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Uses of Radioactive Tracers 261
isotopic exchange mechanism is valid, it could be proposed that the reaction mechanism
would be
Cr(III)* + X- + Cr(II)-~ [Cr*-X-Cr] 4+ ~ Cr(II)* + X- + Cr(III)
Such a reaction mechanism would be fostered by the presence of anions that form
complexes more readily than perchlorate ion. If HC1 solutions are used rather than HCIO 4
it is found that the exchange takes place more rapidly and the half time of exchange is only
2 rain, which agrees with the proposed mechanism since chloride ions are known to be
more favorable to complex formation than perchlorate ions. Without the use of radioactive
(or isotope separated) chromium to label one of the original oxidation states there would
be no means of identifying the exchange.
9.4.3. Determination of equilibrium constants
Determination of cation (M z+) - anion (L-, for ligand) solution equilibria can
advantageously be done using radioactive metal tracers because of the ease with which the
metal concentration can be measured, as e.g. in the determination of solubility products
Ks0 = [MZ+][L-] z (9.21)
or complex formation constants, also named stability constants
fin = [MLnZ-n]/[M z+][L-]n (9.22)
At trace concentrations of the metal (i.e. [M]tot ,~ [L~ the complexing anion concentration
is unaffected by the metal ion concentration, which allows easy calculation of the values of
these two important variables in the system. The experimental techniques used for this
purpose are based on two-phase equilibria: solubility (solid/liquid), paper electrophoresis
(paper/aqueous solution), solvent extraction (organic solvent/water) and ion exchange
(resin/water). The equilibria measured have been shown to be independent of the metal
concentration in the range 10 .3 to < 10 -13 M, as long as no polynuclear complexes (i.e.
with several metal atoms per complex molecule) are formed (cf. w
(a) Solubility
The sensitivity of tracer detection makes measurement of solubilities relatively simple.
This is illustrated by the first radioactive tracer experiment by de Heresy and Paneth in
1913 in which the solubility of lead chromate was determined. Chromate ions were added
to a solution of PbCI 2 containing a known amount of 21~ precipitating the lead as
PbCrO 4. The precipitate contained 2030 "radioactive units", and had a weight of 11.35 mg.
The specific activity was thus 2030/11.35 = 179 "units" mg -1. Shaking the precipitate with
water dissolved 2.14 units per 10~ ml. The solubility was calculated to be 2.14/179 =
0.012 mg 1-1 or 3.7 x 10 .8 M Pb 2+. If [Pb 2+ ] = [CrO42"] the solubility product would be
Ks0 = (3.7 x 10-8) 2 = 1.4 x 10 -15. The modem value is 2x 10 -14.