Characteristics of Radical Reactions, Spin Rules, and a Suggestion for

ARTICLE pubs.acs.org/jchemeduc

Characteristics of Radical Reactions, Spin Rules, and a Suggestion for the Consistent Use of a Dot on Radical Species L
aszl
o Wojn
arovits* Institute of Isotopes, Hungarian Academy of Sciences, H-1525 Budapest, P.O. Box 77, Hungary ABSTRACT: In many chemical reactions, reactive radicals have been shown to be transient intermediates. The free radical character of a chemical species is often, but not always, indicated by adding a superscript dot to the chemical formula. A consistent use of this radical symbol on all species that have radical character is suggested. Free radicals have a spin quantum number of 1/2 and the allowed changes of the net spin quantum number (s) are 0, (1, (2, ... in any transformations including chemical reactions. By applying this simple rule and a consistent use of a radical symbol on all radical species, the construction of chemical reaction equations and the reaction mechanism of radical reactions can be clarified. The examples of decomposition of water and cyclohexane molecules induced by high-energy photons or ionizing radiation and the example of the complex reactions taking place during the irradiation treatment of flue gases are used to demonstrate these suggestions. KEYWORDS: First-Year Undergraduate/General, High School/Introductory Chemistry, Chemical Engineering, Organic Chemistry, Physical Chemistry, Textbooks/Reference Books, Free Radicals, Mechanisms of Reactions, Reactions, Reactive Intermediates

’ DESCRIPTION OF A FREE RADICAL Free radicals are atoms or molecules possessing one or more unpaired electrons that can take part in chemical bonding. They are formed, for example, in homolytic dissociation of covalent bonds, when one of the bonding electrons remains with each fragment: A:B f A• + B•. Radicals can be produced in gas, liquid, and solid systems, and their physical and chemical properties may depend on the phase. There are several techniques for the experimental demonstration of the free-radical character of a species. Among them the most direct method is electron paramagnetic resonance (EPR) spectroscopy. This method is based on the paramagnetic properties of free radicals. When a free electron is situated in an applied magnetic field, there are two possible orientations for its magnetic vector. At lower energy, the direction of the magnetic moment vector of the electron is parallel with the direction of the applied field, and in the orientation of higher energy, it is antiparallel with the direction of the applied field. When the energy difference between the antiparallel and parallel orientations (in the form of a microwave photon of the given energy) is pumped into the system, the orientation can be reversed, and the absorption of the photon can be measured. This reversible orientation of the magnetic moment vector is a property not only of free electrons, but also of the unpaired electron bound to an atom or to a molecule. Pairs of electrons with their magnetic moment vectors in opposite directions have no net magnetic moment and so cannot exhibit such absorption phenomena. The electron, similar to the other constituents of atoms (proton, neutron) and also the other particles that are emitted in radioactive decay (positron, neutrino, antineutrino), has a spin quantum number of 1/2, whereas the photon has a spin quantum number of 1. The allowed changes of the net spin quantum number (s) are 0, ( 1, ( 2, .... (Here the reader is reminded of the

I

n the construction of chemical equations, the number of atoms of all individual elements on the left side of the equation must be equal to those on the right side. Thus, by counting the number of elements on both sides of the equation, the correctness of the equation can be checked. When charged species are involved in the chemical reaction, in addition to the parity of elements on both sides of the equation, the net charge (number of positive charges minus number of negative charges) on the left side should be equal to the net charge on the right side of the equation. Recently in many chemical reactions, including such diverse processes as autoxidation, electrolysis, polymerization, photochemistry, radiation chemistry, and pyrolysis, reactive radicals have been shown to be transient intermediates.1 As an example, the cleaning of flue gases of coal-fired electricity power stations by high-energy electron irradiation, which is a technology now used on an industrial scale (Figure 1), is examined. The flue gases usually contain substantial quantities of nitrogen oxides (mainly nitrogen oxide, NO•) and sulfur oxides (mainly sulfur dioxide, SO2). In this process, combustion flue gas passes through a spray cooler to decrease the temperature. After adding ammonia, the flue gas is irradiated with an electron beam in a reaction vessel. During irradiation, reactive intermediates, mostly free radicals, form in the gas phase or inside the water droplets in the gas stream due to the chemical decomposition of the components. In the reaction of these reactive intermediates, by rather complicated reaction mechanisms, nitrogen and sulfur oxides are converted to nitric acid and sulfuric acid and are finally changed to ammonium nitrate and ammonium sulfate, which can be used as agricultural fertilizers. The cleaned gas is emitted from a stack. A selected group of chemical reactions are shown in Table 1.2,3 Using examples of the main reaction types shown in Table 1, the colorful world of radical reactions is examined. By putting a superscript dot on all species that show free radical character and using a rule especially for the radical reactions, valuable help in construction of equations involving reactions of radicals can be obtained. Copyright r 2011 American Chemical Society and Division of Chemical Education, Inc.

Published: August 25, 2011 1658

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Table 1. Some Basic Chemical Reactions in Electron Irradiated Flue Gases

Figure 1. General scheme of a flue gas purification plant.2,3.

β+ and β
radioactive decays. In β+ decay, in addition to the emission of a positron from the atomic nucleus, emission of a neutrino is also needed to bring about the net spin quantum number change of 1. In β
decay, an electron and an antineutrino are emitted together.) This law according to which the net spin quantum number change is 0 or an integer is valid also for the radical reactions.

’ RADICAL TYPES A characteristic property of free radicals is the instability associated with the presence of the unpaired electron. The reactivity, or conversely, the stability of radicals depends to a great extent upon their structure. Radicals are often extremely reactive, reacting in such a manner that the unpaired electron becomes paired with a similar electron in another radical. The reactive radicals have only transient existence under normal reaction conditions and are generally atoms or molecule fragments with a small number of atoms formed from relatively small molecules. In the following, the formation, reaction, and decay of such reactive radicals such as H• (hydrogen atom), HO• (hydroxyl radical), and c-C6H11• (cyclohexyl radical) are discussed. The relatively stable organic radicals are generally formed from large molecules, where the unpaired electron is distributed over a larger molecular volume. In some cases, steric factors may enhance the radical stability by hindering the dimerization reactions. The structural formulas of two well-known, relatively stable, free radicals are shown in Figure 2: triphenylmethyl radical (TPM) and diphenylpicrylhydrazyl radical (DPPH). The reaction of the latter with smaller radicals is often used for quantitative determination (titration) of radical concentrations.4 Nitrogen oxide (NO•) and nitrogen dioxide (NO2•) both have an odd number of valence electrons (11 and 17, respectively). Therefore, it is not possible to have all the electrons paired; these molecules behave as rather unreactive inorganic free radicals.5 Free radicals can be electrically neutral or charged. Examples of charged radicals will be shown later. ’ FORMATION OF FREE RADICALS The formation of free radicals with paramagnetic properties is shown using the examples of water and cyclohexane

This table contains the first 27 reactions, and the numbering of other reactions starts with 28. The bent-line arrow is used to indicate highenergy radiation initiated reaction. b Data from refs 2 and.3.

a

decomposition.a,b In a water molecule, the 6 electrons of the oxygen atom in the L shell and the single K shell electron of each hydrogen atom constitute the molecular architecture with 4 molecular orbitals. On each molecular orbital, there are two electrons with antiparallel spins (Pauli exclusion principle). When very high energy is pumped into the water molecule either by absorption of a photon with energy above ca. 8 eV, or by gaining energy from ionizing radiation, an electronic excited water molecule (H2O*) may form that decomposes by breaking one of the O
H bondsc:6,7 H2 O f HO• þ H• 1659

ð28Þ

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HO• þ HO• f H2 O2 •

Figure 2. Structures of two relatively stable organic radicals: (A) triphenylmethy radical (TPM) and (B) diphenylpicrylhydrazyl radical (DHHP).

In reaction 28, free radicals, a hydroxyl radical and a hydrogen atom, form. On the valence level, HO• now has 7 electrons and H• has 1 electron. The unpaired electrons bound in HO• to the oxygen atom and in H• to the proton show properties in a magnetic field similar to those of the free electron, as was mentioned before. Because both species have one electron with unpaired magnetic moment with a spin quantum number of 1/2, the net spin quantum number change in reaction 28 is 1. In cyclohexane liquid after gaining energy from a high-energy photon or ionizing radiation, some fraction of the electronic excited cyclohexane molecules (c-C6H12*) decompose by hydrogen atom elimination. In this reaction, an H• atom and a c-C6H11• cyclohexyl radical form. The quantity of cyclohexyl radicals produced is often measured by EPR detection:7 c-C6 H12  f c-C6 H11 • þ H•

ð29Þ

In the reactions 28 and 29, very high energies are needed to promote an electron in the molecule to produce the excited state and hence bring about the radical-producing decomposition. Stable free radicals can also be produced under much milder conditions. For instance, by simply heating nitrous acid, nitric acid, and chloric acid (or their salts), nitrogen oxide, nitrogen dioxide, and chlorine dioxide, respectively, can be formed:5 3HNO2 f 2NO• þ HNO3 þ H2 O

ð30Þ

4HNO3 f 4NO2 • þ O2 þ 2H2 O

ð31Þ

8HClO2 f 6ClO2 • þ Cl2 þ 4H2 O

ð32Þ

ð21Þ

•

When HO or H reacts with some “other” radical, the spin quantum number change is also
1. As examples, the reduction of the paramagnetic copper(II) ion by means of a hydrogen atom (reaction 35), and the nitric acid forming reaction of a hydroxyl radical with nitrogen dioxide (reaction 23) are shown: H• þ Cu2 þ • f Hþ þ Cuþ

ð35Þ

HO• þ NO2 • f HNO3

ð23Þ

The latter reaction is a basic process in cleaning of the flue gas by irradiation. Among the over 100 “important” reactions occurring in this process, it is the only one that leads to the key product, nitric acid. It is important to mention that the reaction of two radicals does not necessarily lead to the disappearance of two radical species. Occasionally, there is an atom transfer, for example, in the gas-phase reaction of nitrogen oxide with the perhydroxyl radical. In this reaction, the net spin quantum number does not change: NO• þ HO2 • f NO2 • þ HO•

ð24Þ

When H• or HO• has a nonradical reaction partner, the reaction causes no spin quantum number change. Two basic types of radical reactions are mentioned: addition to compounds with unsaturated double bonds, such as olefins, aromatic compounds, aldehydes, and hydrogen atom abstraction from saturated compounds. The latter reaction may also be called a hydrogen atom transfer reaction:7 H• þ CH2 dCHCðOHÞO f CH3
• CHCðOHÞO

ð36Þ

HO• þ CH2 dCHCðOHÞO f HO
CH2
• CHCðOHÞO ð37Þ

In these reactions, the acids on the left side are nonparamagnetic. NO•, NO2•, and ClO2• are paramagnetic and all have spin quantum number of 1/2. The net spin quantum number changes in reactions 30, 31, and 32 are 1, 2, and 3, respectively.

’ REACTIVITY OF FREE RADICALS As mentioned before, free radicals are often highly reactive. For example, HO• and H• radicals formed during the decomposition of water in reaction 28 readily react with most of the solutes in water. In the absence of solutes, that is, ultra pure water, they disappear in radical combination reactions. For the combination, two radicals are needed with 1/2 spin quantum number for each, and the products are stable molecules without paramagnetic properties; in all cases there is a
1 net spin quantum number change:

H• þ CH3 CH2 OH f H2 þ CH3 • CHOH

ð38Þ

HO• þ CH3 CH2 OH f H2 O þ CH3 • CHOH

ð39Þ

•

•

In reactions 36 and 37 where H or HO combines with acrylic acid, the organic radical formed has the unpaired electron in the α position to the carboxyl group, and the radical is called α-carboxyalkyl radical. The reaction of an α-carboxyalkyl radical with an acrylic acid molecule initiates a polymerization chain. In reactions 38 and 39, the hydrogen atom or hydroxyl radical abstracts a hydrogen atom from ethanol forming a hydrogen molecule or a water molecule, respectively. In these two reactions, the “spin bearing” species α-hydroxyethyl radical is also produced. The cyclohexyl radical and the hydrogen atom formed in the decomposition of a cyclohexane molecule in reaction 29, in recombination (reaction 40) reforms the starting molecule. H• þ c-C6 H11 • f c-C6 H12

ð40Þ

H• þ H • f H2

ð33Þ

2c-C6 H11 • f c-C6 H10 þ c-C6 H12

ð41aÞ

H• þ HO• f H2 O

ð34Þ

2c-C6 H11 • f ðc-C6 H11 Þ2

ð41bÞ

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Scheme 1. Ionization of H2O Molecules and the Subsequent Reactions in Liquid Water

Scheme 2. Ionization of Cyclohexane in the Liquid State

radical pair as intermediates. They transform to stable products in a large variety of radical
radical reactions. In reactions 21, 43
46, there is a
1 net spin quantum number change: The reaction of two cyclohexyl radicals takes place with two mechanisms: in one of them (radical disproportionation, reaction 41a), a cyclohexyl radical abstracts a hydrogen atom from one of the neighboring CH2 units of the radical site of the other cyclohexyl radical, and in the reaction, cylohexene and cyclohexane molecules form. In the other reaction (radical dimerization, reaction 41b), a covalent bond forms between the two radical sites yielding a dicyclohexyl molecule. The reaction of two H• atoms is highly unlikely in a cyclohexane system,7 as the hydrogen atoms react with the cyclohexyl radicals in reaction 40 (Δs =
1) or they abstract a hydrogen atom from a cyclohexane molecule in reaction 42 (Δs = 0): H• þ c-C6 H12 f c-C6 H11 • þ H2

ð43Þ

O2 •
þ HO• f O2 þ OH


ð44Þ

O2 •
þ HO2 • þ H2 O f H2 O2 þ O2 þ OH


ð45Þ

2HO2 • f H2 O2 þ O2

ð46Þ

In the reaction of two superoxide radical íons, reaction 47, O
O
O
O
as an intermediate probably forms, but this intermediate is unstable and decomposes to O3•
and O•
. The net quantum number change of this reaction is zero:




2O2 •
f O3 •
þ O•


ð42Þ

’ RADICAL IONS AND THEIR REACTIONS In the previous reactions, uncharged radicals were the reaction partners or products. In many chemical reactions, charged radicals are the intermediates. Such radicals may form in ionization reactions of the uncharged molecules. Scheme 1 shows the ionization of H2O molecules and the subsequent reactions in liquid water. The H2O•+ radical cation formed during the ionization of a water molecule may migrate a distance of a few water molecules by resonance electron transfer (H2O•+ + H2O f H2O + H2O•+). Because H2O•+ is a strong acid, within 10
14 s it gives a proton to one of the surrounding water molecules. By this process, the positive charge and the radical site gets displaced onto two different species.7
10 The e•
electron released in the ionization of H2O molecules loses its kinetic energy in collision with surrounding molecules and in less than 10
12 s is localized in a potential energy well as a result of molecular dipoles becoming oriented under the influence of the negative charge. Thus, the eaq•
hydrated electron, the smallest anion, forms. The hydrated electron is also called an aqueous electron. When the water contains dissolved molecular oxygen (O2), the hydrated electron eaq•
readily reacts with it forming the socalled superoxide radical anion (O2•
). This radical anion is also produced in biochemical processes under the normal operation of cells and contributes to the so-called oxidative stress.11 The superoxide radical anion is in equilibrium with its protonated form, with the perhydroxyl radical (HO2•) (the O2•
and HO2• concentrations are equal at pH 4.8, the pKa). In an aqueous solution containing dissolved oxygen, the ionization of water molecules finally yields HO• and the HO2•/O2•


HO2 • þ HO• f O2 þ H2 O

ð47Þ

When liquid cyclohexane is irradiated with ionizing radiation (γ
, or electron) or with vacuum-ultraviolet photons of sufficient energy (Scheme 2), one electron can be expelled from a bonding molecular orbital and the remaining positive ion (c-C6H12•+) has an odd number of electrons (Δs = 1). It is paramagnetic, which was demonstrated by paramagnetic resonance techniques.12 c-C6H12•+ in reaction with a cyclohexane molecule forms c-C6H13+ (nonparamagnetic) and c-C6H11• (paramagnetic) species (Δs = 0). The reaction actually leads again to a separation of the radical site and the positive charge site; in the products, the unpaired electron and the lack of electron (vacancy) are in different molecular entities. The ejected electron is naturally paramagnetic. When the liquid contains a small quantity of alkyl-halide (e.g., ethyl chloride), the expelled electron readily reacts with the solute forming a short-lived radical anion, C2H5Cl•
. This radical anion decomposes to C2H5•, ethyl radical, and Cl
, chloride ion. Here, there is also a separation of the radical and the ion.

’ INDICATION OF THE RADICAL CHARACTER The presence of an unpaired electron on an atom or a molecule is indicated by adding a superscript dot to the chemical formula of the radical. In the literature, the dot is generally omitted for simple radicals, such as a hydrogen atom, chlorine atom, or hydroxyl radical. A consistent use of the dot on all species that have radical character is encouraged. For example, in the case of hydroxyl radical, there are three possibilities for showing the radical character: OH•, •OH, and HO•. IUPAC recommends the use of HO• because in this way the placement of the unpaired electron is identified.13 It should be mentioned, however, that the placement of the unpaired electron is not 1661

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Journal of Chemical Education always well-defined. In the larger organic radicals with a conjugated double bond system, the unpaired electron may be distributed over a larger molecule volume. In such case, the chemical formula could be put in parentheses and the superscript dot placed outside the parentheses to signify the uncertainty in location or delocalization of the electron. There are certain circumstances using simple text fonts when the dot symbol is not available. Acceptable substitute methods, for example, for HO• are the written terms hydroxyl radical or OH radical. The radical character is usually not indicated on the radical cations and practically never indicated on the electrons formed in ionization. The charge sign and the radical sign should be used both on radical anions and cations and also on the released electron. The question remains whether to put the charge sign first and then the radical sign (e.g., H2O+•, c-C6H12+•, e
•, O2
•), or to use the reversed order (e.g., H2O•+, c-C6H12•+, e•
, O2•
). Examples for both types of notations are found in the literature. The indication of first the charged character and then the radical character is more often used than indication in the reversed order. However, IUPAC13 suggests to put radical character first and then the charged character. In this article, the indication of radical character has been consistently used on all radicals. It is obvious from the examples shown that the rule related to the spin quantum number change (0, ( 1, ( 2, etc.) gives an additional possibility for checking the correct writing of chemical equations of reactions in which radicals are reaction partners. For practical purposes, the rule can be formulated as follows: when on one side of the equation there is one radical species, the other side should bear also at least one (rarely three, five, etc.) radical species. When on one side there are no radical species, or there are two, four, and so forth, the other side should contain zero, or an even number of radical species. The rule can easily be incorporated into computer programs used for checking or generating chemical equations. In Table 1, the radical sign on all species that have a free radical character is indicated. In the ionization reactions (reactions 1
4), both the positive ion and the free electron have radical character, so the net change of spin quantum number is 1. In the neutralization reaction (reaction 7) and the radical
radical reactions (reactions 21
23), two radical species in each reaction disappear and the net spin quantum number change is
1. The reaction of HO2• and NO• yields an HNO3 molecule with high internal energy, and in the gas phase, it may decompose to NO2• + HO• (reaction 24). The neutralization reactions (reaction 5 and 6), the ion
molecule reactions (reactions 8
15), and the radical
molecule reactions (reactions 16
20) do not involve any spin quantum number change. The consistent use of the dot on all radical species in university textbooks and the incorporation of radicals in the general chemistry curriculum are recommended.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

ARTICLE

’ ADDITIONAL NOTE a Molecules in the triplet electronic excited state have two unpaired electrons with parallel spin, so these molecules are paramagnetic. Triplet-state molecules generally form by excitation of one of the electrons in the molecule to a higher energy orbit while maintaining the antiparallel spin orientation to the counter electron in a so-called singlet electronic excited state, followed by a spin flip to parallel orientation (intersystem crossing). The oxygen molecule is an exception, having a triplet ground state (•OdO•).6 Triplet excited states often behave as though they were biradicals with two unpaired electrons in the molecule. Thus, oxygen can combine with a free radical to give a peroxy radical: R• + •OdO• f R
O
O•. b

Some transition-metal complexes may have so-called high-spin states, that is, states in which there are more than one unpaired electron. c

Decomposition to radicals is often called homolytic or triplet excited-state decomposition (e.g., reactions 28 and 29), to make a distinction from the heterolytic or singlet excited-state decomposition that gives nonradical products, for example, c-C6H12* f c-C6H10 + H2.7

’ REFERENCES (1) Baird, N. C. J. Chem. Educ. 1997, 74, 817–819. (2) Namba, H. Electron beam applications to flue gas treatment. In Charged Particle and Photon Interactions with Matter. Chemical, Physicochemical and Biological Consequences with Applications; Mozumder, A., Hatano, Y., Eds.; Marcel Dekker, Inc.; New York, 2004; pp 729
742. (3) Busi, F.; D’Angelantonio, M.; Mulazzani, Q. G.; Rafaellini, V.; Tubertini, O. Radiat. Phys. Chem. 1985, 25, 47–55. (4) Molyneux, P. Songklanakarin J. Sci. Technol. 2004, 26, 211–219. (5) Holleman, A. F.; Wiberg, E. Inorganic Chemistry; Academic Press: San Diego, CA, 2001. (6) Salem, L.; Rowland, C. Angew. Chem., Int. Ed. 1972, 11, 92–111. (7) Wojn
arovits, L. Radiation chemistry. In Handbook of Nuclear Chemistry, Vol. 3; V
ertes, A., Nagy, S., Klencs
ar, Z., Lovas, R. G., R€ osch, F., Eds.; Springer: Dordrecht, 2011; pp 1265
1331. (8) Spinks, J. W. T.; Woods, R. J. An Introduction to Radiation Chemistry; Wiley-Interscience: New York, 1990. (9) Swallow, A. J.Radiation Chemistry. An Introduction; Longman: London, 1973. (10) Buxton, G. V. The radiation chemistry of liquid water: principles and applications. In Charged Particle and Photon Interactions with Matter. Chemical, Physicochemical and Biological Consequences with Applications; Mozumder, A., Hatano, Y., Eds.; Marcel Dekker, Inc.: New York, 2004; pp 331
363. (11) Von Sonntag, C. Free-Radical-Induced DNA Damage and Its Repair; Springer: Berlin, Heidelberg, 2006. (12) Shkrob, I. A.; Sauer, M. C.; Trifunac, A. D. Stud. Phys. Theor. Chem. 2001, 87, 175–221. (13) Connelly, N. G.; Damhus, T.; Hartshorn, R. M., Hulton, A. T. IR-4.6.2 Formulae of radicals. In Nomenclature of Inorganic Chemistry, IUPAC Recommendations 2005; Royal Society of Chemistry Publishing/ IUPAC: Cambridge, U.K., 2005; p 66.

’ ACKNOWLEDGMENT The author thanks the Hungarian Science Foundation (OTKA, No. CK 80154) and the International Atomic Energy Agency (Contract No. HUN8008) for the support and also A. Horv
ath, A. V
ertes, and A. Tungler for their suggestions. 1662

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