Isotopic Effects In Chemical Reactions

Type of physical science: Chemistry

Field of study: Chemical reactions

"Isotopic effect" is the term used to describe the effect that substituting one isotopic form of an atom for another has on the rates of chemical reactions. It is defined as the ratio of the speed of the reaction with the heavy isotope in place to the speed with the light isotope in place. Study of the isotopic effect gives insight into the details of atomic motion that occurs during chemical reactions.

Overview

The isotopic effect is the name given to the change that is observed when a physical or chemical process is repeated with the molecules involved having some of the atoms replaced by different isotopes. As an example, consider hydrogen atoms. Hydrogen atoms exist in nature primarily as the mass-one isotope. About three out of every twenty thousand atoms, however, is a heavy hydrogen--that is, a hydrogen atom with a mass equal to two. It is possible to concentrate the heavy versions in water to obtain virtually pure heavy water, that is, water with both isotopes of hydrogen being the mass-two isotopes. The change of a given physical property measured for the heavy water relative to that measured for the normal water is the isotopic effect for that property. For example, the melting point of ordinary water is 0 degrees Celsius, whereas that for heavy water is 3.82 degrees Celsius. The normal boiling point of ordinary water is 100 degrees Celsius, while that of heavy water is 101.44 degrees Celsius. It takes slightly more energy to vaporize a given amount of heavy water than it does the same amount of ordinary water.

Examples could be multiplied.

In explaining these changes in properties, one only has to consider the change in mass on going from ordinary water to heavy water. Molecules of the latter are about 11 percent more massive than the former. Although it is a simplification, the isotopic effect is attributed to this change in mass.

Isotopic effects are also observed for other kinds of atoms. For example, chlorine exists in nature principally in two forms differing in mass by about 5 percent. When a molecule containing chlorine is studied in two isotopic versions, however, what must be compared is the total change in mass in going from the form with the lighter chlorine molecule to the heavier one.

Since the chlorine atom only contributes a part of the total mass of the molecule, the percent change in the total mass of the molecule will be much smaller than 5 percent. Any isotopic effects on physical properties will be very small and difficult to measure.

In addition to isotopic effects in physical processes, there are isotopic effects in chemical reactions. When one studies the same reaction first with one isotope of a given atom present and then with a different isotope present, one normally observes that the rate of the chemical reaction is significantly affected by the change in isotope. Because of the large change in mass on going from ordinary hydrogen to heavy hydrogen, most studies of rate isotope effects have been conducted on systems in which the isotopically substituted atom is hydrogen.

In this case, however, an explanation of the isotopic effect involves more than merely noting the presence of a change in the mass of the atom. In a chemical reaction, the isotopic effect is a manifestation of what are called quantum effects.

A molecule is a collection of atoms held together in a definite geometry by what are called chemical bonds. These bonds are not rigid, like the ball-and-stick models that are often used to illustrate molecules; each bond can stretch and bend a little. Because of this flexibility, molecules vibrate. To appreciate the source of the kinetic isotopic effect, it is necessary to examine these vibrations carefully. Take, as a simple example, a molecule such as hydrogen chloride (HCl). Because of the fact that there are only two atoms present, there is only one way that this molecule can vibrate, by stretching the bond connecting the two atoms. It is possible to derive a mathematical expression describing the manner in which the molecule vibrates. Of main interest is the formula for the energy that the vibrating molecule possesses. The energy is given by E = (s + 1/2)hv where v is the fundamental vibrational frequency of the molecule and s is a constant (called a quantum number) that can only take on the values 0, 1, 2,....

The fact that only certain energies are allowed (as defined by s) is an illustration of the phenomena of quantization. What is of peculiar importance is the observation that, although s can equal 0, the energy can never equal 0. This remaining energy is called the zero point energy of the molecule. Polyatomic molecules have much more complicated vibrational motions.

Nevertheless, the equations that describe this motion indicate that zero point energy exists in these cases, too.

In order to understand the kinetic isotopic effect, it is necessary to consider the details of a chemical reaction. Take a simple case of two molecules coming together in a collision and then interacting to produce a different molecule or molecules. As the molecules collide, some bonds are broken and some are formed. During the process, a well-defined chemical species, called an activated complex, or transition state, is formed. This species has the characteristic of having an energy higher than either reactants or products. In fact, it is a species of maximum energy. In typical theoretical calculations of the isotopic effect, it is necessary to calculate the rates for conversion of the reactants into the transition state for each isotopic system, and then calculate the isotopic effect by taking the ratio of the rate for the system containing the heavier isotope to that for the system containing the lighter isotope. This ratio is defined as the isotopic effect. It turns out that the part of the resulting equation that accounts for the total mass of the two isotopic forms cancels out. That is, simply taking into account the total mass of the system does not give rise to any isotopic effect. The same is true of taking into account how fast the molecules rotate, or spin. Molecules with heavier isotopes will rotate more slowly. Here, again, when one examines the mathematical expression for the isotopic effect, one finds that the quantities accounting for change in rotation in going from the lighter to the heavier species cancel out. There is no isotopic effect arising from the slower rotation of heavier molecules. It should be noted that the two forms of motion described here, translation (motion of the molecules as a whole around the inside of the container, which depends on the total mass of the molecules) and rotation, are motions that can be described using the equations of classical mechanics; the peculiar effects called quantum effects do not arise in these motions. When one examines the contribution to the equation for the isotopic effect arising from vibrations, one observes that using the equations that describe translation and rotation gives rise to invalid results. It is necessary to introduce quantum mechanical equations to describe the vibrational motion; the isotopic effect results. A closer examination of the theory shows that the Heisenberg uncertainty principle is the culprit here. It is not possible to measure a system's velocity and position simultaneously to an arbitrary degree of precision.

Applications

The isotopic effect is used primarily to understand details about chemical reactions.

There are many questions that the researcher can ask. Which atoms actually move significantly during the reaction process? How high is the energy barrier encountered on going from reactants to products? Is the transient molecular species that is created on the route from reactants to products and that possesses the maximum amount of energy more like the reactants or the products? These are clearly questions in which only the specialist would be interested.

To understand the role that measurements of the isotopic effect plays in practical applications, one must appreciate the need for the chemist to understand the details about chemical reactions. Some of the questions considered by the chemist have just been listed. All these questions are concerned with what is called the mechanism of a chemical reaction, which involves two kinds of information. The first piece of information is the list of elementary reactions that compose a description of the overall reaction under investigation. The second piece of information is a description of the motion of the atoms on the way from reactants to products.

It is in this second arena that a study of isotopic effects becomes important.

Knowledge of the mechanism of a reaction is fundamental knowledge that can be built upon. For example, knowing something about the mechanism of reaction for one type of molecule allows one to make predictions about the reactivity of other, similar molecules. This sort of information would be important in, for example, the design of drugs. Often a molecule that has valuable therapeutic properties is extracted from some sort of natural source, such as a plant or marine animal. The extraction method is expensive and time-consuming, however, and usually yields only very small amounts of the active compound. If the molecule is to have any widespread use, it is essential that it be synthesized first in the laboratory and then in the manufacturing plant. In order to create a method of synthesis, it is necessary to know something about the reactivity of readily available materials. Part of this information arises from a study of the mechanisms of chemical reactions, which in turn utilize, as part of the researcher's repertoire, a measurement of isotopic effects.

Knowledge of mechanisms also aids in understanding the pathways of reactions in living systems. Often a pathological condition can be traced to the absence of a needed chemical species, or to the presence of a modified form of a needed species. By understanding how the normal species reacts compared with the interloper, researchers can sometimes create therapies appropriate for the disease. These examples should make it clear that the intellectual distance between the measured effect (in this case the isotopic effect) and the application of the results of the measurement is rather great, and that the isotopic effect is only one small part of the knowledge needed to understand chemical reactions completely.

Most of the studies of isotopic effects have centered on the two isotopes of hydrogen, which differ in mass by a factor of two. This doubling of mass allows the largest isotopic effects.

Other isotope systems have been used, but because of the similarity of masses (in the case of chlorine, the two common isotopes have masses that differ only by about 9 percent), the observed isotopic effects are quite small and in most cases unmeasurable.

Physical properties that depend upon isotopic effects can give rise to practical applications. An important example of this is the separation of the two isotopes of uranium, uranium 235 and uranium 238. Uranium 235 is the isotope of uranium used in nuclear reactors.

In nature, this isotope makes up about 0.7 percent of uranium atoms. In order to have a usable fuel, it is necessary to enrich uranium to about 3 percent uranium 235. This is done by synthesizing the volatile molecule UF6 and then separating the two isotopic forms, taking advantage of the fact that the form containing uranium 238 diffuses more slowly than the form containing uranium 235. That this process is successful is all the more amazing when one realizes that there is only a 0.8 percent difference in the masses of the two species.

Context

The specialized nature of the isotopic effect limits its impact on the overall structure of modern chemistry; however, there are two interesting points to be made about it.

The isotopic effect is an example of a phenomenon that depends upon what are called quantum effects. To the ordinary observer, molecules can be viewed as made of balls of matter connected by sticks, a model that has become familiar in many popular drawings of molecules.

The chemist transfers this simpleminded picture to the material actually studied. Molecules are treated as masses attached to one another by flexible springs, the masses representing the atoms, the springs representing the chemical bonds. To a large extent, the mathematical description of these incredibly small particles is the same as that for ordinary masses and springs. The laws governing the motions of clocks, automobiles, and baseballs are the same as those governing atoms in motion within molecules. At least, this is true for all motions except molecular vibrations. The isotopic effect arises from what are called quantum effects on vibrational motion.

Quantum mechanics modifies the laws of motion (actually introduces new laws of motion) at the scale of molecular and atomic sizes. In particular, quantum mechanics states that when a molecule vibrates, it is not possible for its vibrational motion to come to a complete standstill.

There must be some residual motion in every molecular vibration, even at the absolute zero of temperature, although it is sometimes erroneously stated that at that point all motion ceases. This is a purely atomic phenomenon that does not have its counterpart in the world of automobiles and baseballs.

Studies of the isotopic effect became routinely possible only when the existence of isotopes became known and when methods were developed for concentrating a given isotope in amounts above those encountered naturally. The most commonly studied isotopic system (ordinary hydrogen, with a mass of one, and heavy hydrogen, deuterium, with a mass of two) depended upon the discovery of the heavy isotope in 1931 by Harold Urey, who ultimately won the Nobel Prize for his work. Within a few years, it was possible to isolate 82 milliliters of water in which the hydrogen atoms were mainly of the heavy variety. In this process, 2,800 liters of ordinary water were used. During the development of the first nuclear weapons, large amounts of heavy water were needed to serve as a possible moderator in nuclear reactions. This gave rise to a technology that allowed the ready production of heavy water for research purposes; heavy water is now supplied by most chemical supply houses.

Principal terms

CHEMICAL BOND: the name given to the force connecting two atoms within a molecule and having a measurable length and direction

CHEMICAL REACTION: a process in which one or more chemical substances are converted into different substances

ISOTOPE: a form of a given atom characterized by the number of neutrons present in the nucleus of that atom

NEUTRON: an elementary particle found in the nucleus of an atom possessing unit mass and no charge

PROTON: an elementary particle found in the nucleus of an atom possessing unit mass and a positive electrical charge

REACTION RATE: the rate, usually measured in molecules per second or moles per second, at which a given reactant is consumed or product is produced during a chemical reaction

Bibliography

Ege, Seyhan N. ORGANIC CHEMISTRY. Lexington, Mass.: D. C. Heath, 1989. This modern textbook of organic chemistry is typical of the elementary textbooks that provide a discussion of the topic at a level accessible to anyone who has studied some chemistry in college. It discusses the kinetic isotopic effect and how the organic chemist uses it as a diagnostic tool. It also describes in sufficient detail chemical reaction pathways.

Ihde, Aaron J. THE DEVELOPMENT OF MODERN CHEMISTRY. New York: Dover, 1964. This detailed history of chemistry discusses the discovery of isotopes and their uses. Helps create the background necessary for a discussion of isotopes.

Laidler, Keith J. CHEMICAL KINETICS. New York: Harper & Row, 1987. This is an upper-level chemistry text. Chapter 11 provides a good discussion of kinetic isotopic effects. There are numerous references to more specialized books on the subject, so that this text could serve as a good starting point for extensive study.

Melander, Lars, and William H. Saunders. REACTION RATES OF ISOTOPIC MOLECULES. New York: Wiley-Interscience, 1980. This is one of the classic studies of the subject. Although it is intended for the specialist, as are all the available treatises on the subject, it will give the general reader the sense of technical expertise needed to study the subject.

Rae, Howard K., ed. SEPARATION OF HYDROGEN ISOTOPES. Washington, D.C.: American Chemical Society, 1978. Several methods of preparing heavy water and heavy hydrogen are discussed. Although technical details are spelled out, there are very readable accounts of experiences with existing facilities. The initial chapter is especially valuable.

Rahn, F. J., A. G. Adamadntiades, J. E. Kenton, and C. Braun. A GUIDE TO NUCLEAR POWER TECHNOLOGY. New York: John Wiley & Sons, 1984. Chapter 6 of this commendium is entitled "Enrichment Technologies" and discusses the various methods used for enrichment of uranium isotopes. It is replete with diagrams and photographs that show just how difficult it is to take advantage of the slight difference in the mass of the two uranium hexafluorides to obtain a 3 percent enrichment for use as a fuel.

The Structure of the Atomic Nucleus

Chemical Bond Angles and Lengths

Dynamics of Chemical Reactions

Nuclear Reactors: Design and Operation