Hans G. Forsberg Bj'drn Widell and Lars-G. Erwall
The Rovol
Institute of Technoloav -. Stockholm, Sweden
I
II
Distribution Coefficients and Ionization Constant
A radioactive tracer method
Radioactive isotopes of diierent elements provide rich possibilities for instructive experiments illustrating the laws of physical chemistry and their application.' The equilibrium of a substance distributed between two immiscible solvents, a problem of great interest for modern extraction technology, can be easily studied using radioactive tracers. A good example of a n equilibrium of this type is the distribution of chloroauric acid (HAuClJ between water and an ether. This equilibrium was first studied by Myliu~.~ From one single experimental series, it is possible to estimate not only the distribution coefficient but also the ionization constant of HAuCL. This can be done if the excess of HC1 in the water phase is different in the different experiments. The mechanism for the distribution of HAuC14 between water and ether is complex, various molecular species being present in both phases.3 I n this simplified treatment, the following species are assumed to be the only ones present in appreciable amounts: ether phaae: HAuCI. aqueous phase: H+, CI-, AuC1,-, HAuCl,
The results obtained indicate that this assumption is correct. Investigations concerning the detailed mechanism for the distribution are in progress a t this laboratory. The following symbols will be used: C'A,, total concentration of gold in the ether phase; C"*., total concentration of gold in the water phase; C"E~I,total concentration of HC1 in the water phase. Ionization of HAuCL in the aqueous phase, in terms of activities, can be represented:
Distribution of HAuCl, between the two phases:
The activity coefficientsfor HAnCl, are assumed to be equal to 1, thus a a ~ ~=~car.cl, , , and
If only undissociated molecules are present in the ether phase: C'*" = c'a*,cr. (4) If both phases have the same volume and if HC1 is BLEULEB, E., AND GOLDSMITH, G. J., "Experimental Nucleonics," Rinehart & Company, Inc., New York, 1952. ' MYLIUS,F., Z. anorg. Chem., 70,203-31 (1911). SALDICK, J., J. Phys. Chem., 60,500-1 (1956).
44 / Journal o f Chemical Education
01 HAuCll
assumed to remain quantitatively in the water phase, we get: If a large excess of HC1 is employed, (5) may be approximated by: Cml = en + (6) Combination of equations (2), (3), and (4) gives
Omitting the activity coefficients for the ions, equation (I) can be written
Combining (7), (S), and (9) gives
which can be written
I n the experiment, Cfa. and C"A, are determined at different values of CXC,. If C"AJC'AU is plotted against l/CECI,a straight line is obtained with the intercept K and the slope K X K t . Deviations can be expected a t high values of Cnclsince the ionic strength is not kept constant. The Radioactive Tracer. About 25 pC Aulg3was used. This isotope can be produced by irradiation of AuC13 in an atomic pile. AnLg8 decays, by 8- and 7-radiation, with a half life of 2.70 days. The long half life in comparison with the period of measurement has the advantage that, in most cases, no correction for the decay is necessary. On the other hand, the half life is so short that there is no risk for any lingering contamination of the glassware used. The Experiment
To 80 ml of a AuC1, solution (4 g AuC13/l), a small quantity of a solution of radioactive AuC1, was added. After careful mixing, 5 samples of 5-ml and 5 samples of 10-ml volume were taken out. These were transferred to measuring flasks of 100-ml volume and named sample oneten accordiig to Table 1. Then, 3 M HCI was added to each and the solutions were diluted to 100 ml with distilled water. The solutions were thereafter transferred to separation funnels together with 100 ml isopropylether. The funnels were shaken for 15 min and the phases allowed to separate for 30 min.
The most convenient way of performing the measurements was to use a Geiger-Miiller jacketed tube of about 10-ml volume connected to a ~ c a l e r . ~ The background was determined with the tube filled with both water and ether for 15 min a t the operating voltage. The activity of each sample was measured over about 5 min. After each measurement, it was checked that the background had not increased. If this should happen, due to the sorption of gold on the glass walls of the tube, it is necessary to wash the tube with aqua regia. When calculating the results, it must be kept in mind that the absorption of @-radiation is greater in water than in ether. A correction for this must therefore be applied by multiplying the activity values for the water phase with a factor that is determined in separate experiments with the same amount of gold in water and ether respectively. We obtained the value 1.25 1 0.02 for this factor which is in very good agreement with the value calculated from what is generally known concerning the absorption of @-radiationin different media. A correction for the background and dead time of the counting system was always made.
physical chemistry laboratory course employed a t this Institute. The mean values thus obtained from 30 determinations are: K = 0.6 1 0.3, K , = 4 1 3 M. Each determination was, however, based on only three measurements and hence these values were obtained
Typical Results
I n two typical series, the following values were obtained after correction for background and dead time. Table 1
Sample
Activity in HCI, ml, AuCL, ml, Water phase, Ether phase, 3M 4 a/l cum cum
From these results, the following data were calculated: Table 2
Distribution of HAuC14 between water and ikopropyl ether plotted against reciprocal of concentrationof HCI in water phase.
from correspondingly less accurate values of intercept and slope. Certain interesting experimental observations have been made. It was found that there is always a certain sorption of gold on all glass walls. If the gold concentration is too small, the values obtained are affected by this sorption. However, when the concentration is kept higher than 0.05 g Au/l, the sorption is not serious. The concentration of HC1 should neither be too small nor too high since, otherwise, one phase would he impoverished with respect to gold and this would result in a considerable degree of uncertainty in the activity determination. Each experimental series can be readily performed within 4-5 hrs. As far as can be seen, no values for the ionization constant of HAuC14 have been published earlier. The attempts to obtain a more accurate value will be published later. Acknowledgment
Figure 1 shows CnA,/CfA,plotted against (l/Cncl) M . From this K was found to be 0.85 and K , 1.35 M. ~ u toe the earlier mentioned deviations expected a t high iollic strengths, the values obtained in that region have not been considered. This experiment has been used for three years in the
The authors are indebted to Professor Ole Larnm, head of the Division, for his help and never-failing interest in this work. Valuable discussions with Drs. G. Lundgren and M. Mhtensson are also gratefully acknowledged. WHITEHOWE,W. J., AND POTMAN,J. L.,"Radioactive 180topea,l~Oxford University Press, Inc.,London, 1953, FRIEDLANDER, G., AND KENNEDY,J. W., "Nuclear and Radiochemistry," John Wiley & Sons, Inc., New York, 1955.
Volume 37, Number
I, January 1960
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