tron counters and reducing the source background to 50% and the cosmic background to 0.1 of its present value (advanced model). A further precision increase can be obtained by using a 1.5-mCi source and reducing the total background to 0.1 of the present one (optimum model).
specificity; and (h) necessity for safety precautions. e. and f. may be corrected by the improvements of the present analyzer and g. by a more advanced concept. These will be achieved at the expense of h.
CONCLUSION
A. Schoenberg contributed basic data and measurements. A. Aladjem contributed through source development. A. Kedem advised on engineering design, and Y. Nir-El in theoretical subjects.
The apparatus described previously shows the following advantages: ( a ) possibility of nondestructive testing of liquids, solid, gaseous, and chromatogram samples; (b) no necessity of sample preparation; (c) no need for highly skilled personnel; and (d) possibility of an on-line analysis. Disadvantages in comparison to mass spectrometry are: (e) lower sensitivity; (f) lower precision; (g) lack of
ACKNOWLEDGMENT
Received for review August 25, 1972. Accepted December 26, 1972. This research was supported in part by Yeda and Miles-Yeda Companies, Rehovot.
Isotopic Analysis of Tritiated Water Claude Genty and Guy Reversat Commissariat a I’Energie Atomique, Centre d’Etudes de Bruyeres-le-Chatel, 6.P. 67, 92120. Montrouge, France
Isotopic analysis of mixtures of H20-HDO-HTO-D20DTO-T2O can be carried out to a satisfactory approximation by infrared spectrophotometry, based on the measurement of two independent ratios such as [DTO]/[T20] and [HDO]/[D20]. This method, which precludes any absolute measurements, has the advantage of eliminating a certain number of experimental errors. The calculation procedure is based on statistical theory and uses approximated values of the equilibrium constants. Experimental results are cross checked by comparison with microcalorimetry.
The problems relating to the isotopic analysis of mixtures of heavy and light water have been studied and resolved by infrared spectrophotometry (1-5). Mixtures of tritiated water, heavy water, and light water involve far more complex analysis. The number of constituents is increased from 3 to 6 (HzO, HDO, HTO, DzO, DTO, TzO) and in order to determine isotopic ratios H / ( H + D + T ) , D l ( H + D + TI, T / ( H + D + TI, the analyst is obliged to determine the six individual concentrations or to resort to chemical transformations (6). But it has been shown previously that isotopic ratios are obtainable when two independent measurements of molecular concentrations are known (7). For the mixture of the six compounds, the measurement of two concentration ratios such as [DTO]/[D20] and [HDO]/[D20], which can be done by infrared spectrometry, allows determination of the isotopic ratios, H / ( H + D T ) , D / ( H + D + T ) ,T / ( H + D T).
+
Apparatus. In view of the large quantities of tritium handled, the cell of the infrared spectrometer Beckman IR9 is installed in a glove box with air ventilation. The cell is made of barium fluoride which is not hygroscopic but has a transmittance of 50% a t 1000 cm-l. Reagents. The pure tritium for research purpose was supplied 71 > by the Commissariat h 1’Energie Atomique, T / ( H D 99.5%. The pure deuterium was supplied by the Commissariat I 1’Energie Atomique, D / ( D + If) > 99.410. The 99.75% heavy water was supplied by the Commissariat I 1’Energie Atomique. Identification of Absorption Bands. Water containing the isotopes hydrogen and tritium was synthetized by the combustion of an hydrogen-tritium mixture, with the water recovered in a trap cooled by Dry Ice. The purpose was only qualitative involving the identification of the bands. The study of the infrared spectrum of this water (Figure 1) revealed the following absorption bands
+
+
Molecule
Assignment
Obsd freq cm-’
T20 HTO H20
v2
1024 1388 1645
v2 u2
The bands of the type v3 H20 at 3400 cm-l and T20 at 2200 cm-1 were ignored because of their large width (400 to 500 cm-I). Besides HDO also exhibits an absorption band a t 3400 c m - l . Water containing the three isotopes of hydrogen was obtained in the same way, starting with a hydrogen-deuterium-tritium mixture. The spectrum (Figure 2) revealed the following absorption bands
+
(1) J. Lecomte, M. Ceccaldi, and E. Roth, Commis. Energ. A t . [ F r . ] , Rapp.. 313 (1954). (2) M . Ceccaldi, Commis. Energ. A t . [ F r . ] . Rapp., 1285 (1959). (3) M. Ceccaldi. Commis. Energ. At. [ F r . ] . Rapp.. 2441 (1964). (4) R. D.Kirnbrough and R . W. Askins,Anal, Chem.. 41, 1147 (1969). (5) W. E. Keder and D. L. Kalkwarf. Anal. Chem.. 38, 1288 (1966). (6) M. Goldblatt, J. Phys. Chem.. 68, 147 (1964). (7) C. Genty. Anal. Chem.. 45, 505 (1973).
1710
EXPERIMENTAL
Molecule
Assignment
Obsd freq cm-’
T20
u2
DTO
u2
Dz0
v2
1024 1130 1220
The absorption bands of type v 3 caused hy molecules of T20 and D20 at 2200 c m - l and 2500 cm-l, respectively, are very intense, but very wide and practically overlapping. The five absorption bands retained were those of fundamental frequencies, without any interference from other molecules. The measurements, from which the isotopic ratio T / D in the water sample was determined, were the ratios of absorbances of the absorption bands of the different molecules.
A N A L Y T I C A L CHEMISTRY, VOL. 45, NO. 9 , AUGUST 1973
The following ratios were determined
RESULTS AND DISCUSSION Equilibria. The hydrogen isotopes H, D, and T lead to the immediate formation of the following three equilibria.
Calibration. In order to obtain the different calibration lines giving the ratio [ T I D ] it was necessary to have a sample of tritiated heavy water wit) a known [ T I D ]ratio. This water was obtained either from samples containing known quantities of pure deuterium and tritium and in ensuring that complete oxidation of the sample was achieved (more than 99%), or in using pure tritium oxide and deuterium oxide obtained by independent cornbustion. When the combustion procedure involving tritium and deuterium gases is used. the protium contamination during synthesis is no problem because the isotopic ratio is not affected. The other points for plotting calibration lines were obtained by isotopic dilution with 99.75% pure heavy water. In order to do this, it was necessary to determine the hydrogen content of the initial water and a t successive dilution stages. The calibration lines giving the ratio [ H I D ] were plotted by using heavy water-light water mixtures.
H,O D,O TZO
+ + +
DZO 2HDO T,O e 2DTO H,O & 2HT0
The concentrations of the six compounds are linked by the relations
A N A L Y T I C A L CHEMISTRY, VOL. 45, N O . 9, AUGUST 1973
1711
K1 = 3.8 a t 25 "C (8-lo), the values of KS and K3 are not exactly known but are in the neighborhood of 3.8. Determination of the Ratio [TID]. Relations such as Equation 1 were derived from the ratios
01'
The values obtained in a number of typical cases are reported in Table I. By the direct application of statistical theory, it is seen that the error remains a t an acceptable level, justifying the use of relation 2 as a first approximation. where is the molar extinction coefficient and 1 the length of the cell. Value of the Ratio (T2O/DTO]. The application of statistical theory to isotopic analysis ( 7 ) shows that a t equilibrium, the ratio of the concentrations of T20 and DTO is expressed by the relation
It is known that this relation is only an approximation. However, with a more exact formula, incorporating equilibrium constants, relation 2 can be used with very satisfactory results. Setting down K , = 4 + 4aJ K, = 4
+
4u2
K, = 4
+
4a3
u1, 6 2 , and u3 represent minute quantities, so in making calculations all terms of second or higher order may be ignored. In these conditions it is shown (Appendix I) that [TzO/DTO] may be written as
[%I
=
(2) Calculations show that the errors incurred in the determination of T / D by statistical theory with the assumption K1 = 3.8, Kz = 3.9, K S = 3.7 are not very different from those of Table I. ( b ) The error resulting from the displacement of an equilibrium by a third isotope. From a practical point of view, this kind of error is the most important one because the calibration curves are plotted by means of mixtures for which the ratio T / D is known. Therefore, the error made when analyzing an unknown sample is only due to the displacement of the equilibria entailed by the presence of hydrogen in variable quantities. The points of the experimental curve [TzO/DTO] = f [ T / D ]will be right for the same concentration of hydrogen in the sample as in the standard. If the hydrogen isotopic ratio is Htfor the standard and He for the sample the error in the measurement of [TIL)] will be
Setting down
or as
ACT ID;
'[TTIDI- =
Two kinds of error can be estimated. ( a ) The error incurred when the relation given by the statistical theory 2 is used instead of the general formula 3.
-io,
-
6H 2
a I'
- -022
[T/D] - 1 [T/DTR
''
and
(4)
This can be expressed as follows
In practice, since only constant h'l is known, it is impossible to estimate the error involved in using statistical theory. However. an attempt can be made t o estimate this error, assuming that k'l = K2 = K3 = 3.8. The error value is
(8) J. W. Pyper, R. S. Newbury. and G. W. Barton, Jr., J . Chern. Phys.. 46. 2253 (1967). (9) L. Friedman and V. J. Shiner, J . Cheni Phys., 44, 4639 (19661 (10) M. Wolfsberg. J Chern. P h y s . 50, 1484 (1969). 1712
The errors involved in the measurement of [ T / D ]by hydrogen are given in Table 11. It can be seen that the quantity of hydrogen, insofar as it stays low ([HI < 0.2), has little influence on the value of the ratio [T'/D] especially in the neighborhood of [T/D] = 1. It is impossible to determine [T20/DTO] directly. As telation 1 shows, the actual concentrations are related to a factor, since spectrophotometric methods only give absorbance values. Actually c(T2O) and c(DT0) do not exactly correspond to the true molecular extinction coefficients, because the base line is hard t o locate accurately and the determinations are marred by a systematic error. The line of least squares plotted from these experimental points corresponds to the equation
A N A L Y T I C A L CHEMISTRY, V O L . 45, NO. 9, AUGUST 1973
~
The constant reflects the fact mentioned above about the determinations proceeding from an arbitrary, estimated base line. However, within the limits of experimental error, the ratio d’r,o/dnTO has a linear relationship with the ratio [TI/ [DI. Determination of [DTO/DzO]. Calculations resembling those carried out for the ratio [TzO]/[DTO] lead to a similar equation
Table I. Error Incurred in the Determination of [ T I D ] by Statistical Theorya [TI [Dl [HI E % 4 4
0 2 0 5
08
4 1 1 1
0 2
05 08 02
0 25 0 25 0 25
which may be rewritten
a
1 1 2 2 2 2 3 3 2
0 5
08
3 7 2 5 5 5 7 2 8
Measurement of [ T 2 0 , D i O ] Assumption K , = K: = K, = 3 8
Tabie II. Error Caused to the Measurement of [ T I D ] by the Presence of Hydrogen [TI01
It can be shown, in a similar manner as above, that the error incurred by application of statistical theory remains acceptable. For K1 = K2 = KS = 3.8 the error is
4 4 4 1 1
0.5 0.2
1
0.1 0.5 0.2 0.1
0.5
0.2
0.25
0.25
The values obtained are reported in Table 111. It was observed that when [ T / D ] < 0.8, determinations of the ratio [DTO]/[DzO] give values closer to the true isotopic ratio [TiD] than determinations of [TzO]/[DTO]. When TIL) > 0.8, the reverse is true. It was also observed that the displacement of equilibrium D20 + T z O 2 2DT0 by hydrogen is low. The calculated values are the same as in Table 111. The concentrations are related to optical intensities by the relation
-0.75 -0.3 -0.15
Table I l l . Error Incurred in the Determination of [ T / D ] by Statistical Theorya [ T , oj
H
0.2
0.1 0.2 0.1 0.2 0.1 0.2 0.1 0.2 0.1 0.2 0.1 0.2 0.2
0.4
0.6 0.8 1
For reasons set forth above, only apparent extinction coefficients can be obtained. The line of least squares plotted from the experimental points corresponds to the equation
2 5 a
Determination of the Ratio [H]/[D]. The value of [H]/[D] can be obtained from the determination of ratios such as [HDO]/[D20] or [HTO]/[DTO]: in this case, the ratio [HDO]/[DzO] was used, since calibration is far easier with nonradioactive compounds. On the basis of aswmptions explained above, [HDO]/ [D20] was calculated as
O/O
0.75 0.3 0.15 0 0 0
0.1
0.25
01’
E,
6H
E.
Oh
-1.0 -1.1 -1.5 -1.6 -1.9 -2.0 -2.25 -2.3 -2.5 -2.5 -3.1 -3.1 -3.8
Measurement of [ D T O / D 2 0 ] Assumption: K , = K 1 = K 3 = 3.8
‘The error contributed t y the ratio [HID] when the variations of the concentration of tritium are neglected can be calculated as formerly. The calibration [HL)O/D20] = f[H/D] is done by means of a mixture of light water and heavy water which does not contain tritium; the error generated when using this curve for the determination of [HID] in mixtures of light water, heavy water, and tritiated water is calculated and given by the formula
Thib can be rewritten
I@[&OI
-
with the assumption K1 = K Z = K3 = 3.8 and with
6T
=
[T,]
-
[T,]
=
[T,]
Tr is the isotopic ratio for the standard and topic ratio for the sample.
T,is
A N A L Y T I C A L CHEMISTRY, VOL. 45, NO. 9, AUGUST 1973
the iso-
1713
The error in [HID] when T is ignored is l o r as long as [TI < 0.4 (the ratio [H/D] is changed by less than 0.5% when [TI = 0.2 and the error in the most unfavorable case is lower than 2.5%). Thus, for calculating the ratio [H]/[D], the calibration curves plotted for heavy water-light water mixtures not containing tritiated water may be used. Calibration was carried out for 0 < [ y / [ D ] < 0.22. The line of least squares obtained from the experimental points corresponds to the equation
and
3
Tk
=
11 H20
T%
=
6.87
+
T2O D20
+
T20
For the value of [TIL)] and [HID]two kinds of error can be calculated: (1) The experimental error which can be estimated as
A[T / Dl
m
= 0.02
Calculation of Isotopic Ratios. Setting down
[TID] [HID]
(2) The error resulting from the displacement of equilibria which has been calculated previously, formulas 4 and 5 . The error on the value of T can be calculated as follows
= a
b
=
The isotopic ratios can subsequently be determined using the formulas
[HI [HI
+
[TI [D]
+
[Dl [D]
+
[HI
[HI [D]
-
+
[TI
+
[TI - a
+
+
a
a
b
+1 LH
1
+b +
+D+
_ _ TJ
1
- A [$])[TI
(-A[$]
b
[TI
=
af6-+T
The results may be expressed differently. by calculating the weight percentages of HzO, 0 2 0 , and TzO which would have been required to obtain a product of similar composition to the one analyzed.
and
+ [$]A[:]
ACT1 = -[Tl([g]A[$] [TI =
