A Relative Isotope Dilution Analysis C. 0. Johnston, G. Wilson Drake, and W. E. Wentworth Univrrsity of Houston Houston, Texos 77004
Using Samples of lnfiaite Thickness
I
For undergraduate instrumental analysis
T h e following is a description of an isotope dilution analysis experiment which has been used in this department for about four years. Some obvious advantages of the method are listed. The use of an infinitely thick sample for counting greatly simplifies the determination (1, 8 ) . The difficulty encountered in forming and drying thin layers of precipitate without cracking or curling is eliminated. The problem of varying absorption and backscattering disappears when the use of a thin layer of precipitate is abandoned (3). It is unnecessary to weigh the precipitate in the method suggested or to determine the specific activity of the original radioactive isotope used in the experiment. For this reason the age of the radioactive isotope is unimportant as long as the activity is great enough for accurate counting. A minimum amount of time is required since the determination can be performed in six hours. Some time is required to digest precipitates, filter them, and dry them. Some of these operations require very little attention on the part of the student. If calcium ion is to be determined a sufficient quantity of the radioactive isotope, calcium 45, can be obtained without a license, rather promptly, and at small expense. The isotope is safe enough to handle since its radiation is P- at .25 MeV with no gammaradiation. The half-life is 165 days. The equipment required for the experiment is the usual laboratory glassware, a drying oven, balance, and counter. A special planchet to hold the precipitate as it is counted was designed. The student gains experience in handling a radioactive substance and in counting the samples. Finally, after the initial weighing out of the sample and reference material, no further weighing is necessary. Procedure
I n principle, two samples containing known amounts of calcium ion can be used to make a calibration curve, but, in practice, the student is required to employ five samples. A dried sample of pure calcium carbonate is weighed out and dissolved in hydrochloric acid and diluted to a known volume. Different aliquot parts of this solution are pipetted int,o each of five beakers and distilled water is added to each beaker to make approximately equal volumes. The unknown sample is weighed, dissolved, and made up to a known volume. An aliquot is taken which is estimated to be between the largest and the smallest known samples. I t is diluted in its beaker so that its 284
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volume is about the same as the volume of one of the known samples. Now add to each of the six samples, the knowns and the unknowns, an identical amount of calcium 45. This is conveniently done by attaching a micropipet to a Clay-Adams pipettor and employing this comhination to measure the radioactive isotope solution. Then the calcium ion is precipitated as the oxalate (4). The precipitates are digested, filtered on filter paper, and placed in the oven to dry at a temperature of 105llO°C (5). This should form the calcium oxalate as the monohydrate. The first known sample is removed from the filter paper, the precipitate is crushed with a spatula and the powder is packed into the planchet. The cavity in the planchet is deep enough to insure infinite thickness of the sample (Fig. 1). The planchet and cover, shown in
Figure 1.
Crou sedion of planshot and cover.
cross section, are cylindrical and of such size as to fit our counter. A machinist should be able to make both pieces in less than an hour from aluminum stock. The surface of the packed powder is polished off by sliding a piece of glass tubing across the planchet. The sliding motion produces a uniform surface on the powder. It is impractical to wipe off the excess powder around the surface surrounding the sample. Therefore, the cover, with sloping sides to the hole, is placed over the sample. This makes a geometrically reproducible surface for counting and a t the same time radiation from any spillage is blanked out. The sample is routinely counted and recorded. The process is repeated on each remaining sample including the unknown. Data and Calculallons
To make the standards for preparing the calibration curve a 0.05 M solution of Ca2+ was made up ac-
curately by weighing dry, purified calcium carbonate. 25.0, 50.0, 75.0, 100.0, and 125.0 ml portions of this solution were diluted to 250 ml in volumetric flasks. Onc ml of stock radioactive CaZ+solution was added to each solution. I t is only necessary that enough activity be added so that the background count will be a reasonably small fraction of the sample count. The fact that the activity added need not be known is the heart of the method described. I n one series of ten experiments a total of approximately 4 microcuries was used. Students should be instructed in the proper handling and disposal of radioactive materials even though the level used is quite low. The solutions were mixed thoroughly and the CaZ+was precipitated with excess 0.05 M sodium oxalate under conditions given by (4). Of course, the unknown is treated in the same way as each of the standard samples.
Table 1 .
Data from Five Determinations
Theory
The justification of the straight line plot is obtained in the following manner. First, it will be assumed that the activity is related to the thickness of the sample by an exponential law. The activity, A, in an element of thickness dx is given by
where A' is the specific activity, k is the absorptivity of radiation under the conditions prevailing.
A is directly proportional to A". An equation generally used to relate weight and activity is (6)
Wl = weight of radioactive substance added, W = weight of unknown non-radioactive substance, Ao = specific activity of mixture, and A,' = specific activity of added component. Then The data (Table 1) from five determinations are plotted in the curves (Fig. 2). The number of millimoles is used instead of concentration since each sample was made up to the same volume. The reciprocal of the number of millimoles is also plotted against the couuts per minute and since this plot is a straight line it is the one preferred for reading the value of an unknown from its count. In order to establish the probable precision resulting from the techniques in the experiment, the following procedure was carried out. Ten identical samples of calcium salt solution, .05 M, were pipetted into beakers and were treated with equal quantities of 45Ca,precipitated, filtered, dried, and counted as described above. Thc results are given in Table 2.
The weight W 1is very small compared to W and may be neglected in the denominator.
A" is proportional to 1/W or, as we have seen above, Table 2.
Data for Ten Identical Samples to Determine Precision of Experiment
Sample
Countslrnin less background
Deviation (counts/min)
614.9 629.8 628.4 640.3 630.6 625.5 627.8 661.6 641.6 638.7 633.9 630.8
19.0 4.1 5.5 6.4 3.3 8.4 6.1 27.7 7.7 4 . 8 9.3
1 2 3 4 5
6 7 8 9 10 Average (all) (Exclude #8)
Dev excluding #8 (counts/min)
15.8 1.0 2.4 9.5 0.2 5.3 3.0
...
10.8 7.9 6.3
Q = (#8 - {9)/(#8 - $1) = 20/46.7 = .43. Confidence factor for 90% confidence for 10 samples = .41. Therefore, #8 is excluded in further ~lculations.because its 0 value exceeded . .... .the 90% confidence quotient for 10 samdes. Standard deviation (counts/rnin)
Probable error (connts/rnin)
P. Figure 2. minotiom.
Plot of countr/rec. versus amount of C d O s for flve deter-
=
,6745 X 8.4 counts/min
=
5.67
Percent standard deviation = 8'4 loo = 1.33 630.8 Volume 46, Number 5, M a y 1969
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A is proportio~ialto 1/W. This is well illustrated by the experimental plot of cou~itsper minute, Al, versus the reciprocal of millirnoles of the itmctive calcium carbonate. Discussion
The method described for the determination of CaZ+ is subject to the usual errors of the gravimetric method (5). Discussion of these is fourld in many texts on quantitative analysis. I n addition, errors in counting enter in and they are the controlling factors in the precision of the method. Since this is a relative method errors are minimized by treating the Bnowns and the unknowns as alike as possible.
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Literature Cited
(1) ATEN,A. H. W., JIL, Nucleonics, 6, 68 (1950). (2) ~ C H W E I T Z I : K , G. K., A N D STKIN,B. I(., Nucleonics, 7 , 131, 6; (1950). (3) I ~ A D ~N.NS., , J. CHKM.EDUC.,38, 344 (1961). (4) PIERCI:, W. C., A N D HAENISCH, E. I., "Quantit~tiveAnslysis" (3rd ed.), John Wiley & Sons, h e . , New York, 1948,p. 414. ( 5 ) KOLTHOFF, I. M., A N D SANDELL, E. B., ''Textbook of Quantitative Analysd' (3rd ed.), The MaeMlllan Co., New York, 1952, p. 339. 16: EWING.G. W.. " I n ~ t r u m e n t ~Methods l of Chemical Analysis'; (2nd ed.), hleGraw-Hill Rook Co., New York, 1960, p. 273.
