i 0.27 0.45 0.19 0.29 given a t the end of this report.) S e t between-laboratory pre1.05 0.20 0.62 hlthough these seven labora0.32 1.84 1.23 2.08 cision, p ( 0 . O b , z) 5 tories represent only a fourth .Inalysis of Tithin-Laboratory Variance 0.0000 0.0003 0.0003 of the total number cooper0.0013 0.0001 0.0017 Contribution of calculators 0.0000 0,0424 0,0401 0.0482 Contribution of spectrograms 0.0114 0,0020 0.0061 0.0121 a,ting, their 56 replicate anal0.0065 0.0065 0,0303 Contribution of operators 0.0175 0.0429 0.0014 0.0079 p e s represent a sufficient 0.0006 0,0050 0,0069 0.0026 0.0030 0.0037 Residual variance 0.0083 sample for a reliable estimxte ~of precisions. Tahle I1 gives the variances and precisions The split between carbon monoxide and nitrogen by mass for this group of seven laboratories. A comparison of the total variances for these seven laboratories spectrometer is a difficult analysis because the principal contribuand the variances of the other laboratories with these laboratories. tion of each gas is to the 14 mass peak. The results of several of omitted is shown below together with the standard variance the laboratories were studied with the carbon monoxide and niratio test, F , for the various gas components. trogen analyses combined, but no significant difference in the reported precisions was obtained by pooling these two gases. 7 Labs. 20 Labs. Ratio F(81. 55; Twenty-five cooperating laboratories employed one manufacKO.of Analvses 56 82 20/7 0.05) Total Variance ture of mass spectrometer and two laboratories employed a mass 0,0825 coz 0.0207 3.98 1.52 spectrometer of another manufacture. There was significant 4.2864 K2 0.7563 5.68 1.52 H2 0.3473 5.9516 17.1 1.52 difference between both the average within-laboratory variances co 0.9750 10.0066 10.12 1.52 and the average between-laboratory variances for the two different 0.8619 CHI 0.2393 3.62 1.52 CZH6 0.0162 0.0185 1.14 1.52 makes of equipment. However, the difference in variance be0.2978 CZH4 0.0870 3.41 1.52 tween laboratories using the same equipment was too great to In all cases, except for the ethane analysis, the variance for permit pooling or averaging for purposes of comparison, and the seven laboratories is significantly smaller than for the other therefore no conclusions should be drawn from the differences in laboratories. The reason for this difference cannot be deterequipment. The results from the two laboratories using different mined from the data available. I t is interesting to note, however, types of mass spectrometers are included in the calculation of that the laboratories that were careful enough to foIlow the prethe variances between laboratories, hut are not included in the scribed experimental program were also apparently sufficiently calculation of the within-laboratory variances. more careful in their analytical procedures to produce results No other data are omitted in the calculations that follow. with less variance. If these seven laboratories are taken as STATISTICAL RESULTS typical of the best performancr at the time of the experiment, it can be seen from Table I1 that the within-laboratory precision All Laboratories. Table I gives the over-all mean, the total is A0.2 to iz0.401,units, and the check between laboratories precision for all the data, the within-laboratory precision, and varies from zt0.2 t o zt2.070 units depending on the gas comthe between-laboratory precision. The results shown in Table I ponent. The larger difference between laboratories than within indicate an average within-laboratory precision of from A0.2 laboratories may be in part due to a real difference between the to A0.6% units, and an average check between laboratories gas samples arising from residual gas in the sample vessels and from &0.3 to A5.97, units depending on the gas component. from sampling techniques. Table I also shows the results of the analysis of within-laboratory variance for all the laboratories using the same type of mass PROPOSAL FOR IMPROVING PRECISION spectrometer where sufficient data were available for the calSince the variance between spectrograms is the largest source culations. A number of laboratories did not carry out the full of imprecision, it is obvious that this point offers the most likely experimental program, and some of the data were not suitably place for improvement. The spectrogram variance includes not identified for distribution into operator and calculator categories, only all the vagaries of the instrument and any real difference in In those cases where each operator ran only one spectrogram, gas analyzed arising from outgassing of the sample vessel, hut or where one operator ran two spectrograms and the other opalso the effects of variation of sensitivities from day to day of erator ran only one, it is impossible to differentiate between the the component gases. The data analyzed in this paper were not operator and the spectrogram contribution to the variances. identified according to the time they were taken, so that the dayIn these cases the variance was included in both categories. to-day variations could not be separated. The first step in loA study of the analysis of within-laboratory variance shows cating the source of the spectrogram variance would be to perthat operators and/or spectrograms make the largest contribution form a series of analyses by different operators on the same and to the variance, The unaccounted for variance or residual and different days. An experimental program similar to that enithe contribution of the calculators account for only a third to Table I.
All Laboratory Results5 NZ Hz co
1773
V O L U M E 26, NO. 1 1 , N O V E M B E R 1 9 5 4 plo3wl for these data, but Jvith clifterent days substituted for the different calculators would provide a laboratory with data for establishing whether the principal source of imprecision was in the mass spectrometer it,self or in the daily fluctuation of the component sensitivities. If the principal source of variance was found to be due to time fluctuations in the sensit,ivities, then the precisions could be improved by preceding and/or following analyses with sensitivity determinations; or at least by more frequent determinations depending on the precisions desired. If the principal source of variance was ultimately found to reside in the instrument itself, then short of improving the equipment, any increase in precisioiis would have to come from running analyses in replicate, which, of course, improves the precision by the square root of the number of replicates. The routine use of the mass spectrometer includes sources of variance that were not included in t,he data used for the results presented here. The precisions reported from these dat,a are more nearly idealized minima than practical experience. Laboratories customarily collect gas samples as composites over an inert liquid and then transfer these samples to mass spect,romet,er sample bottles or to :tusiliary transfer vessels and then t o mass spectrometer sample bott,les. Each of these steps is a source of variance that was not present, during the collection of the data investigated here, its the samples analyzed for the Bureau of Standards ivere passecl direct,ly to the mass spectrometer from mples in petroleum laboratories the original sample vessel. G sometimes are scrubbed of carbon dioxide before the mass spectrometer analyses to simplify the spectrogram calculat.ion for light hydrocarbons. The carbon dioxide scrubbing introduces another source of variance. Also the mass spectrometer precisions can be expected to be affected by the number of components in the gas. Any laboratory wishing to establish the precision of its mass spectrometer analyses for routine work should include all such sources of variance in a planned analysis program. An enlargement of the example of the analysis of variance given a t the end of this paper can readily be made to account for each source of error being investigated. COMPARISON WITH CHEMICAL ANALYSES
ence in chemical method. There is in these earlier data information about the difference in variance between different chemical methods of analysis. However, it has not been worked out at this time. Table I11 indicates that the mass spectrometer gives a much better precision within a laboratory. The checks betrveen laboratories, however, is poorer over-all for those using mass spectrometers than’ for those using chemical methods. The better performance between laboratories using chemical methods may be due to the longer history of experience and a more firmly established procedure. The check between the seven laboratories which followed completely the design test program indicates that the mass spectrometer can give as good a check between laboratories as the chemical method, and for hydrocarbons above methane it gives a better check. EXA3lPLE OF ANALYSIS OF VARI4NCE
The following elample is presented as a typical analysis of variance. The form may be folloned with different categories or additional categories if the time factor or sample handling factors for example are included in the study. The category of “calculators” can be eliminated once a laboratorv has established that the variance between calculators is insignificant, as it was for the work presented here. The data in the example are for the nitrogen determination of laboratory 11 in the original Bureau of Standards ( 5 ) tabulation. 0 refers to the operator, S refers to the spectrogram, and C refers to calculator. The original data vvere as follows: Key 6.5 6.7 6.1
6.2 5.9 5,s 6.1 6.1
These data are adjusted by 6.2 to simplify the arithmetic arid retabulated as follows:
C‘ 0.3 -0.1 -0.3 -0.1 -0.2 Prior to the cooperative mass spectrometer analyses, a coopera0 . 4 0 . 1 0.0 0 . 5 c z 0.0 __ ___ tive group of 24 laboratories ran chemical analyses on a similar 2 0 . 8 -0.1 -0.7 -0.2 __ gas for the Bureau of Standards (4). The only difference be-0.9 -0.2 2 0.7 tween the gases analyzed by the two methods was about 0.7% oxygen which was present, in the sample used for chemical analThe sums of the squares of each category are computed directly from the table above. The sums of squares of the deviations ysis but was scrubbed from the sample used for mass spectrometer analysis. The chemical analyses were standard absorpfrom the means of each category (here called the “sum of squares”) are computed simply as illustrated below. Since the tion and combustion methods. They are described in detail in this earlier report. of the Bureau of Standards. The two sets variation between the spectrograms includes any variation beof results wcre subsonuentlv reuorted (,9) in a series of frequency tween operators, the calculation of the “sum of squares” ffir distribution plots. i h l e “theA frequency distribution plots give a graphical cornparison of Table 111. Comparison of M a s s Spectrometer and Chemical Analyses of Carbureted the results, i t is felt that a nuWater Gas merical statistical comparison Over-all Mean, Z cos N2 H2 co CHI C2H6 CZH4 would be of interest. Table I11 Mass spectrometer gives a tabular comparison of 4 . 5 6 . 2 3 4 . 8 3 0 . 3 7 . 8 3 . 3 12 8 All laboratories 8.0 3.1 13.0 4.5 6 .O 35.1 29.8 Selected seven laboratories” the mass spectrometer preciChemical analysesb 4.4 6.3 34.1 29.7 8 6 2.6 13 0 sions with those of the chemical Within-Laboratory Precisions, p ( 0 . 0 5 , 2) analyses. The precisions for Mass spectrometer All laboratories *0.26 0.99 0.34 0.80 0.37 0.20 0 34 the chemical analyses were calSelectedsevenlaboratoriesa f0.27 0.48 0.49 0.53 0.45 0 19 0 29 Chemical analyses =tO.21 1.16 0.96 0.63 1 46 0 89 0 3.5 culated in the same manner as those for the mass spectrometer Between-Laboratory Precisions, ~(0.05, 2) Mass spectrometer analyses. When different All laboratories fO.64 4.02 4.46 5.98 1.78 0.36 1.14 chemical methods were used by Selected seven laboratories” f0 . 3 2 1.84 1.23 2.08 1.05 0.26 0.62 Chemical analyses f0.19 1.14 2.61 1.07 1.37 1.15 1.08 the same laboratory, the preciSee text. a Selected because of the plan followed in obtaining the data not because of high precision. sions were calculated for each b Samples tested, by chemical and mass spectrometer m e d o d s were identical except for about 0 . 7 % oxygen method separately so as toelimwhich was present In the former but sorubbed from the latter. inate any variance due to differ-
1774
ANALYTICAL CHEMISTRY
spectrograms is corrected for the “sum of squares’’ for operators according to the arithmetic example given below.
n
0.005
=
8; Z.C = -0.2;
ZX2 = 0.62
2(X-Z)’
= 0 . 6 2 - 0.005 = 0.615
zc2
Z(C-(?)2
= --
202
=
=
0.04
1 30
Z(0-6)’
(ZZ)’/~=
0.04 4
1 30 4
= ---
- 0.005
-0
005
Degrees of Freedoin 1 2 1
3
Sum of Squares
= 0.005
=
0 320
Mean Square 0.0050 0.1325 0.3200
0.005 0.265 0 320 0 028
0 0083
The mean square tabulated values are estimates of the following variances, where the variance is designated s*: Mean Square Calculators Spectrograms Operators Residual
Variance Estimated (calculator) 8 2 (resid ) 2s2 (spec ) s2 (resid.) 492 (opr.) 292 (spec.) 8 2 (resid ) s 2 (resid ) 452
+ ++
(calculator) = 0 , 0 0 0 0 a* (spec.) = 0.0621 s2 (opr.) = 0.0469 s2 (resid.) = 0,0083 0.1173 52
The analysis of variance is most simply given by another table as follows: Source of Variance Calculators Spectrograms Operators Residual
From these relations the estimated variances are now coniputed:
+
Before carrying out the calculation of the estimated variances, the mean squares are tested for significant difference from the residual mean square by the standard F test for variance ratios. I n the illustrat.ive example both the spectrogram and operators mean squares are significantly larger than the residual mean square and therefore j ust’ify calculation of the individual variances. LITERATURE CITED
(1) Blears, J., and Waldron, J. D., J . Inst. Petroleum, 40, 1-6 (19543. (2) Brownlee, K. -4., “Industrial Experimentation,” 4th ed., London, H.M. Stationery Office, 1949. (3) Shepherd, Martin, AKAL.CHEM.,22, 885 (1950). (4) Shepherd, Martin, Natl. Bur. Standards (TJ.S.),Research P a p e r
R P 1740 (March 1946). (5) Ibid., R P 2098 (May 1950). (6) Snedecor, G. W., “Statistical Methods,” 4th ed., arnes, Iowa, Iowa State College Press, 1946.
RECEIVED for review August 3, 1953. Accepted August 12, 1951
Determination of Trace Amounts of Iron, Nickel, and Vanadium on Catalysts by Fluorescent X-Ray Spectrography G. V. DYROFF and PAUL SKIBA Esso Laboratories, Research Division, Standard O i l Development Co., Linden,
The deleterious effect of minute amounts of metallic elements, notably nickel and vanadium, on cracking catalysts has been known in the petroleum industry for some time; accordingly, much time and effort have been expended in developing suitable methods of analyzing catalysts for these contaminating metals. Both chemical and spectrochemical methods have been used with varying degrees of success. The former method is time-consuming and both methods appear to lack the desired degree of precision for distinguishing between a good and a poor catalyst. A method for determining trace amounts of iron, nickel, and vanadium on a given cracking catalyst by means of x-ray fluorescence is described. The method is rapid, requiring about 15 minutes for a complete analysis. As little as 2 grams of sample can be used for the analysis, and because the method is nondestructive, the sample can be recovered completely after the analysis.
I
NASMUCH as both chemical and spectrochemical methods
of determining trace elements on cracking catalysts appeared to lack the desired degree of precision for distinguishing between a good and a poor catalyst, a more precise method of analysis was desirable. The introduction of the x-ray spectrograph as a tool for quantitative analysis seemed t o offer a method of determining trace elements rapidly and precisely. Consequently, after making a thorough study of the different variables, a method for determining trace amounts of iron, nickel, and vanadium on cracking catalysts by x-ray fluorescence has been developed. The method is rapid, requiring only 15 minutes for a complete analysis.
N. 1.
The present procedure uses approyimately 20 grams of sample, but a 2-gram sample could be used. I n either case, however, the sample is not destroyed and can be recovered completely after the analysis. Finally, the method is precise. The principle, upon which the analysis of elements by their characteristic x-ray spectra is based, is fundamental and is dependent upon the atomic properties of the element. When a given element is irradiated with x-rays, it will fluoresce other longer x-rays, and each element has a characteristic x-ray fluorescence spectrum. The emitted rays are passed to an analyzing crystal where they are diffracted and reflected into a Geiger tube which measures the intensity of the radiation. This intensity is proportional to the concentration of the element being counted ( 2 , 4-41. APPARATUS
The apparatus used for the development of this procedure is a modified North American Philips Geiger counter spectrometer. Many modifications of the basic equipment as well as specialized techniques are re uired when trying to determine trace elements on catalysts. ?‘he following modifications of the standard equipment have been made. Collimation. The spectrograph, as it was received from the factory, had four sets of collimators, a pair each of 8- and 4-inch aluminum 3/8-inch-square tubes, containing either l / 3 r or I/la-inch nickel tubes. (The newer models do not have this type of collimator and therefore, the following modification may not be necessary with the present collimators.) When using the l / l ~ inch tube of 4-inch collimator a desirable counting rate as not obtained. By removing the nickel tubes from the lower collimator (the one that sees the sample), higher intensities were obtained without loss of a significant amount of resolution. The half-height breadth of the peaks is of the order of 1.3” to 1.5”, more than enough resolution for the present requirements ( 1 ) Helium Atmosphere. Increased intensities can also be ob-
