1939
V O L U M E 2 7 , NO. 1 2 , D E C E M B E R 1 9 5 5 (2) Belcher, R., and Ingram, G., Aaal. Chim. Acta, 4, 124, 401 (1950). (3) Bernstein, W.,and Ballentine, It., Rea. Sci. Instr., 21, 1-58 (1950).
(4) Bradley, J. E. S., Holloway, R. C., and McFarlane, A . S., Biochem. J . ( L o n d o n ) , 57. 192 (1954). (5) Bnchanan, D. L., and Nakao, A. J . A m . Chem. Soc , 74,2389 (1952).
(e) Glascock,
R. F..“Isotopic Gas -inalysis for Biochemists,” pp. 103, 109, 130, Academic Press, Sew York, 1951. (7) Innram. G.. -llakrochm. Acta. 1953, 7 1 . ( S ) Kirsten, W., ASAL. CHEU.,25, i - 4 (1953). (9) Iiirsten, W., M i k r o c h e ~ n i ez>e,.. ~lI.%lih.vochini. d c t a , 35, 217 (1950).
(10) Neville, 0. K., Nuclear Instrumelit and Chem. Corp., Chicago,
Ill., private communication.
(11) Xiederl, J. B., and Siederl. V.. ”Organic Quantitative Microanalysis,” p. 122, Wiley, New York, 1942. (12) Ibid., p. 135. (13) Shell Development Co., Emeryville, Calif., private communication. (14) Sinex, F. 31.,Plasin, ,J., Clareus, D.. Bernstein. W., Van Slyke, D. D., and Chase, It., J . Biol. Chem., 213, 673 (1955). (15) Van Slyke, D. D., Steele, R., and Plazin, J., Ibzd., 192, 769 (1951). RECEIVED for review M a y 0 , 19.55, Arcepted August 1 5 , 19%. RFsearch carried out under the auspice? of t h e U. 9 . I t o n i i c Energy Coinriiission.
Inherent Errors and lower limit of Activity Detection in Gas-Phase Proportional Counting of Carbon-I 4 DAVID R. CHRISTMAN and ALFRED
P. WOLF
Chemistry Department, 6rookhaven National Laboratory, Upton, Long Island,
The precision of the method of carbon-14 assay used in this laboratorj-by measwenlent with gas proportional counters-is discussed from the standpoint of the identity and magnitude of the various errors involFed. The lower limit of activity detection in these gas proportional counting tubes has heen investigated,
I
N VIEW of the interest which has been manifested in the carbon-14 assay method used in this laboratory (1, 4 ) , a discussion of the errors inherent in the system seems appropriate. The systematic errors affect all analyses equally and are therefore important only from the standpoint of the correctness of the absolute activity values reported. Others do not affect different analyses equally and therefore contribute to the deviation in results betneen samples. I n this article, the errors are discussed approximately in the order in which they are encountered in prartice, folloned by a discussion of the lower limit of activity detection using the present method of analv+. The equation used t o calculate the Ppecific activity of a given sample is: net counts per minute Mpc./mg. C = 2220 X T’e X E X mg. C The constant 2220 is the number of disintegrations per minute in 1 mwc. of activity. Ve is the fraction of the total counting tube volume, V t Jwhich is contained within the silvered cathode volume, V , and is therefore defined by Be = V s / V t( 2 ) . E is the apparent counting efficiency of the tubes within the volume fraction Ve, and is now determined by comparisorl with a standard supplied by the National Bureau of St,andards ( 3 , 7 , 8). The milligrams of carbon present in the counting tube is determined by pressure-volume-temperature measurement by means of a calibrated manometer (I, 4 ) . Each of these factors, except the constant 2220, is subject to one or more errors of various types. I n no case does the original weighing of the combustion sample have any bearing on the isotopic assay, so long as the analytical result indicates reasonably complete combustion of the sample. This holds because the sample is not quantitatively transferred t o counting tubes, but rather the amount which is placed in the counting tubes is measured by the pressure change on a calibrated manometer (1, 4 ) . The manometer on the sample loading line ( 4 ) is calibrated by observing the rise obtained from carbon dioxide evolved from weighed amounts of barium carbonate, by decomposition with sulfuric acid. The purity of this barium carbonate, in terms of carbon dioxide content, must therefore be accurately known. It is also necessary to ensure quantitative evolution and trapping of the carbon dioxide evolved. As this is done a t a preswre of
N. Y.
about 10-3 mm. of mercury, great care must be taken t o prevent spraying of the barium carbonate powder when it is first attacked by the sulfuric acid. At the end of the reactmion,the acid must be heated until solution of the carbonate occurs, in order to ensure its complete decomposition. ‘The result of such measurements is expressed as centimeters of rise per milligram of carbon present, and the root mean square deviation from the mean of 12 determinations made on the sample loading line is f 0.73%. This error in the standard rise affects all samples equally and so need not be taken into consideration when comparing activities of different samples among themselves. d similar error occurs in the calibration of the manometer on the combustion line itself, 17hei-e the standard rise per milligram of carbon is determined by averaging t.he rise obtained from a number of standard carbon-hydrogen sample runs and/or from carbon dioxide evolved from barium carbonate. The reproducibility of these determinations is of a similar order t o that obtained ivith barium carbonate on the loading line, so for counting tubes loaded directly from the combustion line and not on the loading line a similar error must) st’illbe considered. Correction should be made on bot.h calibration and analysis measurements t o a standard reference temperature, in order to minimize the effect of hemperatwe on the observed gas pressure. If this is done, the effect of this error is small (probably less than 0.2%). On the two-liquid manometers previously described ( 1 , 4 ) , the reproducibility of a given reading of the manometer is about 0.01 em., with t,wo readings being involved in each tube filling and each calibration determination. The percent’ageeffect of this error decreases as the amount of carbon dioxide being measured increases, but x i t h a filling of 1 mg. of carbon on a system where the standard rise is about 5 cm. per milligram of carbon, it amounts to f 0.2%. ilnother error stems from the calibration of the volume fraction, Ve, wit’hin the cathode volume of each counting tube. It is measured by filling the tube t o the various levels necessary with redist.illed toluene from a buret, then calculating the fraction from the relative volumes so determined. .4s the use of buret readings taken to 0.05 ml. gives results nearly identical to those obtained by weighing the tube a t each stage, the more rapid buret readings are considered sufficient. However, while the root mean square deviation in results on a given tube, as determined by any one person, averages about i.0.25%, the deviation when the tube is calibrated by several different persons is =!= 0.4%. Results obtained by four different persons on one tube are as follows: 0.838 f 0.002; 0.845 + 0.001; 0.844 f 0.004; 0.847. The over-all value is 0.843 =!= 0.0035 (root mean square deviation cal-
+
1940
ANALYTICAL CHEMISTRY
culated separately, on the basis of 12 values). Since a tube is ordinarily calibrated once or twice by only one person, the assignment of uncertainty from this source is 0.5%. This error, and that in the manometer readings, are the chief operational errors which do not affect each sample equally. An uncertainty exists in the calibration of the counting efficiency within the “active volume” of the counting tubes. Its determination is subject to all of the above operational errors, and to the effect of the counting statistics involved, as the calibration must be made on the basis of counting carbon dioxide evolved from a standard sample. This determination has been made a number of times, and the root mean square deviation of the results of these determinations is therefore a g3od measure of the actual effect of the operational and statistical errors on this system. The results of 30 different determinations of three different treatments of the standard sample show a root mean square deviation of 1.93% from the average value obtained. I n any counting procedure, the statistics of the counting must be considered. The standard deviation of any count or series of counts may be easily calculated by standard methods ( 5 ) . I n the present work, with tubes of about 100-cc. volume, the background is approximately 70 to 80 counts per minute. When the sample counting rate is below 3000 counts per minute, the standard deviation due to the background must also be taken into consideration. Above that counting rate, the uncertainty in the background becomes insignificant, statistically, and may be ignored. I t should also be recognized that, a t very low sample counting rates, deviations due to such untoward effects as electronic aberrations and external sources of various types become increasingly important. This does occur occasionally, and must be watched for a t all times. The use of calibrated external sources to determine that the counter is behaving normally is of value in this connection (4). The precision with which a sample can be determined varies with the net counting rate of the sample. Table I lists the approximate precision at various counting rates, for a typical sample counted in two counting tubes to a point where 10,000 total
*
*
counts are registered, or a t least 3 minutes has passed (to reduce possible errors in the counting time), on each tube. This precision includes operational errors and statistical counting errors, but does not include any errors which affect the samples equally. With activities of about 300 counts per minute or more, it is possible to approach a precision of =k 2% by burning and counting a sample a number of times, as Statistical errors are thereby minimized and the operational errors become the chief contributors. At very low net counting rates, the operational errors become relatively insignificant, with counting statistical deviations and nonstatistical events playing the dominant role in the precision obtained. At low net counting rates, another factor operates to lower the precision which is attainable. At a gross counting rate of about 100 counts per minute, each count by which the background (70 counts per minute) is incorrect contributes an error to the net sample counts of about 3%; and, since the background cannot be counted simultaneously with the sample, on the same counter and in the same counting tube, some uncertainty in its actual value is inevitable. With a given counting tube on a given counter, the background may vary 1 to 2 counts per minute from hour to hour, about 3 to 4 counts per minute in a day. Occasionally a variation of as much as 10 counts per minute has been observed with 1-hour counts taken on different days. The actual counting efficiency, E, is determined by the magnitude of the end effects of the counting tubes, but in practice is based on a comparison rrith the Xational Bureau of Standards sodium carbonate carbon-14 standard. The absolute value of this standard is at present open to question, however ( 3 , ?‘,8),and until the discrepancy concerning it is resolved, an unknown and possibly large error in the absolute specific activity values obtained by this method must be considered. At present, the value given by the National Bureau of Standards for this standardnamely, 1280 disintegrations per second per milliliter-is used to calculate the counting efficiency of 0.975. This error does not affect relative values betiyeen samples assayed on the same system and may be ignored from that standpoint. LOWER LIMIT OF ACTIVITY DETECTION
Table I.
Precision of Activity Determination a t Various Operational Error Levels
I t was considered desirable to determine the reasonable lower limit of detectable activity with this counting system, and to dePrecision of Specific Activitya,b,c for Several termine the precision with which such measurements could be Operational Error Levels. i%balbtc S e t Counting made. To this end, benzoic acid, the activity of R-hich had been Rate, C.P.M. 2% 3% 4% determined 13 times and was known to within 3= 27,, was diluted 50 5.1 5.5 6.1 100 3.3 4.0 4.8 with inactive benzoic acid to obtain material which contained 300 2.5 3.4 4.3 2.4 10.1 & 0.2 and 2.02 f 0.04 counts per minute per milligram of 500 3.3 4.2 2.2 1,000 3.2 4 1 carbon. About 1 mg. of carbon, as carbon dioxide, from each 2.2 3,000 3.1 4.1 2.1 3.1 10,000 4.0 sample, was placed in each of two counting tubes and counted Standard deviation of the background taken t o be 1 2 o.p.m. in each case. under optimum conditions. For this pulpox?> counting tubes b For one sample in two countine tubes. counted for 3 minutes or 10.000 . were selected which showed long counting plateaus and stable counts (gross). C Includes operational and statistical errors, b u t n o correction for absolute h a c k a r o u n d characteristics. counting efficiency. The results are shown in Table 11. Table 11. Low-cr Limit of Activity Detection T h e s e r e s u l t s shorn that, under these conditions, even 2 Background Sample ._ Time Time Av. net sample counts per minute can be deSample Nature of Background a counted, Sample counts, counted, Net sample counts/mg. C, SO. Sarnpleb counts, c.p.m. min. c.~.m.~ min. counts, c.p.m.‘ c.~.m.%~,d tected with a standard devia1 Inactive 72.6 i 0 . 3 0 79 1 73 0 i 0 . 6 4 176 0 . 6 + 0.51 0 . 4 + 0.71 tion of about 20%. Variation 73.9 i 0.31 785 74.7 i 0.66 0 . 8 zt 0 . 7 2 172 2 70.8 i 0.38 443 Inactive 7 1 . 0 I0 65 165 0 . 2 & 0.75 0 6 = 0.54 in the actual division of count73.2 i 0.39 479 74.2 zt 0.68 I58 1.0I 0.78 ing time betreen sample and 3 7 7 . 0 i 0 44 Inactive 398 76 8 + 0 . 5 8 224 0 . 2 + 0.55 -0.7 1 0 . 7 3 7 5 . 5 zt 0 . 4 6 76.6 i 0.67 360 169 1.1 i 0.81 background is allowable, but 4 71.5 i 0 . 4 4 1 0 . 3 zt 0 . 2 370 82.1 10 . 6 7 181 1 0 . 0 + 0.56 10.6 i 0.80 10.2 i 0 . 2 7 3 . 6 + 0 42 83 2 i 0 . 6 8 420 182 it is desirable to count the 9 . 6 zt 0.80 5 7 2 . 0 i. 0 . 4 4 2 . 0 8 zt 0 . 0 4 73.5 i 0 . 0 4 364 2 . 7 i 0 53 1.5 i 0.78 177 background as long as the sam0.04 74.1 i 0.45 2.14 365 7 8 . 2 I0 . 6 6 178 4 . 1 I0.80 ple itself in such cases (6). I n Deviations shown are calculated standard deviations. * Where expected counts are listed they are based on original activity and standard deviation then calculating this case, the background activity of sample from dilution by \,:eight with inactire material. Corrected for actual amount ‘of carbon dioxide present. counted both before and after With inactive samples no correction is made for milligrams of carbon present. the sample vias counted, with d Expected counts per minute per milligram of carbon are: sample 4, 10.1 f 0.2; sample 5 , 2.02 i 0.04. the time period of each back~~
I
*
1941
V O L U M E 2 7 , NO. 1 2 , D E C E M B E R 1 9 5 5 ground counting period and the sample counting period being approximately equal. This means that for each sample the background was counted approximately twice as long as the sample, and each sample was counted to well over 10,000 counts. For the calculations, the total background time was taken for each tube, rather than considering the two background periods separately. METHOD OF CALCULATING c
The standard deviations shown in the tables were calculated by the usual methods ( 5 ) . I n Table I, the deviations are a combination of the standard deviation of the gross counts involved, the standard deviation of a normal background count (taken to be f 2 counts per minute in all cases), and the indicated contributions from the operational errors. The percentage deviations listed mere determined from the square root of the sum of the squares of the numerical values for each of these deviations. I t has been shown that under the present conditions the operational errors are about Z%, and the column under that heading is taken to apply. In Table 11, the deviations shown are the calculated standard deviations, in counts per minute, based on total counts in each case. The deviation for the net sample counts for each tube is the square root of the sum of the squares of the appropriate background and sample deviations, and the average net sample deviations are half the square root of the sum of the squares of the deviations of the two values used to obtain the average value. With the inactive samples, no correction is made in the average value for the amount of carbon dioxide in the counting tube, as this contributes no statistical variations to the background count so obtained. Present eyperience indicates that with very low counting rates, such as those under discussion, it is best to do all of the counting, during the working day. When these counting tubes were left counting overnight, either on background or on sample counts, deviations were often observed which were far outside of the expected statistical deviations. 4 s a result, all of the data presented in this paper 1%-eretaken during the working day, when external conditions appear to have remained more or less constant The counting rates tend to be sonie~vhatlower during the night than during the day, although this is not found to be universally true.
It may be significant that the deviation from the expected counts per minute is generally positive, including those casee where inactive carbon dioxide mas employed. The filling gas was introduced into the counting tubes from the same vacuum line in all cases, for both samples and backgrounds, so it is unlikely that this effect is due to contamination from the line. Sample 3 was obtained by burning an inactive sample on a combustion line which had never been used x i t h an active sample. I t may be that the presence of carbon dioside in these counting tubes causes a slight rise in the counting rate observed. I n view of these results, it appears that as little as 2 counts per minute can be detected in a counting tube of this type with the background conditions prevailing here. Those samples which show counts indistinguishable from background, in terms of the standard deviation, are considered inactive. However, even 1 count per minute might be detected by this method, with somewhat longer counting periods. Certainly it is possible, with the counting conditions described, to state definitely that a sample has less than 2 counts per minute, if such is the case, and for practical purposes 2 counts per minute is considered the loner limit of activitg detection by the method described. ACKNOWLEDGMENT
The authors are indebted to Richard W. Dodson and Gerhart Friedlander for valuable discussions concerning the statistical aspects of this paper. LITERATURE CITED
(1) .Inderson, R. C., Delabarre, Yvette, and Bothner-By, A . A , . ANAL.CHEM.,24, 1298 (1952). (2) Bernstein. W.. and Ballentine. R.. Rev. Sei. Instr.. 21. 158 (1950,. (3) Caswell, R. S . , Brabant, J. AI., and Schwebel, A . , ’ J . Rksearch -Vatl. Bur. Standards, 53, 27 (1964). (4) Christman, D. R., Day, S . E., Hansell, P. R., and Anderson, R. C., ANAL.CHEM.,27, 1935 (1955).
(5) Friedlander, Gerhart, and Kennedy, J. W.,“Introduction to Radiochemistry,” p. 199, Wiley, New York, 1949. ( 6 ) Ibid., p. 216. ( 7 ) Natl. Bur. Standards ( E . S)., Tech. ‘Vews Bull., 38, 72 (1964). ( 8 ) U.S. Atomic Energy Commission, Atomics and Atomic Techno!., 5 , 340 (1954). RECEIVED for review M a y 6 , 1955. Accepted ;Iugust 15, 1955. Research 8. .itomic Energy Commission. carried out under the auspices of the
r.
laboratory Methods for Evaluation of Evaporation losses of Petroleum Prodwcts JOSEPH HOLOWCHAK’ and E. L. BALDESCHWIELERZ Products Research Division, Esso Research and Engineering Co,, Linden,
Two laboratory methods have been developed for the accurate determination of evaporation losses. The first procedure is a modified Chenicelc-Whitman vapor pressure method, in w-hich measured amounts of dry air are bubbled through a known amount of a hydrocarbon mixture at a fixed temperature and at a rate to ensure saturation of the air with hydrocarbon vapors. The vapor pressure of the hydrocarbon mixture is calculated from the volume of the vapor evolved, the total amount of air and vapor, and the pressure of the gasmeasuring device. In the second procedure a densityevaporation curve is established to determine the effect of the evaporation loss on the density of the sample under investigation. Both procedures are accurate, convenient, and applicable to almost any type of evaporation problem. The vapor pressure method can accurately determine evaporation losses as low as 0.04oJ00; density method can detect losses as low as 0.01%.
N. 1.
E
CONOPIIIC and weather conditions may require extended storage of crudes and finished petroleum products. The relatively high volatility and values of these materials justify the attention paid to evaporation-control measures. The magnitude of the evaporation losses in handling and storage of petroleum and its products has to be determined accurately in order to provide economic justification for evaporation-loss prevention programs in balancing the savings against the cost of equipment and preventive measures. Methods which can be applied to determine these evaporation losses may be based on direct measurement, such as by gaging, where the volume is measured prior to and after the loss has been incurred, or on some change in physical property such as vapor pressure or density. The petroleum industry has long felt the gaging method to be unsatisfactory as a practical procedure in spite of its suitability as to theory. The most significant factor contributing to its 1
Deceased.
* Present address,
17 Central Ave., Cranford, N. J.
