Examples Resulting from Isotopic Dilution After Synthesis GUS A. ROPP Oak Ridge National Laboratory, Oak Ridge, Tennessee
INRECENT years isotopic tracer techniques have found an increasing number of applications to investigations of organic reactions where these are involved in chemical, physical, biochemical, and other types of studies. Therefore, any principles hearing on the accuracy of quantitative tracer studies of organic reactions may be of interest to scientists in various fields of research. A number of reviews which discuss the applications of isotopic tracers to organic chemistry are available. These adequately explain the techniques of analyzing mixtures of labeled compounds, measuring reaction yields, tracing laheled atoms through reactions, estimating rates of exchange reactions, studying reaction mechanisms by measuring extents of isotope fractionation, etc. For some purposes only qualitative answers are demanded of tracer studies. For example, the question as to whether or not the hydrogen atoms of acetone exchange at all with those of water in aqueous solution under specified conditions can be given a yes or no answer after a relatively crude tracer experiment. More frequently, however, the results of tracer studies must be quantitative or a t least semiquantitative to be of value. For example, the analysis of a mixture of labeled compounds is often expected to reveal the amount of one or more components present with less than 1% analytical error. The present paper deals with a definite type of error mhich can occur in the latter type of experiment. I n a recent commmicationl the possibility was stated that an apparent "reverse isotope effect" might have been caused by the fact that the carbon-14 labeled reagent used had been diluted with the corresponding nonradioactive compound after synthesis. It was pointed out' that such errors could also appear in other types of tracer experiments employing isotopicallylabeled compounds diluted after synthesis. If these sources of error seem obvious to some users of isotopic tracers, they may not he so obvious to others who make only occasional application of tracer techniques. I t appears that such sources of error deserve more emphasis than they have so far received in the literature, particularly in their applications to tracer studies using labeled organic compounds. Therefore an attempt has been made here to illustrate with several hypothetical examples the ways in mhich this type of error might appear during the application of several isotopic tracer techniques commonly applied to organic reaction studies. Experimental conditions which have a reasonable probability of occurring in practice have been assumed. Some general methods of preventing ROPP,GUSA,. J . C h m . Phys., 23,2196 (1955).
such errors are discussed, but the important point is that the possibility of these faults should not be lost sight of among the complexities of tracer studies of organic reactions. It may be assumed that a reaction of which a tracer study is being made is: R-P
(8)
where both the reactant R and the product P are isotopically labeled; that is to say, that perhaps 1% or fewer of the molecules of these compounds contain distinguishable isotopes. The reactant R is assumed to be synthesized by a series of organic reactions of labeled compounds: G-H-I-R.
(8)
For practical reasons the procedure often followed is to carry out the synthetic series (s) using only a few millimoles of G and ending with a few millimoles of R. Quite frequently the intermediates H and I are not isolated. Then R is recovered from the small-scale product mixture after dilution with ten to one hundred times its meight of pure unlabeled R which serves as a carrier. Finally the isotopically diluted R is purified by chemical and/or physical methods and used in the study of reaction (a). If, in spite of the purification processes used, one per cent by weight of G, H or I remains in the "purified" diluted sample of R, the accuracy of the results of the tracer study of reaction (a) may he jeopardized. If it is assumed as an illustration that R is diluted by a factor of ten and that 1% by weight of the mtermediate I is left in R, after dilution and purification it is apparent that about 10% of the total activityz in any sample of R is present not in the form of labeled R hut as labeled I. The influence which the impurity I can exert on the outcome of the tracer study of reaction (a) may he far out of proportion to its per cent by meight in the sample of R. The influence may rather he more nearly proportional to the per cent of the activity of the sample of R which is in the form of the contaminant I. I n any case the extent of any error resulting from the presence of I in R will depend upon various factors including the nature of reaction (a), the design of the tracer experiment being carried out, and the ease of separation of I from R and P. The following is an attempt to estimate what might reasonably be For simplicity the term "activity" has been used throughout the present paper to refer to the concentration of tagged molecules. The term "activity" applied to tracer experiments ordinarily implies radioisotopiclabeling, but the discussions hereapply equally well to experiments with stable isotope labeling.
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the magnitude of errors arising from this source when the reaction (a) is subjected to three different types of isotopic tracer studies which are often used in organic chemistry, physical organic chemistry, biochemistry and elsewhere. The three are: isotope dilution technique, rearrangement studies, and rate isotope effect studies, and during each of the three discussions the reactant R is assumed to contain-as a result of the ten-fold isotopic dilution after synthesis-l0yo of its activity in the form of I as described above. ISOTOPE DILUTION TECHNIQUE
The application of the isotope dilution principle in its various forms to the analysis of mixtures and determination of reaction yields has been explained many times in the l i t e r a t ~ r e . ~We may assume that reaction (a) is being studied using labeled R to determine the per cent yield of P and that the true yield of P from R is 80%. To take a hypothetical example we may suppose that reaction (a) whose actual yield is 80% under the conditions used is the condensation of malonic-2-CL4acid with benzaldehyde. The product (P)would, therefore, be labeled cinnamic acid:
The malonic-2-C14 acid would probably be prepared using reactions which may be represented as follows:
I n parallel with the discussion above we shall say that this synthesis would be performed at an activity level of about 100 PC.per mmole, that the malonic-2-CL4 acid would he recovered after 10-fold dilution with the C.P. malonic acid, and that even after purification it would retain 1% by weight of labeled, undiluted cyanoaceticacid (I)which would necessarily still have an activity level of about 100 PC. per mmole. Thus the starting material (R) to be used in reaction (a') would contain about 10% of its activity in the form of I, labeled cyanoacetic acid. The yield study would then involve dilution of a sample of the crude mixture produced by reaction (a') containing labeled product P, cinnamic acid, any labeled byproducts, and labeled reactant R, malonic acid, with 100 times its weight of pure unlabeled cinnamic acid. From the 100-X diluted material a small sample of pure isotopically diluted cinnamic acid would then be isolated and its molar activity, S,, determined by assay. Separately, the molar activity of a sample "ALVIN, M., d al., ''I~otopicCarbon," John Wiley & Sons, Ino., New York, 1949,AppendixI. For a review which discus~es applications of the dilution principle to orgmic chemistry, see ROPP,GUS A., AND 0. KENTONNEVILLE, nucleonic^, 9, 22 (1951).
V O L W 34, NO. 2, FEBRUARY, 1957
of the reactant, S,, would also be measured and the yield, Y, would be calculated from the equation:
The effect of the 1% of undiluted cyanoacetic acid in the malonic acid would be to raise S , by about 10% above its true value. If now the diluted sample of cinnamic acid were purified in such a way that it contained no I,R or other labeled impurity, and the correct value were obtained for S,, it is apparent that the calculated yield of cinnamic acid from malonic acid n-auld be about 72%, instead of the true value, 80%. Such errors in isotope dilution technique actually have been incurred during competitive rate studies using isotopes, and the care necessary to eliminate these errors has been described.' The question as to why the impurity I could be completely removed from P and not completely removed from R must be answered. The answer is simply that there are great differences in the ease with which various organic compounds may be freed of impurities. Liquids are often more difficult to obtain pure than crystallizable solids particularly if only classical purification methods such as distillation are applied. Furthermore, the relative solubilities of any impurities as compared with Ron the one hand and P on the other would be quite important where recrystallization is relied upon for sample purification as is often the case. It should be reaffirmed here that all samples assayed a s part of tracer studies should first be purified to constant molar activity. For crystallizable solids recrystallizatidn to constant molar activity may be the preferred technique. In other cases if two or more solid derivatives prepared from R, for example, yield on repeated crystallization molar activities which agree, it can be said that the molar activity of R is known with considerable confiden~e.~This procedure, which is perhaps one of the best for preventing errors of the type described in this paper, is, however, laborious and is sometimes neglected. Since the origin of errors in the present discussion lies in the dilution of R after synthesis and before use in a study of reaction (a), a desirable procedure, where it can be followed, is t o avoid the dilution altogether. Thns the synthetic series (s) cat1 sometimes be carried out on a 100 to 1000 mmole scale, for example, at the act,ivity level desired for the study of reaction (a) so t,hat no dilution of R with unlabeled K is necessary. A third device may be used in cases where the identity of the contaminant I, which is causing an error is known or suspected. I n such cases the contaminant I present in R may be diluted with unlabeled I in the same ratio t,hat R is diluted. Then after purification of R, residual I present in R will have relatively little influence on the molar activity of R and the source of error will have been eliminated. This technique, usually referred to as "hold-hack carrier" technique, has been applied during certain organic tracer studies,&but it can lead to difficulties in the separation of pure R from I. DEWITT,E. J., C. T. LESTER,AND G . A. ROPP,J . Am. Chem. Soe., 78,2101 (1956). An actual study designed to prove the reliability of one method of radioassaying carbon-14 labeled organic compounds has been based on this principle. See COLLINS, C. J., AND G. A. ROW, J. Am. C h m . Soe., 77,4160 (1955).
Further speculation as to what might actually occur during the application of dilution technique to the reaction (a') could be helpful at this point. Malonic acid is often purified by crystallization from ether followed by vacuum sublimation. Since malonic, cyanoacetic, and chloroacetic acids have similar solubilities in water and organic solvents, and since both cyanoacetic and chloroacetic acids are more volatile than malonic acid, it seems quite possible that malonic-2-C14 acid "purified" by this method might retain as much as 1% of either or both of the contaminating acids. On the other hand, since cinnamic acid is much less water soluble than malonic, cyanoacetic,and chloroaceticacids, it should be more readily freed from contamination by the other acids. It might, therefore, be possible that S , determined by assaying the malonic acid could be high by 10y' while S , obtained by assaying the cinnamic a c ~ dafter dilution could have the correct value with the result that the calculated yield of cinnamic acid could be low by 10% of its value. Whether or not a more accurate value of 8, could be obtained by preparing and assaying derivatives of malonic acid would depend upon the facility of separation of the derivatives chosen from the corresponding derivatives of the contaminating acids. The preferred reagents for forming such derivatives of the malonic acid mould be those, if any, which mould not a t the same time react with cyanoacetic or chloroacetic acid. I n the foregoing account of the introduction of an error during the processes of synthesis of R and study of the yield of reaction (a) by isotope dilution technique, only the error due to 10-X dilution of R after synthesis and the consequent effect on the molar activity of R were considered. In other cases it is possible that, because of the 100-X dilution of P during the yield determination, an even larger error effected in the molar activity of P might cause a proportionately larger error in the yield, 1,' since greater dilution ratio4 would tend to produce errors of greater magnitude. REARRANGEMENT STUDIES
Molecular rearrangements during reactions of organic compounds are often readily followed with the aid of isotopic carbon labeling.a The present discussion can be facilitated by use of a simple example based on an actual rearrangement s t ~ d y . ~ Ethylbenzene-a-CL4 rearranges under definite conditions as indicated by the equation:
The extent of rearrangement under given conditions may be measured by comparing the initial molar activity of the ethylbenzene-a-C'4 used with the molar activity of benzoic-a-C14acid formed by degradation of a sample of the rearranged hydrocarbon according to the following equation which is used for brevity and is not intended to imply that there are two carbon-14 atoms in one ethylbenzene molecule: 'ROBERTS,R. M.,G. A. ROPP,AND 0. K. NEVILLE,J . .4m. Chem. Soc., 77, 1764 (1955). In the present paper the sources of error assumed in connection ~ , i t this h work are purely h,ypothetical. Such errors were not observed in practice where the approach to the rearrsngement study was somewhat different from that hypothesized here.
C,H,CJIH,-+C'~H~
oxidation
C6H6CL400H (d)
The molar activity of the benzoic-a-C14 acid is used as a measure of the amount of "unrearranged" ethylbenzene-or-C14 since labeled atoms from the methyl group are cast off as carbon dioxide. The ethylbenzenea-C14 used in the study can be prepared by a reaction series which may be represented in outline form as:
I t so happens that the intermediate acetophenonea-C14 may be oxidized under the conditions of reaction (d) to form the same product, benzoic-a-C14 acid: oxidation
CH3C"OCeHa
CsHsCL400H
(d')
We may now assume, as explained earlier, that the synthesized ethylbenzene -a-Cl4 is isolated after 10-X dilution with unlabeled ethylbenzene, and that the "purified" sample of the labeled hydrocarbon contains 1% by weight of acetophenone-a414 so that about 10% of its activity is actually present as acetophenone-a-CL4. Also we may assume a t first that acetophenone-a-C14 does not rearrange under the conditions used in reaction (r). Then if the trne per cent rearrangement in a given experiment is 50y0, it is readily seen that the extraneous activity in the benzoic-a-C'4 acid derived from the acetophenone-a-C14could result in a measured per cent rearrangement of only about 45%. I n a similar study performed in an analogous manner by using synthesized ethylbenzene-8-C14 and measuring the degree of rearrangement as proportional to the molar activity of the derived ben~oic-or-C'~acid, still more drastic errors might obtain. Thus if acetophenone-13-C" should undergo skeletal rearrangement to the extent of joyo under the conditions of reaction (r):
lor
&&(an
unspecified oridissble product)
1 I a measurement of the molar activity of the benzoica-CI4 acid produced might indicate a degree of rearrangement up to about 4.5% under conditions where, in fact, no rearrangement of the ethylbenzene-6-C14 occurred at all. The possible errors so far discussed were based on an assumed dilution factor of 10 X and on the presence of lY0 of the intermediate I in the reactant R. In practice, dilution ratios of 100 X are sometimes used as has already been mentioned in the section devoted to isotopic dilution technique. With a 100-X dilution rather appreciable errors so far estimated could be caused by the presence of only one-tenth of one per cpnt of I remaining in R. ISOTOPE FRACTIONATION STUDIES
I n much the same way as in yield studies and rearrangement studies, results of investigations of isotope effects on reaction rates' may in some cases be ques7 For a discussion of the purposes and methods of rate isotope D. A., I N D J. D. ROBERTS, J. CHEJI. effect studies, see SEMENOV, Eouc. 33, 2 (1956): ROPP,Gus A,, .V~rleonies,10, 22 (19521.
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tionable if the reactants were recovered after synthesis with the aid of isotopic dilution. Intermolecular isotope effects are usually reported as k/k*, the ratio of specific rates of reaction of bhe unlabeled and labeled molecules determined in experiments involving competition between the two isotopic species. Usually the ratio, k/k*, is calculated as a function of the ratio, r, of the measured molar activity, Slo,of the reaction product a t partial reaction (often about 10% reaction) to the measured molar activity, Sloe, of the product at 100% react,ion. Any influence which causes a deviation of either one of Sloor Sloa from its true value without a t the same time altering the other proportionately will result in an erroneous estimate of the ratio k/lc*. With the exception of hydrogen isotope effects, this ratio of specific rates usually lies between 1.0 and 1.1. Consequently extremely accurate estimates of molar activities are needed if isotope effect ratios and variations in these ratios are to be reported with confidence. It is apparent that errors of similar magnitude to those already discussed as possible in isotope dilution technique and rearrangement studies cannot be tolerated in experiments which seriously attempt to evaluate k/k* ratios quantitatively. During a study of the value of k/k* in the reaction (a) me may assume as an example that the impurity I, originally carried as a 1% contaminant in R, tends to adsorb preferentially and completely on the product P and to remain adsorbed on P throughout "purification" of samples of P. In an extreme case it is seen that Sloe could be altered by about 1070, that Slomight be altered as much as 50%, and that r could be in error by perhaps 30% or 40% of its value. Improbable as such an extreme case may be, it is not difficult to believe that an apparent "reverse isotope effect" equivalent to r = 1.01 to r = 1.10 might arise in a similar way during studies of a reaction having a true value of r = 1.00. On the other hand, should I tend to remain preferentially adsorbed on R as long as any of R remained and to adsorb on P in the absence of R, a false "normal isotope effect" having a value equivalent to, perhaps, r = 0.90 might result in the limiting case. Again, although this extreme is improbable, it seems quite reasonable that inaccurate estimates of the value of some "normal isotope effects" might be brought about in this manner. Simply recrystallizing the products repeatedly-a process sometimes relied upon for purification in such studies--may fail in some instances especially if the impurity is slightly less soluble than the parent compound. Under some circumstances, even recrystallization to constant molar activity might not lead to
VOLUME 34, NO. 2, FEBRUARY, 1957
products with the necessary radiochemical purity. I n rare cases1 the impurity I might react under the conditions used for reaction (a) : I
-
P'
(b)
If now reaction (b) mere faster than reaction (a) and if separation of P' from P were difficult or for any reason incomplete, an apparent "reverse isotope effect" might again result. Under these circumstances Sla could appear to be greater than Sloe if, after "purification" of the reaction products, a higher percentage of the impurity P' remained in the product of partial reaction than in the product of 100% reaction. I n a few intermolecular isotope fractionation studies, the degree of isotope fractionation has been calculated from the ratio, r', of Slot o the molar acivity of the reactant R. While this is sound in principle, it could very well tend to increase the probability of errors caused by dilution of R after synthesis since any contaminant I would not likely be retained to an equal extent in "purified" samples of two different compounds. I n general, errors due to contamination by I might more likely cancel out if r were calculated as the ratio of the molar activities of two samples of the same compound, P. XONCLUSIONS
7
1
The hypothetical cases give here, which are merely intended to illustrate how errors might occur in a few typical tracer experiments, obviously cannot demonstrate all the various experimental combinations which might lead to such errors. I t remains for every experimenter to examine critically the design of his tracer experiments with a view to eliminating such flaws. Errors such as those described here might also arise during studies of isotopic exchange rates s s well as in some types of biochemical tracer experiments. Indeed, certain biological and biochemical tracer experiments may be even more susceptible to these faults than the chemical studies discussed above. Possibly the literature may contain inaccurate data introduced from such sources as those described here. In particular, some isotope fractionation studies might be questioned on some such h a ~ i s . ~ In any case, the practice of isolation of labeled compounds with the aid of dilution after synthesis should be handled with due consideration of the possible pitfalls in the tracer experiments employing the diluted samples.
For an example of what appears t o be an erroneously reported equilibrium isotope effect arising from causes like those described E., AND B. LIZARD, J. Inorganic and Nuclear here, see SAITO, Chemistry, 218-27 (1955), Pergamon Press Ltd., London.
