Performance appraisal of a micro-dumas nitrogen procedure

lIUCROCHEM1CAL JOURNAL

9, 449-464 (1965)

Performance Appraisal of a Micro-Dumas Nitrogen Procedure MARJORIE

F.

BUCKLES

Chemical Research Division, U. S. Army Chemical Research and Development Laboratories, Edgewood Arsenal, Maryland Received August 2, 1965

INTRODUCTION

In the micro-Dumas determination, the percentages of nitrogen , or final results , are obtained from a series of measurements: weight, volume, temperature, and pressure readings, each with attendant corrections. The accuracy of these results can best be characterized by determining (a) their imprecision, as expressed by their standard deviation, and (b) the bias, or systematic error of the procedure (5 ,7,8,10,13). As Eisenhart has pointed out, if measures of precision and bias are to provide realistic indications of the accuracy of a process, then the "allowable variations" must be of sufficient scope to bracket the range of circumstances commonly met in practice (5). A procedure employing a nickel oxide/copper/copper oxide combustion tube filling has been used in these laboratories for a number of years (2). During this time, reagents, apparatus, micro balances , and analysts have been replaced ; and a significant change has been made in the operating procedure. Data are available, therefore , which reflect an appropriate random sampling of a range of circumstances, and this study was undertaken to evaluate the method. INVESTIGATIONAL PROCEDURES

In the studies which follow, no attempt has been made to select values obtained under optimum conditions (e.g., "ideal" sample weight for the range of nitrogen content, newly prepared combustion tubes, fresh potassium hydroxide solution in the nitrometer, etc.); rather, the results were taken in sequence as they appeared in the laboratory notebooks, with inconsistent values included in each series. An exception was made only in those few instances where it was definitely indicated that the discrepancy was due to a digression from the regular procedure. 449

450

MARJORIE F . BUCKLES PRELIMI~ARY STUDIES

When wire-form nickel oxide was first adopted as the temporary filIing in the combustion tube, all determinations were made with both furnaces operated at 800°C. During the course of a three-year period, three analysts, with varying degrees of experience in microanalysis, used the established procedure and obtained results on different days and with several similar sets of apparatus. ACCURACY AND PRECISION: PRIMARY STANDARDS

Three pure compounds were repeatedly analyzed by one or more analysts. Appropriate statistical values were calculated for the data and compared with those given in probability tables (6, 9) to determine whether the samples differed among themselves, or from standard values, more than would be expected from random-sampling errors . Acetanilide

Data from a study of 76 determinations on standard (NBS) acetanilide are shown in Table 1. Included in the table are: n, the number of observations ; x , the individual values; .i', the mean ; s:l, the variance estimate from }:(x - .iY/(n - 1); s, the standard deviation or square root of the variance; and ss, the standard deviation of the mean, from [~(x - .r):l/ n(n-l)Jl /2 .

In order to pool information about the standard deviation of these 76 determinations, it is necessary to establish that the sets of data that are of unequal length , and obtained by different operators, are really comparable. The precisions of the three analysts were compared by applying the Bartlett test for homogeneity of variance, using the algebraic expressions as defined by Bennett and Franklin (1) in the equation : 1

B

= -

C

(n loge 52

-

~nj

loge 5,2) ,

where

L~-~ n, n

e -1+----3 (k -

and k=number of sets of determinations.

1)

451

DUMAS NITROGEN: PERFORMANCE APPRAISAL

TABLE 1 DETERMINATIONS ON ACETANILIDE (10.36% N) BY THREE ANALYSTS Analyst Range of sample weights, mg

x,%N

B

C

2,638 to 8,857

4.980 to 6.619

A 3.993 to 7.759 10.31 10.36

10.33 10.47

10.42 10.37 10.46 10.17 10.14 10.09 10.59 10.31 10.29 10.44

10.45 10.00 10.35 10.42

10.52 10.58 10.04 10.35 10.05 10.23 10.24 10,40 10.35 10.22 9.88 10.25 10,39 10.44 10.30 10.46 10.70 10,34

10.39

10.19

10.51

10.34 10,45 10.53 10.34 10.54 10.35 10,42 10.55 10.29 10.36 10.23

10.41 10.45 10.33 10,41 10.75 10.52 10.38 10.34 10.80 10,26 10.32 10.33 10.46 10,20

10,47 10.59 10.38 10.02 10,47 10.36

10,47

10,47 10.44 10.56 10.51

10.43

n

18

34

24

x

10.332

10..n 1

10.407

.,

s-

s~

0.035lO-~

0022368

0.017371

0.150

0.187

0.132

O,O.H

0,032

0.Q27

The value found, B = 3.391, is well within the acceptable upper limit for B read from a statistical table of Chi Square: entering the table with k - 1 or 2 degrees of freedom, the critical value is 5.991 at the 5% level. A joint estimate of variance, sw 2 = 0.026551, is derived from the equation: sw 2

=

~niSj2/n.

The means of the three analysts were then subjected to an analysis of variance, using the algebraic identities for sums of squares data as defined by Davies (4). Table 2 shows the two independent estimates of the variance. Applying the F test to the two independent variance estimates of Table 2, we have:

452

MARJORIE F. BUCKLES

F

0.029050 = 0.026552 = 1.0941.

Entering the table with 2 and 73 degrees of freedom, we find the Po 05 and values for F are about 3.12 and 4.90, respectively. Since the observed ratio is well within these limits, the agreement between the set averages is acceptable as measured by the agreement between determinations within the sets. PO.Ol

TABLE 2 ANALYSIS OF VARIANCE: ACETANILIDE DETERMINATIONS

Source of estimate

Sum of squares ~Inl (Xi -

Between analysts

k-l

N-k

xI)2

73

1.9383 ~i.J (x -

Variance

VI

=

2

0 .0581 ~j.J (x -

Between replicates

x)2

df

N-l

x)2

~inl (Xi -

x)2

k -1 0 .029050

V2 =

~i.J (x -

Xi) 2

N-k 0.026552 ~i.J (x-X)2

N-l

Total

75

1.9963

0.026619

Pooling the information from these determinations, we obtain estimates based on 75 degrees of freedom for the mean, 14, and variance, 0 2, for the population of all determinations on standard acetanilide using this particular analytical method:

x=

10.373

= 0.026619 s = 0.163 s;;; = 0.0187. S2

The 95% confidence limits, based on po.os (75 df)=I.992, become 10.373 ± 0.037. In other words, nineteen out of twenty determinations on acetanilide may be expected to yield results between 10.34 and 10.41% N. These values bracket the theoretical value of 10.36% N and are therefore consistent with the theoretical result.

453

DUMAS NITROGE N : P ERFOR MANCE APPRAISAL

3,5-Dinitrobenzoic Acid

Data from a study of 11 determ inations on pure dinitrobenzoic acid are shown in Table 3. TABLE 3 D ETERM INATIONS ON 3,5-D INlTROBEN ZOIC AC ID

( 13.210/0 N)

BY

T wo

ANALYSTS

Analyst

B

C

Ran ge of sample weights , mg

2.718 to 4.978

to 4.615

x,

'70 N

3.303

13.32 13.41 12.92 13.20 13.24

13.40 13.42 13.09 13.36 13.16 13.34

5

n

6 13.295 0 .018630 0 .136 0 .056

13.218 0 .034220 0.185 0.083

s

The precisions of the two anal ysts were compared by the varianc e ratio: F

= 0.034220 = 1.8368. 0.018630

For 4/5 degrees of freedom, p() O~ is 5.19 and P O.OI is 11.39. Since the F found is well below the critical values, there is no evidence for a difference in precision between the two analy sts . The means of the two analysts were subjected to an analysis of variance, with calculations following the same pattern as those used for the preceding standard. The results are shown in Table 4. The F ratio of the two variance s, 0.0256 (9 df) /0.0162 (1 df) gives F = TABLE 4 ANALYSIS OF VARIANCE :

3,5 - DI N I T ROBENZOI C ACID DETERMINATIONS

Source of esti ma te

Sum of squares

df

Between analysts Bet ween replicates

0 .0162 0 .2300

1 9

0.2462

10

T otal

Variance 0.0 162 0 .0256 0.0246 2

454

MARJORIE F. BUCKLES

1.58. Since F is 59.9 at the 10'70 probability level, the found value is not judged to be significant. The data from the dinitrobenzoic acid determinations may then be regarded as random drawings from a universe with mean and variance estimated by the following:

x=

13.260

= 0.02462 s = 0.157 sr = 0.047.

S2

The 95% confidence limits, based on po 05 (10 df) being 2.228, become 13.260 ± 0.105. The values of 13.37'70 Nand 13.16% N are not likely to be exceeded more than once in twenty determinations; these values bracket and are consistent with the theoretical nitrogen content (13.2170 N). Cystine Data from 27 determinations on standard (NBS) cystine made by one chemist (Table 5) yielded the following:

x=

11.532 0.016869 s = 0.130 sr = 0.025. S2

=

The precisions obtained by this analyst on the three standards were examined and no significant differences were found by application of the appropriate F tests. However, with Po 05 (26 df) = 2.056, the confidence limits for the cystine determinations become 11.58'70 and 11.4870 N. These values do not bracket the theoretical (11.6670 N) and suggest the possibility of a constant error in the analyses. EVALUATION OF SYSTEMATIC ERROR: PRIMARY STANDARDS

The differences between the means of the determinations on the standard materials and their theoretical nitrogen content were compared by Youden's (15) formula,

t = [( I- - theory)] (n) 'f,/ s; (n -

1) d f.

+

Acetanilide, with a mean minus theory value of O.013j'c, has a calculated t of 0.695; dinitrobenzoic acid, with a difference of +0.050%, has

455

DUMAS NITROGEN: PERFORMANCE APPRAISAL

TABLE 5 DETERMINATIONS ON CYSTINE

(11.66% N) i

Two COMBUSTION TEMPERATURES

800·C

900·C

Analyst

C

C

Range of sample weights, mg

2.871 to 5.372

to 5.583

2.866

x, 'foN

11.72 11.49 11.39 11.55 11.26 11.63 11.30 11.74 11.64 11.62 11.30 11.51 11.38 11.59 11.48 11.72 11.59 11.52 11.53 11.61 11.40 11.5'2 11.70 11.49 11.59 11.52 11.57

11.68 11.72 11.49 11.53 11.61 11.60 11.63 11.67 11.75 11.61 11.74 11.75 11.55 11.66 11.58 11.78 11.59 11.58 11.68 11.60 11.74 11.57 11.61 11.63 11.65 11.70 11.58

n

27

27

11.532

11.640

0.016869

0 .005592

s

0.130

0.075

s-: JI

0.Q25

0.014

a calculated t of 1.056. Both t values are well within the critical values tabulated at the five per cent confidence level when the table is entered with 75 and 10 degrees of freedom, respectively.

456

MARJORIE F . BUCKLES

Cystine, with a difference between mean and theory of - 0.128 70 , has a calculated t = 5.116, which is far greater than the tabulated value for 26 df at the five per cent level. Since the cystine determinations were made on samples ranging in weight from 2.87 to 5.37 mg, Youden's correlation method (11-14) was applied. A regression line was fitted to the data by the method of least squares. Computations for intercept and slope, and their standard deviations were made for the straight line, Y = a bx, from which was found the intercept , a = 0.004246. This was less than the standard deviation of the intercept , the relatively large value of the latter (s" = 0.007458) being due to the rather small range in nitrogen content of the samples . It is possible that a larger spread in weights would have shown the intercept value to be beyond the reasonable limits of acceptance. Application of the t test, however , did not indicate that the intercept differs from zero more than can be accounted for by the analytical errors. Likewise , the slope of the line, b = 0.980113, appears acceptably close to unity as determined by the appropriate t test. For a precise method, the line is anticipated to have a slope of one , and to pass through the origin. After fitting a line to the cystine data by means of the above equation , which is free to have any intercept a, a comparison of slopes was made by fitting the line, Jl = b'x , which is the equation for a straight line constrained to pass through the origin. Computation of this slope, b' = 0.988816, its standard deviation, Sb' = 0.002146, and application of the t test show that the difference between b' and unity is greater than a reasonable multiple of the standard deviation of the slope. It must be concluded , then , that the intercept does differ significantly from zero . In other words, the data warrant the use of a correction term based on the value of the constant a and equivalent to 0.0042 rng of nitro gen.

+

EVALUATIO:'l1 OF CURRE:-':T PROCEDVRE

While the nickel oxide tube packing and an 800°C combustion temperature provided a method with excellent precision, both between analysts and between replicates, the over-all accuracy was not impressive: nitrogen results on some thirty research compounds of high purity were only within ± 0.32% of theory. Literature sources indicated that many investigators were turning to high-temperature, oxygen-catalyzed combustions in order to improve results obtained by Dumas procedures ; most of these are complex systems with elaborate techniques and high-maintenance requirements. We sought

DUMAS NITROGEN: PERFORMANCE APPRAISAL

457

to retain our relatively simple system and to achieve greater accuracy by making minor modifications. The current procedure has been described in an earlier paper (3) and differs from the preliminary method mainly in that the sample is now pyrolyzed at 900°C. ACCURACY AND PRECISION: PRIMARY STANDARDS

Cystine, Correlation of Data

In order to observe the effect of increased combustion temperature, the same chemist made the same number of determinations on standard (NBS) cystine with the results that are shown in Table 5. With po 05 (26 df)=2 .056, and a standard deviation of the mean, s;;; 0.014, the confidence limits for the second set become 11.640 ± 0.029% nitrogen and the theoretical content (11.66%) is bracketed. 11.640 and %2 Tests of significance were given the means, .1'1 11.532. An F test established a difference in precision when a calculated F of 3.017 was obtained from the ratio of their variances , (S:;'1)2/(S-rl) 2. This value is larger than 1.93, the critical 570 value for F (26/26 df) , and since the larger variance was arbitrarily placed in the numerator indicates significance at the 100/0 level. A t test establi shed a difference in accuracy between the two means. By assuming the null hypothesis and pooling the two estimates of 0 2 (52 df) , an estimated standard deviation, s = 0.1060, was obtained. Using this in the equation

=

=

=

=

3.67 which is much larger than the critical 170 value for t. gave t Not only have the accuracy and precision changed significantly, the application of Youden's equation for detecting constant errors shows that this second set of data has a difference between mean and theory of - 0.020 % nitrogen, and a calculated t of 1.3856 which is well under the tabulated value for 26 df at the 5% level. The bias equivalent to 0.0042 mg of nitrogen has apparently been removed by raising the temperature to 900°C and thus assuring more complete combustion. Selected Pur e Compounds

In addition to cystine, which has been demonstrated to be a most rigorous standard and is used regularly to check out the Dumas system,

458

MARJORIE F. BUCKLES

fourteen other pure compounds have been analyzed by the current procedure. The group of compounds was selected to reflect a broad range in nitrogen content (4.84 to 66.64% N) and also to include at least one amenable structure, acetanilide, and several structures frequently reported to be difficult to analyze by the classical Dumas procedure: sulfur-containing compounds, a nitrate, a dinitrophenylhydrazone, and various heterocyclics, among which melamine was chosen because of the considerable difficulties ascribed to symmetrical triazines; and atropine and caffeine were chosen because of the added possibilities of error deriving from the N-methyl groups. The results from 115 determinations combining the work of three analysts are shown in Table 6. It is desirable to consider the deviations from theory in terms of parts per thousand (ppt) as well as in terms of absolute per cent. (8) Caffeine TABLE 6 RESULTS ON SELECTED PURE COMPOUNDS: 900·C COMBUSTION Nitrogen, Compound Acetanilide» Ammonium bromide'[

AtropineBenzylisothiourea, hydrochloride b Caffeine« 5-Chloro-4-hydroxy-3-methoxybenzylisothiourea phosphate" Cyclohexanone, 2,4-dinitrophenylhydrazonev Cystine a m-Dinitrobenzene~

MelamineNicotinic acids p-Nitroaniline b NitrobenzenePhenylthioureas Potassium nitrated a National Bureau of Standards.

British Drug Houses, Ltd. Eastman Kodak Co. d Fisher Scientific Co. b

c

x

%

n

Theory

x-Theory

s

6 1 1

10.36 14.30 4.84

10.377 14.26 4.85

+0.02 --{l.04 +0.01

0.050

2 5

13.82 28.85

13.785 28.706

--{l.03 --{l.14

0.034

3

8.13

8.050

--{l.OB

0.020

4 65 3 6 2 4 6 5 2

20.14 11.66 16.66 66.64 11.38 20.28 11.38 18.40 13.85

20.165 11.683 16.673 66.538 11.380 20.230 11.370 18.388 13.895

+0.03 +0.02 +0.01 --{l.10 0 -0.05 -0.01 --{l.01 +0.05

0.077 0.100 0.148 0.201

Mean,

0.078 0.079 0.132

D1Jl\lAS NITROGEN : PERFORMANCE APPRAISAL

459

shows an error of - 5 ppt and the benzylisothiourea phosphate is - 10 ppt, while the other values range from - 1 to +4ppt. These figures reflect an accuracy that is satisfactory for the different levels of nitrogen content shown. EVALUATION OF SYSTEMATIC ERROR: PRIMARY STANDARDS

The algebraic sum of the deviations from theory of the individual determinations ( - 0.37% absolute) cannot be considered a priori evidence of a large systematic error in the determinations. Since the group of standard compounds was preselected to contain predominately "difficult" structures, it is reasonable to assume that inclusion of an equal number of tractable compounds would alter this value, and any well-informed estimate of the size of the systematic error of the procedure would have to apply to all the measurements made by it. The ten compounds on which three or more determinations were made were examined by means of the equation t=[(.i·-theory)J (n) %/s; (n-l) df and only caffeine and the benzylisothiourea phosphate were found to have calculated t values greater than the appropriate tabulated values . Some of these data may be insufficient in precision or number to establish the presence of a constant error , however the 65 cystine determinations yield a calculated t of 1.854 which is well under the tabulated t and gives no evidence for the presence of a systematic error. RESULTS ON RESEARCH COMPOUNDS

Microanalytical data sheets for research compounds submitted for analyses within the past four years were reviewed and only those which could be judged pure on the basis of elemental and /or functional group analyse s, spectrographic determinations, and physical property measurements were considered. These compounds were then classified according to the type of nitrogen-containing structure involved. Tractable Compounds Included in this category are simple amines , nitriles, carbarnates, and other compounds that pose no problems with the classical micro-Dumas procedures. The results on 30 such compounds , having a nitro gen content ranging from 3.71 to 26.69 70 are shown in Table 7.

460

MARJORIE F. BUCKLES

Refractory Compounds Included in this group are compounds for which special tube packings, combustion catalysts, or oxygen-generating systems have been advocated by numerous investigators as a means of improving the reliability of results: organa-boron, SUlfur, and fluorine compounds, heterocyclic and condensed ring structures, and those containing ~-methyl, X-N, or N-O bonds and long aliphatic chains. The results on SS such compounds, having a nitrogen content ranging from 2.99 to 30.647r are shown in Table 8. TABLE 7 RESULTS ON TRACTABLE RESEARCH COMPOUNDS: 900·C COMBUSTION

Identity of significant structural group(s) (Bis) acetimidoAminophenol, phosphomolybdate (Bis) arninophenoxyAmmonium, tetramethylAnisidine Benzoquinone, imlno-, amino Benzoylazide Carbamate, nitrobenzylDiazoDiethylaminoethyl(Bis) dimethylaminoethylDinitrile Diphenylamine, nitro (Bis) glycylHydrazine Isocyanate (Bis) isocyanate Isocyanobutane Nitrile Nitrile, isonitroso, nitro Nitrile, nitrobenzylNitrophenol, aminomethylNitrosaminoOxime (Bis) oxime Phenylhydrazone Phthalimide Phthalimide, cyanopropylTriamide, phosphoroUrea

Nitrogen, 0/0 Theory

Found

Difference

6.58 1.81 10.85 9.09 11.37 7.35 17.72 10.83 6.25 3.71 9.09 16.27 8.97 6.30 26.69 8.08 10.60 16.85 8.18 21.98 14.25 14.28 10.05 10.85 12.28 8.85 9.52 12.17 12.35 11.66

6.59 1.82 10.70 9.07 11.26 7.48 17.62 10.77 6.10 3.79 8.98 16.28 8.92 6.28 26.80 8.11 10.48 16.81 8.21 21.92 14.40 14.29 10.09 11.02 12.32 8.81 9.59 12.19 12.28 11.55

+0.01 +0.Ql --{l.15 --{l.02 --{l.ll +0.13 --{l.10 -0.06 --{l.15 +0.08 --{l.ll +0.01 --{l.05 --{l.02 +011 +0.03 --{l.12 --{l.04 +0.Q3 --{l.06 +0.15 +0.01 +0.04 +0.17 +0.04 --{l.04 +0.07 +0.Q2 --{l.07 +0.11

461

DUMAS NITROGE N: P ERFORMANCE APPRAISAL

TABLE 8 RES ULTS ON REFRACTORY R ESEARCH COMPOU NDS

Identity of significant str uctural group (s ) Amine, picryl sulfonate ( Bis) amino phosph ono th ioate , ( bis j tet raphenyl boronate Azabicyc!o[3.2.1] octane, picrate Azidoph ospbonate Azidoph osphonothioate Barbituric acid Benzimidaz ole, nitroBenzimidazol e, nitro-, amino, picrate Benzothiazole, cyano, imino Brucine salt of a phosphonothioic acid Carbamate, (bis j amino-, (bisj tetraphe nyl boronate Cy clohepta [ b] quinoline, aminoD ecameth ylene (bis )ammonium salt D iaza chrysene, (bis)a mino D iaza chr y sene, tetran itro-, (bis j arn in o Diazon ium fluoborate, hisEicosane, (bis) carbamoyl, (bis)nit ro Glycine, trifluoroacetylH endecan e, pyridylH eptadec ane , aminoquinolylIm idazole, amino-, sulfate Im idazole, (bis) carbamoyl Im idazoline, amino eth yl- , dipicrat c In dole In dolizidin e, picrat e Indolo [4,3 -Jg [quinoline In dole [4 ,3- f g [q uinoline, ami no M orpholine Ni colinonitrile, sulfoaminoNort ropane, picrate Oxazaphosphorinane, amino-, oxide Oxazolidine Ph enoxazine . Piperazine, dipicrate Piperidine, fluorobenzylidene -, sulfonate Piperid ine, ind olylp yrazolone , aminomethylp yridine , amin o, isonitroso p yridin e, carbamoyl, nitro

900 ' (: COMBU STI ON

Nitrogen,

%

T heory

Fo und

Difference

12.87

12.88

+ 0.01

2.99 15.73 20.68 21.75 11.76 16.59 15.67 13.08 4.94

3.14 15.72 20.81 21.60 11.79 16.50 15.76 13.19

+0.15 -0.01 + 0.1.3 -0.15

3.83 13.20 4.93 12.16 21.93 11.25 7.67 8.19 5.33 6.69 13.41 12.84 17.57 6.68 15.13 9.78 12.99 5.74 13.33 15.81 9.05 5.20 4.41 17.83 2.90 8.17 14.91 30.64 8.12

3.87 13.24 5.02 12.27 21.96 11.57 7.52 8.43 5.45 6.69 13.28 12.94 17.40 6.68 14.99 9.80 12.83 5.83 13.47 15.84 8.96 5.19 4.43 17.86 3.03 8.32 14.84

4 .90

30 .45

8.07

+0.03

-0.09 +0.09 +0.11 -0.04 +0.04 + 0.04 + 0.09 +0.11 +0.03

+ 0.32 -0.15 +0.24 +0.1 2

°

-0.13 +0.10 - 0.17 0 -0.14 + 0.02 - 0.16 +0.08 + 0.14 +0.03 -0.09 -0.01 +0.02 +0.03 +0.13 +0.15 -0.07 -0.19 -0.05

462

MARJORIE F. BUCKLES

TABLE 8 (Co"ti"utd) Identity of significant structural group (s) Pyrimidine, acetamido-, dinitrophenylhydrazone Pyrim idine, aminoPyr imidine, (bis) amino-, monohydrate Pyrimidine, tetrahydroQuinine salt of a phosphonothioic acid Quinolizidine Quinuclidine, dinitrophenylhydrazono-, sulfate Quinuclidine, tetraphenylboronate Semioxamizide Taurine Thiazole, (bis)aminoThiazole, dlnitrophenylhydrazone Thiirane, (bis) pyridylThiobarbituric acid Thiolthionocarbamate, ammonium salt Uracil, diamino-, sulfate

Nitrogen , % Theory

Found

Difference

23.49 23.19 29.78 7.00 5.64 9.02 17.36 3.13 20.28 6.69 20.23 23.88 13.07 10.07

23.66 23.17 29.72 7.03

+0.17 -{).02 -{).06 +0.03 -{).04 +0.03 +0.12 +0.05 -{).14 +0.07 +0.02 -{).21 +0.02 -{).04 +0.05 -{).06

5.60 9 .05 17.48 3 .18 20.14 6.78 20.25

12.60

23.67 13.09 10.03 12.65

29.31

29.25

ESTIMATION OF PROCEDURE: PRECISION AND CONFIDENCE LIMITS

As a means of comparing all the results obtained by the current procedure , pertinent data were reduced to similar form by computing the sum of the squares of the deviations of the individual observed values from the theoretical values, and dividing by the appropriate degrees of freedom , which in this case is equal to the number of determinations. While this approach does not separate a bias or constant error from the random errors associated with precision (12) , the preceding operations have shown that the constant error has at least been reduced by the modification in combustion temperature, and that very little evidence has been uncovered to indicate that this bias is sufficiently large to affect the accuracy of the results. We have in effect, then, data for 100 different compounds of established purity and known nitrogen content from which to estimate the reliability of this microanalytical procedure. The combined estimate of the standard deviation of the differences between theoretical and observed values, derived from the information in Table 9, is 0.1048% . With a deviation of this size, and confidence limits based on Po 05 (co df) = 1.960; Po 01 (co df) = 2.576, we could expect 9570 of all determinations

DUMAS NITROGEN: PERFORMANCE APPRAISAL

463

TABLE 9 RELIABILITY ESTIMATES BASED ON DIFFERENCES BETWEEN THEORETICAL AND OBSERVID PER CENT NITROGEN Compounds

n

~d'2

s2

s

Cystine Other standards Tractable, research Refractory, research

65 50 30 55

0.6735 0.6344 0.2218 0.6683

0.01036154 0.01268800 0.00739333 0.01215090

0.1018 0.1126 0.0860 0.1102

2.1980

0.0I 099000a

Total a

200

Combined estimate of variance,

s2

= 2.1980(200.

to fall within ± 0.205% of theory, and only one determination in 100 to exceed the limits of ± 0.27070 of theory. SUMMARY Realistic estimates of accuracy and precision have been established for a microDumas nltrogen procedure which departs from the classical method in that wire-form nickel oxide is used as the temporary filling in the combustion tube. Data have been collated which reflect an appropriate random sampling of circumstances under which this method has been used (e.g., replacement of microbalances, apparatus, reagents; a change in environmental conditions; different analysts) . The variance between analysts and within sets of measurements on standard reference compounds has been determined, and a systematic error detected and effectively reduced in size by a modification of the given procedure. The over-all performance of the method has been judged by statistically analyzing results obtained on 100 compounds of established purity which represent a wide variety of nitrogenous structural groups, and which have a range in nitrogen content of 1.81 to 66 .64'/'0. ACKNOWLEDGMENTS The author wishes to acknowledge the work of Mr. John M. Corliss in developing the improved filling for the combustion tube, and is further indebted to Mrs . Natalie B. Scholtz, Mr. James Kesterson, and Miss Eleanor Lipsitz for some of the nitrogen determinations used in this study. REFERENCES 1.

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MARJORIE F. BUCKLES

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