Roger A. G. Marshall Thames Polytechnic London. SE18. United Kingdom
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Direct and Reverse Isotope Dilution Analysis
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A simple experimental approach using volumes
A perennial problem in designing practical courses is to balance the need to demonstrate as manv useful scientific principles as possible in the time available with the necessitv to give the student lahoratorv skills. This exercise laree1; faiG in this latter respect, hut has been found very useful in illustrating the concepts of direct and reverse isotope dilution analysis in less than two hours practical work. It has been used successfully with degree level chemistry and biology students over the last four years. Direct isotope dilution analysis is a useful technique for analyzing complex mixtures and its reverse form is applied when the compound to he determined is radioactive as in a tracer experiment or after activation.' The techniques require the separation, purification, and counting of a radioactive compound usually in the solid state. This can .often he time-consuming, inaccurate, and can easily lead to laboratory contaminatinn. Major sources of error in counting a solid are self-ahsorption and irreproducihle counting geometry. These may he partially removed by counting a sample a t infinite thickness with careful planchet desigm2 None of these problems arises if we set out to determine volume instead of mass. This is of course a common use for the method anyhow, as for instance in the estimation of body blood volumes3 or underground water reservoir cont e n t ~ An . ~ additional convenience of the technique is that any radionuclide, which can he counted easily in solution, can he used. We have always utilized 32P (Em., = 1.718 MeV; half-life = 14.3 da) as phosphate ion despite its propensity to adsorb on glass and have used a liquid GeigerMiiller tube, capacity 10 ml, for activity determinations Theory
Let a volume V1 of a radioactive solution of specific activity A1 he added to an unknown volume V2, and let the
320 / Journal of Chemical Education
new specific activity of the diluted volume he A%Therefore
and rearranging . . a
In reverse isotope dilution analysis a volume V3 of inactive liquid is added to the active solution, in this case (VI V*), and dilutes the activity to a lower value As. Therefore
+
and rearranging .
.
An "unknown" volume of approximately hut not exactly 500 ml has been found convenient; in this case the volume added in the reverse step can he 250 ml and the whole can he contained in a 1-1flask. Experimental Procedure Direct Isotope Dilution Analysis
Measure the background activity of the liquid Geiger-Mliller tube containing 10 ml distilled water. Add 1ml active carrier-free
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Tolgyessy J., Braun T., and Kyrs M., "Isotope Dilution Analysis," Pergamon Press, Oxford, 1972. * Johnston C. B., Drake G. W., and Wentworth W. E., J. CHEM. EDUC., 46 284, (1969). Hobbs J. T., "Total Blood Volume-its Measurement and Significance." Medical Monoeraoh - . 3.. The Radiochemical Centre. Amershsm, England, 1967. 'Broda E., and Sehonfeld T., "The Technical Applications of Radioactivity," Pergamon Press, Oxford, 1966, Vol. 1,p. 301.
phosphate aolution (200,000 cpm. mT1 (-1 #Ci ml-l)) and -1 g sodium phosphate carrier to at least 11 ml distilled water in a boiling tube and mix (Solution A). Pipet 1 ml Solution A into 10 ml distilled water in a second boiling tube and mix. Take 10 ml and measure the activity in the liquid Geiger-Mdler tube until at least 10.000 counts have been collected. Wash out the tube and confirm that it is clean by remeasuring the background activity. Pipet 10 ml of Solution A into the liquid of unknown volume and measure the activity of a 10-ml sample of the diluted solution (>10,000 counts). When complete, return the sample to the bulk. Apply a dead time correction to each activity, subtract the background, and calculate the volume of the liquid (eqn. (1)). Reverse Isotope Dilution Analysis
Add a known volume of distilled water to the "unknown" volume..~mix..~ and measure the aetivitv of a 10-ml aliauot of the rediluted solution i>ID.ul)O eountw Apph n dead time rorr~ctim. whtract the hackground and reusing rhc activity vnlw nhove ral. eulatr awrond figure tor the vulumr teqn r211. Error Assessment
Examination of the results ohtained, particularly when the determinations are repeated or collated from a class of students, provides an interesting problem in the allocation of error. In addition, since the statistical error due to radioactive decay can he accurately assessed, the calculation of the total error from the source is a good exercise in error summation. Thus the two most probable sources of random error are the error from radioactive decay and errors in the added volumes V1 or V3. The former error can easily be calculated since the standard deviation, s, is given by s = d(tota1number of
counts)
= d m where A is the activity and t is the total counting time. In the summation of error occurring as a sum or a difference,5 i.e. when Q = x ? y . . ., the total standard deviation is SQ
= d(sX2 +syZ.. .)
=d(A,t,+A,ty. ..) In the summation of error occurring as a product or quotient, i.e. when Q = xy . . ., the fractional error is
(4)
SA,/AZ =
In the reverse isotope dilution analysis calculation of the assuming that the radioactivity, error may he simplified error of (A3Vl - AzVd is insignificant compared to that of A3V3 in eqn. (2). In this case the total fractional error due to radioactivity is given by Adz (&
ever re
~irect rnl
rnl
481 481
491
---
498
~ e a volume n = 500 m l Standard deviation = 72.8 m l coefficient of variation = 70.56%
473 510 487 481 475 nan 494 Mean volume = 486 Standard deviation = T I 1 ml Coefficient of variation = 7 2
In each case, when a series of results has been ohtained, the error attributable to the added volume V1 or V3 can he calculated hy use of eqn. (3) where S g will be the fractional error determined from the series of measurements. Results
A series of determinations was carried out on ten "unknown" volumes of exactly 500 ml each using the same active hulk Solution A (see table). The activity of this solution was 19, 197 cpm ml-' and a total of 95,987 counts were collected in three determinations. On dilution approximately 23,000 counts were collected for each sample in 5 min. The coefficient of variation (fractional error X 100) of the volume determination was found to be ~ 0 . 5 6 %while , that calculated from eon. (4) was ~ 0 . 6 6 % . In the reverse isotope dilution analysis 250 ml distilled water were added and the number of counts collected in a 5-min period was approximarel? 15.500. 'l'he coeffic~cntof variation found had increased to -2.2% and that calculated from eqn. 151 was 7 2 . 7 ' ~If. can thsrefnre be concluded that the random error of radioactive decay is the primary source of error in these analyses and that more precise results could have been ohtained by taking longer counting times. Problem
In contrast to the straightforward procedure above, it has been found to he a stimulatina- exercise with students, who have already received some radiochemical training, to present them with an active carrier-free phosphate solution and an instruction to determine the volume by direct and reverse isotope dilution analysis. The results are generally poor due usually to one or more of the following mistakes 1) A failure to add carrier, which produces disastrous results.
..
Therefore in the direct isotope dilution analysis, the fractional error due to radioactive decay (AlIAz) is given by
SAdArA3=d[&+
Replicate Determination. of 5 0 0 4 Volumes bv IsotoDe Dilution Analvser
+ A3t9
- A#
1
(5)
2) Inadequate cleaning of the Geiger-Mijller tube between read-
ings. 3) Inadequate mixing of liquids, particularly in the Geiger-Mdler tube if this is used for dilution of Solution A. 4) A failure to appreciate the statistical error in counting. 5) The omission of a dead time correction, which is particularly
important in the direct analysis when the ratio of activities is large. 6) TOO small a volume is added in the reverse step giving inadequate dilution.
Vantony D. A., "Statistics, Theory of Error and Design of Experiment," Royal Institute of Chemistry, London, 1961, p. 24.
Volume 53, Number 5. May 1976 / 321
