G. Ronald Brown and C. A. Winkler McGill Universitv Montreal. P.O., Canada
The Kinetics of an Exchange Reaction Using a Radiochemical Tracer
I
An undergraduate physical chemistry experiment
I t has been common practice in research, but not in nndereraduate lahoratories. to follow the nroeress of chemical " reactions with radiochemical tracer techniques. An experiment that has been used successfnllv in this laboratorv for teaching purposes is adapted from a &dy by Hodgson, bans, and Winkler (I I of the exchange reaction, in acetonitrile &
The heta-emitting radioisotope, P3', which has a half-life of 8.05 days, presents a minimal hazard and the techniques required to prepare the samples for counting are readily mastered by sophomore chemistry students. The experiment can generally he completed in a 4-hr laboratory period. In acetonitrile NaI is highly ionized and it is ~ossiblefor the iodide ion to exchange i n 6 the organic iodide (1,2) according to reaction (1).The rate of the exchange reaction can he determined from the change in the activity of NaI* with reaction time. The I- (including I*-) is precipitated as AgI and its specific, rather than total, activity is measured to avoid the necessity for quantitative sampling and transfer of AgIb) (3). The total rate of reaction, V, may be represented
Integration of (3), using the boundary condition that x = 0 when t = 0 yields 1 V=- ab (4) (a b)t In 1 - (x/c)(l+ n/b) Because it is exwerimentallv difficult to determine total activity, a conversion is made to specific activities by dividing the total activity terms by the concentration terms associated with each. Hence, the ratio of specific activities is
+
0 - 1-5 A6-c-z (5) Ao a c c where At is the specific activity of the NaI a t time t and A. is the specific activity of the unexchanged NaI. Then 1 in (6) (a + b)t 1 - (1 - AIAo)(l+ alb) The degree of exchange, 0 , a t time t is given by
"*
where A, is the specific activity of NaI a t t = m, i.e., when 'equilibrium has been attained. At equilibrium, the activity originally present in a mole is evenly distributed throughout (a b) moles and Am- a (8) Ao a + b Thus, eqn. ( 6 ) becomes 1 v=- ab ( a + b ) t i n ~ Since the reaction is second-order
+
where f denotes a function of the concentrations a and b of the NaI and CaH91, respectively, and k is the specific rate constant. The rate of the forward reaction to form CaH9I' is oro~ortionalto the total reaction rate and to the ratio of active to inactive NaI. Similarly, the rate of the reverse reaction is proportional to the total rate of reaction and to the ratio of active to inactive C4H& If the initial activity of the labelled I* as NaI* is c (counts Der second) and the activitv of NaI* remaining a t time t is (E - x), corresponding to an activity x of C4HgI*, the rate of exchange may be written
V=kab and eqn. (9) becomes
Experimental Upon request acopy of the informationgiven to the studentsmay be obtained. 'Hodgson. G. W., Evans, H. G. V., and Winkler, C. A., Can. J. Chem., 29,60 (1951). 2MscKay,H. A. C., J Amer. Chem. Soc., 65,702 (1943). 3Friedlander,G., Kennedy,J. W., and Miller, J. M., "Nuclear and Radiochemistrv," 2nd Ed.. John Wilev & Sons. New York. 1964. &AI millillieurie sample of 113', obtainid from New England Nuclear, is sufficientfor the work of 40 students during a minimum of 8 weeks. 5Flatbottom, glass dishes about 1 cm deep and of diametersamewhat smaller than that of the Geiger tube are suitable sample containers
Apparatus Required The primaryrequirementis a gwd beta counter such as the Chiesgo Nuclear Educational Scalar, Model 8770. Other requirements are an infrared lamp for drying the samples, s centrifuge, a suitable timer, a thermostat at 1 5 T , and an analytical balance. Chemicals The following solutions are prepared using actonitrile as solvent: (1) 0.30 M n-butyl iodide and (2) 0.25 M NaI containing sufficient IL3' to yield samples with counts of about 10,000 cpm.' A solution of 0.1 M AgN03 in water is also required.
Volume 53, Number 7, July 1976 / 461
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25
7.-
,">",
Typical student data for dmease in Nal* activity at 14.2"C with time for the reaction Nal' (0.050M) n8ul (0.249 M).
+
Procedure
In preparation for the kinetic study, 20.0 ml of the n-C4Hd solution should be pipetted into a 50-mlErlenmeyer flask and placed into the thermostat at approximately X'C, together with a flask containing 10 ml of the NaI' solution. While waiting for the solutions to attain the thermostat temperature, six numbered sample containers5 should be weighed and their background counts determined. Meanwhile, six 15-ml centrifugetubes should be numbered, about 3 mlof 0.1MAgN03 added to each,and 1.0 ml from the NaI* solution added to the AgN03 in each of the centrifuge tubes # 1and #2. To ensure complete precipitation of all the I- in these two'tubes, the contents of each tuhe should be stirred. The exchange reaction may now be started by adding 5.0 ml of NaI*
462 / Journal of Chemical Education
solution to the n G H d solution in the thermostat. Simultaneously, the timer should be started and the flask agitated to ensure complete mixing of reactants. A sample of about 3 ml is taken at about 5 min, the time being accurately noted, and the sample added to the AgN03 solution in centrifuge tube #3. Again a stirring rod is used to stir the contents of the tube. The formation of AgI stops the reaetion, and a well-defined reaction time is possible only if the above procedure is completed as quickly as possible. Additional samples should be taken at 15, 45, and 75 min and treated in a manner analogous to that for the first sample. During the intervening times, the AgI is settled by centrifuging, the supernatant is decanted, and the precipitate washed twice with 5 ml of Hz0 followed by 4-5 washings with CH30H. The presence of Hz0 tends to cause coagulation of the AgI suspension and self-absorption by the eoagulum. Finally, a small amount of CH30H (-2-3 ml) is added to the AgI, and the contents of the tuhe are stirred and drained into the sample container. Several ml of CHaOH may be added to the AgI in the sample container to promote settling of the suspension into a homogeneous layer. It is not necessary to transfer all of the precipitate from the centrifuge tube. Each sample is dried, without boiling, under an infrared heat lamp, allowed to cool, and weighed, and its radioactivity determined, preferably by duplicate counts. Summary S t u d e n t s a r e able to derive a second-order time-reaction p l o t from the d a t a obtained (the figure gives typical s t u d e n t results) a n d a r e introduced t o t h e kinetics of a reaction t h a t does not go t o completion. It is generally possible to obtain rate constants t h a t a r e in good agreement with t h e literature values.' I n laboratory courses t h a t function o n a modular basis, t h e experiment may b e extended t o determine t h e activation energy b y making t h e s t u d y a t several temperatures, a n d t h e strong electrolyte behavior of t h e acetonitrile solutions of NaI m a y he studied by conductance measurements.
