The Application of Statistics to Quantitative Analysis A. A. BENEDETTI-PICHLER, Washington Square College, New York University, New York, N. Y.
I
T IS GENERALLY recognized that the results of any scientific investigation must prove reproducible. Likewise the value of an analytical procedure is based on the expectation that it may be used a t any future time with the success claimed by its author. Therefore, it is only proper to measure the merit of an analytical method in terms of the certainty, or probability, with which its successful reproduction can be predicted (11). The data required for such a prediction are obtained by the use of the methods of statistics that are customary in the evaluation of physical measurements and in the discussion of determinations of atomic weight. A simple outline is here presented for the organization of analytical research and the presentation of its results, which will be helpful in the establishment of the precision and accuracy of proposed methods.
lishes not only the accuracy related to the constant error, but also the precision determined by the accidental errors of the method. The results of such a set of determinations will never check exactly, if the determinations are carried out to the full delicacy of which the procedure is capable. The best representative value of the discordant set of figures is its arithmetical mean, provided that the results have been obtained under the same conditions and are equally trustworthy (12). The proof rests upon the fact that the positive and negative deviations, being equally probable, will ultimately balance each other ( I S ) , thus clearing the arithmetical mean more or less from the influence of the accidental errors. Accordingly, the discussion of the result of a series of determinations should be based on the arithmetical mean and its precision.
Precision and Accuracy
TABLEI. ASH DETERMINATIOSS ON POTASSIUM SULFATE AND AZOBENZENE
Only numbers derived from definitions are exactly known and can be given with as many significant figures as desired; measured quantities are known only within the limits of the methods used for their determination.
NO.
% 53.4 53.1 52.7 62.8 52.7 52.5 53.5 52.8 53.0
The effect of accidental and of constant errors is demonstrated in Figure 1, which shows the results of four series of determinations plotted as abscissas; the arithmetical mean of each series is indicated by a vertical line. I t is assumed that four different methods have been used for the determinations of the quantity. In series I and I1 the accidental errors are small and the results in either series agree closely among themselves; methods I and I1 show a high degree of precision. With methods I11 and I V the accidental errors are large and the results in either series do not show satisfactory agreement; methods I11 and IV have a low degree of precision. It is obvious that such methods of low precision are highly impractical, since only the mean of a large number of determinations could be of any use. On the other hand methods I and I1 will give satisfactory results in practical application, though with method I1 allowance has to be made for the constant error which appears as the difference, "truth" minus arithmetical mean.
1-
_ I
C.E. ..she
Ash
I1
Arithmetical Mean
% 53:25
53.07 53.00 52.94 52,87 52.96 52.95 52.94
"I
FIGURE1. EFFECTOF ACCIDESTALAND CONSTA'VT ERRORS The purpose of the calibration of a method is the determination of its constant error. The precision of the constant error depends upon the precision with which the arithmetical mean and the expected result (truth) are known (Table IV). The calibration of a method is carried out by its repeated application to the determination of quantities known by the use of other reliable methods. Thus the calibration estab373
o .' io
0.14 0.13 0.11 0.11 0.12 0.11 0.10
One should not rely on the mean of a small number of observations which, by accident, may agree closely and furnish an arithmetical mean of apparently high precision. The author met with an interesting example of the malice of chance in a study on the precision of sampling, in which ash determinations were carried out on 1- to 3-mg. samples of a solid mixture of potassium sulfate and azobenzene. In Table I the results are listed in the exact order in which they were obtained. The first six determinations seemed to indicate the presence of a time factor, as the ash content of the mixture appeared to decrease continuously. Absorption of moisture by the mixture offered a possible explanation. Finally the seventh determination proved the accidental nature of this remarkable series of results. A survey of Table I shows that the arithmetical mean does not become sufficiently constant within the first six determinations to be trustworthy. Also the precision of the mean, a,, is unreliable when the mean is derived from too small a number of observations; in Table I the mean of the first two determinations seems to possess the same precision as the mean of the whole series. Considering everything, it appears proper to require a t least four to ten determinations in every set of analyses carried out for the calibration of a method (8, I S ) ; the number of determinations in a series may be decreased according to the amount of available preliminary information on the precision of the method. As a measure of precision, the average deviation is suggested (8),since it is an appropriate standard of comparison when attention is directed to the relative precision in different series of observations. Furthermore, the average deviation furnishes useful information even when the presence of (unknown) constant errors renders a further application of the theory of errors of questionable utility, because it will allow us t o compare the magnitude of the constant errors
, ~ . . . . : Truth
am
%
374
INDUSTRIAL AND ENGINEERING CHEMISTRY
affecting different series of observations, and so lead to their discovery and elimination (IS). If n is the number of determinations and dl, dp, d, represent the absolute deviations of the individual results from the arithmetical mean, &, the average deviations are calculated as follows : Absolute average deviation of a single determination,
a, =
Relative average deviation of a single determination, Absolute average deviation of the arithmetical mean, Relative average deviation of the arithmetical mean,
=
* (4 + (dz) n
a, = i l
1000 a, _I
+. *
(dn)
/oo
* a,
4
* 1000 a, l o o ~
Q
The absolute precisions have the same dimension as the determined quantity, Q; the relative precisions are expressed in parts per thousand to avoid confusion with the results of quantitative analyses which are usually reported in parts per cent (8). Reports on sets of determinations for the calibration of a method may be reduced to listing the number of determinations, the arithmetical mean of the results, the absolute average deviation of the mean, and finally the relative average deviation of the mean. Thus the table in the report on the calibration of the microdetermination of aluminum by weighing the hydroxyquinolate (3) could have been reduced to the statement: The calibration was carried out with samples of 1.7 to 6.5 mg. of pure KA1(S0&.12Hz0. The arithmeticaI mean of nine determinations gave 10.79 * 0.011 per cent A1203 (* 1 o/oo) ; 10.77 per cent expected. This statement not only has the advantage of brevity, but conveys information which cannot be obtained from the tabulation of the results without calculation. The original figures are not made available, but the customary presentation in table form does not list the figures of the original weighings and buret readings. Furthermore, in presentation in table form one will often be forced to list only part of the results obtained, which leads to a very undesirable selection of the material which in itself constitutes a misrepresentation of facts. On the other hand, the arithmetical mean must include all the results of the series. Inconsistent results can be excluded only if it is definitely proved that the discrepancy is due t o a digression (mistake, accident) from the standard procedure used in the calibration. Otherwise such results, if not included in the calculation of the mean, must be separately reported. As to the immediate information obtainable from the mean and its precision, the probability that in the future an error will occur, which is larger than four times the average deviation, is approximately one in a thousand. This means that a repetition of the calibration of the microdetermination of aluminum will probably give a result between 10.83and 10.75 per cent of alumina. As the expected result, 10.77 per cent, lies within this range, the presence of a constant error cannot be justly assumed. The calibration was actually repeated in a different location, with different apparatus and reagents by another worker (6),and the arithmetical mean of a series of fourteen determinations was 10.78 * 0.006 per cent A1203 (*0.6 O/oo). I n this second series the aluminum determinations mere carried out from solutions containing various concentrations of beryllium. The close agreement of the means proves that the presence of beryllium has no disturbing influence on the determination of the aluminum. The slightly better precision of the second series may be due to the fact that the first series was carried out by seven different experimenters (thus
VOL. 8, NO. 5
including the variation of the personal errors), whereas the second series was performed by one person. The average deviations of a single determination are obtained from the abbreviated report by multiplying the average deviations of the mean by .\/;:
The a,’ indicates that in future application of the method an individual determination ill give on an average a deviation of *3 O/o0 from the expected value, and will hardly ever show a deviation of more than * 12 o/oo from the truth. When predicting the precision of the arithmetical mean of m future determinations, the above precisions for the individual determination are to be divided by .;/\ However, all these predictions hold only if future determinations are carried out under conditions identical with those under which the calibration was performed. Such an exact duplication of the experiment by another person is possible only if the procedure of the calibration is carefully and completely reported. In general the description should include the technic, the material, form, and dimensions of apparatus, and the purity specifications, concentrations, and volumes of the reagents. Usually the description must be the more elaborate, the greater the precision and accuracy of the method. Of course, the development of the proposed method should be sufficiently complete to exclude unnecessary restrictions and precautions. Just as a maze of directions indicates insufficient knowledge of the processes involved, a general disregard of cookbook procedures indicates a woeful misconception of the fundamental principles of experimental work. The degree by which the standardization of a procedure must sometimes be extended to meet the requirements of an increased sensitivity can be demonstrated in the determination of the precision of balances. The precision of an analytical balance is determined by repeating a weighing six to ten times in a series and by calculating the average deviation of a single weighing, a,,from the set of results. If the balance is only arrested and released between consecutive weighings, nothing but the soundness of the balance construction is tested. In order to obtain the conditions of an actual weighing, it is necessary t o lift off the rider after arresting the balance, to move the rider carrier sideways, and then t o replace the rider as exactly as possible in the original position before proceeding t o the next weighing. The determination of the precision should be carried out with various loads on the pans, and the precaution may be taken to shift slightly the positions of the weights on the pans between the weighings. Further specifications appear superfluous when considering the precision of balances for analytical routine work which requires weighings to 0.1 mg. The precision of inexpensive analytical balances, used by students for 3 t o 4 years, has been determined in this way (Table 11). A 5-mg. rider is used with these balances. The precision 10.16 mg. was observed under extreme conditions which should be avoided in actual weighing; the 100-gram weights were placed in different positions so near the edges of the pans that the pan arrests made contact on the opposite side of the circumference of the pans. One hundred grams is the maximum permissible load for these balances. TABLE 11. PRECISION OF BALANCES 7
KO.4764 Zero load rider not touched Zero load’ rider o erated 1OO-gram’load, riier operated 100-gram weights near edge of pans
Mg. 0.005 0.005
... ...
Precision, =tad No. 4751 Mg. 0.007
No. 2288 Mg.
0.00s
...
0.031 0.023 0.076
...
0.16
In microchemical work the attempt is made to reproduce weighings with a precision of a few thousandths of a milligram. No matter whether a precision (analytical) balance, an assay bahnce, or a microchemical balance of the Kuhlmann type is
SEPTEMBER 15, 1936
ANALYTICAL EDITION
used for this work, the following additional factors must be carefully considered in the development of a standard procedure of weighing (16): 1. Special attention must be paid t o the position of the rider and t o imperfections of the rider scale. 2. Special care must be taken t o prevent setting up a temperature gradient in the balance. A variation of the arm lengths of the beam, as well as the formation of convection currents in the case, is to be avoided. 3. The temperature coefficient of balances becomes noticeable in weighings of high precision. A variation of the temperature affects not only the zero reading but also the weighings t o an amount which varies with the load and cannot be exactly calculated. In addition the effects of temperature changes show a marked time lag. To avoid these difficulties, the balance room must be kept at constant temperature, and the experimenter must reduce the duration of his stays in front of the balance to a minimum. 4. If changes of barometric pressure are likely t o occur between consecutive weighings, the variations of the buoyant effect must be considered. 5. Special care must be devoted to the perfect functioning of the arresting mechanism and t o its proper use. Electrostatic charges not only occur on the objects weighed, but also may happen on the agate surfaces of the balance construction and cause a phenomenon similar to the sticking of the arresting contacts. 6. Displacements of the zero reading may be caused by deposition of dust on the various parts of the balance construction.
The history of the use of the microchemical balance (the term “microchemical balance” was originated by Pregl and refers only to balances of the Kuhlmann type) is proof not only of the difficulties encountered in the attempt to increase the sensitivity of the analytical balance, but also of the disregard of the principles of physical measurements. A state of confusion was brought about by incompletely, or not at all, reporting the conditions under which the various accuracies had been observed. Thus Pregl’s original claim (15) of a precision of *0.001 mg. refers to the mean of a series of weighings, carried out in rapid succession with a load of a fraction of a gram, and possibly without touching the rider between the weighings. Even under these conditions the quoted precision can be attained only in the absence of a disturbance of the equilibrium of the balance by the body temperature of the observer. With greater load the precision of the microchemical balance shows a noticeable decrease. If the weighings are taken a t greater time intervals, changes of room temperature and of barometric pressure may cause variations up to 0.1 mg. As a matter of fact, whereas the precision of an analytical balance can be established within one hour, the investigation of Schwarz-Bergkampf (16) had to be extended over more than half a year in order to give sufficient information on the efficiency of the microchemical balance.
Calibration of Chemical Procedures The calibration of chemical procedures for the determination of constant errors is carried out by the performance of control analyses with known quantities of the constituent to be determined or detected; controls, run with zero quantities of this constituent, are called blanks, and in general will give information about interfering matter introduced by the reagents and apparatus. The results of blanks may contradict those of controls. Since controls are carried out under conditions more similar to those of actual analyses, they are better suited for the determination of constant errors (14). Under all conditions, the calibration should be carried out in such a way as to permit establishment of the precision as well as the determination of constant errors. The different effects of additive and proportional constant errors can be seen from Table 111, which summarizes the results of calibrations carried out in connection with an at-
375
tempt to develop a micromethod for the determination of aluminum with the use of alumina as weighing form (4). Pure AlK(SOJ2.12H20 was used in the controls. The solutions of alum were first treated with a constant volume of hydrochloric acid to obtain a standard concentration of ammonium salt. Following this, the solutions were made slightly alkaline with ammonia for the precipitation of the aluminum hydroxide. A blank indicated purity of the reagents, since the negligible increase of the weight of the crucible was accounted for by the weight of the ash of the filter paper. The results of controls with increasing quantities of alum are listed in the second column of Table 111. The fact that determinations on small quantities of alum showed a greater deviation from the truth than those on large quantities indicated the presence of an additive constant error, which was caused by co-precipitation of the silicic acid introduced with the ammonia. The constancy of the amount of silicic acid was explained by the fact that the major part of the ammonia was required for the neutralization of the constant amount of hydrochloric acid added in all determinations. The silica content of the precipitates was determined by treating the precipitates with hydrofluoric acid. The corrected results in the third column of Table I11 agree rather well with the expected results. The ability of aluminum hydroxide to carry down silicic acid is well known. Of course, with blanks the silicic acid remains in solution, because of the absence of a solid phase able to coprecipitate the silica. TABLE111. DETERMINATION O F ALUMINUM
AS
Al2O3
NHs Freshly With Use of NHs from Stock Bottle KAI(S04)z~12HzO Corrected for Distilled Taken AlzOa found -0.021 g. Si01 AlzOa FouAd Gram Uram GTam Gram 1,0000 1 X 0.1288 1 X 0.1078 1 X 0.1087 2 X 0.1089 2.0000 2 X 0.1192 2 X 0.1087 3 X 0.1086 3 X 0.1093 3.0000 3 X 0,1163 4 X 0,1094 4 X 0.1088 4.0000 4 X 0.1147 Expected: n X 0.1077 Arithmetical mean = 10.875 i: 0.005% Alios
The results obtained with the use of freshly distilled ammonia (fourth column Table 111) are not in very good agreement with the theoretical A 1 2 0 3 content of alum; on the average they are 10 O / o o too high. The presence of a constant error is indicated by the fact that the arithmetical mean of a new series of determinations is expected to fall in the range of 10.85 to 10.90 per cent of A1203, which does not include the expected value 10.77 per cent. The good agreement of the results of analyses with varying quantities of sample indicates the presence of a proportional constant error. The same error was discovered by Hahn (10) when he tried to check the weights of aluminum hydroxyquinolate precipitates against the weights of alumina obtained from identical samples of pure aluminum metal. Also Fresenius (9) must have observed the high results obtained with the use of alumina as weighing form. The alumina is extremely hygroscopic (6); even when it h i s been ignited in a platinum crucible over a blast lamp, it will have absorbed from 1 to 2 per cent of water when it is ready for weighing. The water content of the weighed oxide was directly determined (4) by ignition in a sealed tube, centrifuging the condensate into a fine capillary, and measuring the volume of the liquid. In additional experiments it was found that with pure &03, ignition over the blast lamp is indispensable for the reduction of the degree of hygroscopicity to the abovementioned amount, while with mixtures of aluminum and ferric oxides the use of somewhat lower temperatures would be permissible. The idea of using alumina as a weighing form in microanalysis was finally abandoned, since no crucible material is available which shows a sufficient constancy of
376
INDUSTRIAL AND ENGINEERING CHEMISTRY
weight when heated above 900“ C. The aluminum hydroxyquinolate is by far a superior weighing form, as it has all of the properties which seem especially desirable in microanalysis: The precipitate consists of relatively large crystals which are easy to filter and to wash; treatment previous to weighing does not require temperatures above 800” C. (drying a t 140” C. suffices); and the weighing form has a large molecular weight. The above example illustrates the different effects of additive and proportional constant errors. In the case of the former, the absolute error ($0.021 gram of SiOz) and, with the latter, the relative error ($10 o/oo of water) are constant. Additive errors are usually caused by impurities of reagents added in constant quantities, by the solubility of the precipitate in a constant volume of solution, by the excess reagent required to produce the indicator change, or by the losses or gains determined by the constant surface area of apparatus. Proportional errors may be due to basing the calculation on a wrongly assumed composition of the weighing form, to incomplete reactions, or t o faulty calibration of measuring apparatus (weights, balance, burets, pipets, volumetric flasks). Additive errors may become proportional errors, or vice versa, depending on the procedure adopted in a series of experiments. Likewise the terms “constant” and “accidental” cannot be assigned without reference to special conditions. The deviations introduced by the impurities of a reagent appear as accidental if the reagent is used in varying quantities, whereas the use of a definite amount of reagent will produce a constant error. When a series of analyses has been carried out by one person, the personal factor must be regarded as a constant error and will result in a definite deviation from the truth. If the analyses of a series are carried out by a number of people, the personal errors become accidental in nature; they will affect the precision of the arithmetical mean, but will not cause a definite digression from its expected value. In conclusion, progressing standardization will tend to convert accidental errors into constant errors, thus increasing the precision. Calibration allows the correction of the results of precise determinations for constant errors and thus improves the accuracy.
Propagation of Errors The final result of a quantitative analysis is usually derived from the combination of several measurements. For the calculation the following general formula can be used, in which the result, R, appears as a function of the measured quantity, M , the chemical factor, f,the amount of sample, 8, and the capacities, C1, Cz, Cs, of the volumetric flasks and c1, CZ, c3 of the pipets used in taking aliquot parts:
Depending on whether fM and S are both expressed in weight or volume, the result, R, is obtained.in per cent by weight or by volume; if fM is expressed in grams and S has been measured in milliliters, the result is in grams per 100 ml. The meanings of f and M are interpreted according to the method in use. In gravimetric analysis, M is the weight of the “weighing form” and f is the fraction of the equivalent weight of the reported substance over the equivalent weight of the weighed substance. In volumetric analysis, M is the volume of standard solution, and f is the product of the normality of the standard solution times the milligram equivalent weight (in grams) of the reported substance (if M is measured in milliliters). For C and c, the calibrated capacities of the volumetric apparatus should be substituted; if the aliquot part is weighed instead of measured (7), the ratio of the weights is used.
VOL. 8, NO. 5
The transmission of the errors of the quantities f,MI SI C, and c into the final result may be easily calculated with the use of the equations given in Table IV. p, a,p, and y represent the absolute errors, and p’, a’,p’, and y’ the relative errors of the quantities R, A , B, and C. The constant errors possess a definite sign, and therefore when substituting, their sign must be considered. TABLE IV. PROPAGATION OF ERRORS
Constant errore Accidental errors
p p
R Calculated as: ---. Sum or difference, Product or quotients, R = A + B - C R = @ C = 6 y (2) p’ = (I’ 6’ - y ’ (3) = *1/d 6% y2 (4) p’ = * 1 / / a f Z 8’2 7’2 ( 5 ) ( I
+ -
+ +
+
+
+
The formulas are easy to memorize, considering the identical mathematical form of the equations of the same horizontal row and the fact that the left column uses the absolute errors while the right column employs the relative errors. Furthermore, the constant errors are added algebraically, while the accidental errors are added according to Pythagoras. The usefulness of the tabulated equations may be demonstrated with the use of a few examples. Formulas 2 and 3 indicate that, with the type of functions considered, the constant error of the result is equal to the algebraic sum of the constant errors of the determined quantities. Constant errors may compensate one another. If, however, one of the constant errors is outstandingly large, its effect will be essential to determine the deviation of the result. This fact permits the simple evaluation of the significance of accidents in the performance of an analysis. For example, if one drop (0.05 ml.) of a solution is spilled, or is used for a side test, the -0.05 relative error is 1000 volume of solution in ml, o/oo; this is also the relative error caused in any determination hereafter carried out in this solution (Equation 3). Equations 4 and 5 for the propagation of accidental errors show that the precision of the quantity affected with the greatest uncertainty will essentially determine the precision of the result. Furthermore, the precision of the result is inversely proportional to the square root of the number of measurements and operations contributing identical uncertainties. For example, 100 measurements with average combined would furnish a result with the deviations of * average deviation * 10 O/oo (Equation 5). Therefore, it does not seem objectionable to include a large number of measurements or operations in a determination, provided that the precision of the individual procedures is sufficiently high. The practical disadvantage of such determinations lies in the strain imposed on the experimenter, who has to maintain perfection during the performance of a lengthy chain of operations. The fact that most analytical procedures do not possess a higher precision than * renders the direct determination of the major constituent of a high-grade material impracticable. Even with the use of the hydroxyquinolate as weighing form, the aluminum content of metallic aluminum cannot be found with a higher precision than a’ = or, 99.9 * O.lO/oo Al. Such a result would indicate that the true aluminum content may lie anywhere between 99.5 and 100 per cent. If, however, the sum of the other constituents has been estimated with a precision even as low as * 100 O/o0, the aluminum content is obtained with satisfactory precision from the difference
In this way the aluminum content is definitely established within the limits 99.86 and 99.94 per cent. Equation 4 thus
SEPTEMBER 15, 1936
ANALYTICAL EDITION
confirms the rule that i t is unwise to calculate a small quantity (the sum of the impurities in the above case) as the difference of two large quantities. The use of Equations 1 and 5 will be found helpful in the establishment of a proper correlation of the precisions required in sampling ( I ) , measuring the sample, and aliquot partition, and in the determination of M , the measure of the constituent determined. Since all the shortcomings of the chemical procedure usually combine in affecting M , this measured quantity often exhibits the lowest precision. In order not to lessen the precision further, it is then advisable to strive for four to five times better precision in all the other operations. A careful planning of the required precision a t the different stages of work saves time, labor, and apparatus, especially in routine analyses with large samples where the balances and volumetric apparatus are usually capable of a far higher precision than is required. In microanalysis the precision of the measuring apparatus is more likely to be below the required level, and in some cases the precision of the results can be directly traced to the limitations of balances, pipets, or burets. Among others, this seems to be true for a series of copper determinations with the use of cupric oxide as weighing form ( 2 ) .
Summary Suggestions are made for the establishment of precision and accuracy of chemical methods. An efficient and brief form for reporting the results of the calibration of chemical methods is proposed. The difference of the effect of additive and proportional constant errors is demonstrated. The trans-
377
mission of errors to the final result is discussed with reference to the use of a general equation for the calculation of chemical analyses. In general it has been attempted to present the statistical aspects of chemical measurements in a form which seems practical for the discussion of analytical data.
Literature Cited Baule, B., and Benedetti-Pichler, A. A., 2. anal. Chem., 7 4 , 442 (1928). Benedetti-Pichler, A. A., Ibid., 64, 409 (1924). Benedetti-Pichler, A. A,, Mikrochemie, Pregl-Festschrift, 6 (1929). Benedetti-Pichler, A. A,, unpublished experiments (1925-1927). Benedetti-Pichler, A. A., and Schneider, Frank, Mzkrochemie, Emich-Festschyift, 1 (1930). Blum, W., J . Am. Chem. SOC.,38, 1282 (1916). Dienes, L., J . Biol. Chem., 61, 73 (1924). Fales, H. A , , “Inorganic Quantitative Analysis,” New York, Century Co., 1925. Fresenius, C. R., “Quantitative Analysis,” p. 569, Kew York, John U’iley & Sons Co., 1870. Hahn, F. L., and Brunee, H., 2. anal. Chem., 71, 125 (1927). IXD, EXQ.CHEM.,Anal. Ed., 7, 1 (1935). Kolthoff, I. M., and Sandell, E . B., “Textbook of Inorganic Quantitative Analysis,” p, 259, New York, Macmillan Co., 1936. Mellor, J. W., “Higher Mathematics for Studenta of Chemistry and Physics,” London, Longmans, Green & Co., 1922. Park. B.. IND.EXQ.CHEM..Anal. Ed.. 8. 32 11936). Pregl, F., “Quantitative’ organische ’ Mikroan’alyse,” p. 8, Berlin, Julius Springer, 1930. Schwarz-Bergkampf, E . , 2. anal. Chem., 69, 321 (1926).
RECEIVED April 30, 1936. Presented before the Microchemical Section a t the Q l s t Meeting of the American Chemical Society, Kansas City, Mo., April 13 to 17, 1936.
The Sampling and Analysis of Eggs W. S. GUTHMANN AND W. L. TERRE, The Edwal Laboratories, Chicago, Ill.
T
HE rapid growth of the egg-breaking industry has led t o
increased need for accurate and reliable laboratory methods of analysis and control, especially since we are dealing with a product which is highly perishable and cannot be pasteurized as are milk, cheese, and similar dairy products. Preservation is entirely by means of rapid or sharp freezing and any changes in composition of the product packed must be made within a few hours, or before the batch in question is frozen solid. Last year approximately 180,000,000 pounds of eggs were packed in cans for human consumption. The nature of the pack depends upon the industry for which it is intended. Thus we have egg whites for the baking and candy industries; plain yolk and salted yolk for the mayonnaise and noodle industries; whole eggs, sugar yolk, and glycerol yolk for the baking, ice cream, and confectionery trades; and a number of types of egg products packed to definite specifications as to color and composition. There has been an increasing need for rapid and reproducible methods of analysis because of the conditions indicated above. Bacteriological tests are equally important, but will be discussed in a subsequent paper.
Sampling The first difficulty encountered by the chemist in attempting to do control work is the nature of the egg itself. It is very difficult, even in a well-churned batch, to achieve absolute uniformity and the authors have found that samples taken from the top and bottom of the churn vary in total solids content as much as 1 or 2 per cent.
As the result of these discrepancies they determined to take a t least three samples from each churnful sampled: one near the top of the churn, the next a t about the middle, and the third from the last of the egg in the churn. These three samples were then thoroughly mixed in a quart container, such as a mason jar or milk bottle, and constituted one composite sample which represented with a reasonable degree of accuracy the contents of the churn. The use of a sampling thief, such as is used in the dairy industry, has been suggested, but the authors have not found its use to be practical because of the difficulty in sterilizing it properly a t the egg-breaking plant. Table I indicates the differences in total solids obtained from a single sample and from a composite sample. TABLEI. TOTAL SOLIDS
Whole egg Whole egg Salt yolk
Single Sample
Composite Sample
%
%
%
25.6 25.1 48.3
26.2 26.8 49.0
2.3 6.3 1.4
Error
All analyses for total solids were performed by the Association of Official Agricultural Chemists’ official method for eggs. (An atmospheric oven a t 110’ to 120” C. yields results as much as 0.5 per cent higher, depending upon the fat content of the egg. This increase in apparent total solid value is no doubt due to the oxidation of the fat and protein present.) The method recommended by the association is used for the sampling of the frozen product.
