E. A. Guggenheim The University
of
Reading England
Odd Molecules
T h e object of this note is to explain in the simplest possible words why the dimerization of NO and that of NOz occur hardly a t all in contrast to that of CN which is complete. The first step toward solving this problem is to expose and reject the myth that there is some inherent instability in odd molecules. The process: CHa
+ CH,
-
CH$.CH,
goes to completion not because CH3 is an odd molecule, but because the numher of electron pair bonds is increased by one; precisely the same reason that: NHa
+ BFs
+
HsN.BFa
goes to completion. At the end of this paper we shall see that NO and NO, do not dimerize because dimerization does not increase the number of honds. I t is as simple as that. But before we can appreciate the simplicity of the question and its answer, we must make a critical examination and decide precisely what we mean by several important concepts such as st* bility, electronic structure, and bond number. This part of this note is almost entirely a recapitulation of a remarkable article written by Herzberg ( 1 ) in 1932 but generally overlooked. Deftnitions and Notation
We must distinguish sharply between two concepts which, following Herzberg ( I ) , we call LLphysi~al st* bility" and "chemical stability." The former denotes stability of a molecule with respect to its constituent atoms; the latter denotes stability of a molecule with respect to other species into which it might conceivably he converted by a chemical reaction. Table 1
01
NO N. CO CN BO Cn
BN Be0 B. Be, -
All the diatomic molecules in Table 1, except Bez, are spectroscopically stable, and their spectra have been observed. Some of these molecules such as OarN2, and CO are also chemically stable, hut many of them are not. For example owing to: 474
/
Journal o f Chemical Education
the molecules Cz,CN, and NO are not chemically stable. Both kinds of stability must be sharply distinguished from the tendency to react with a foreign molecule. The author remembers being taught that the high st* bility of N, was due to the triple bond and that the instability(?) of acetylene was also due to the triple bond ! The commonly used notation of G. N. Lewis (2), in which electrons are denoted by dots, shows clearly the bonding electrons but does not, in all cases, distinguish unambiguously between antibonding electrons and inert pairs of electrons. It is thus inadequate for our present purpose, and we therefore use a new notation, whichis convenient and incidentally inexpensivetoprint. This notation is used in the second column of Table 1. The numher b of bonding electrons is shown between the symbols for the two atoms. The numher a of antibonding electrons is shown outside the brackets. The remaining electrons form inert pairs, and their numher, which is here unimportant, can be; obtained by counting. The values of b and a, which are well established (1\ are riven in colnmns 4 and 5. resnectivelv. z ~ ~ . We accept the widely used convention that the number of honds is defined as L/z(b- a), regardless of which atom supplies the bonding electrons. These values are given in column 6. In column 3, values (5) are given of -AH for the formation of the molecules from the free atoms. If these values are divided by '/,(b - a ) we obtain values of -AH oer bond. These values nearlv all lie in the range (72 20) kcal. The differencesbetween these "bond strengths" are interesting and important in a detailed discussion of electron distribution, dipole moments, electronegativity, etc. But for our present purpose, these differences are unimportant compared to their approximate sameness. If we divide the values of AH by 72 kcal, we obtain the numbers given in the last column. It is immediately obvious that in almost all cases these numbers are close to the values of '/*(b - a) in the previous column. This provides an extremely useful empirical method of determining, at least approximately, the numher of honds in diatomic molecules composed of the elements beryllium to oxygen without reference to the distribution of electrons. This useful, if only approximate, rule holds also for polyatomic molecules. This is shown in Table 2. The first column gives an atom pair with the numher of bonding electrons, and the second column gives the best average value (5) of -AH. The third column gives %
,
-
~
*
~
Ti)
the values of ' / ~ b (the value of a being zero). The fourth column gives values of AH/72 kcal. We see that these values agree with 'lzb to within *I/% and the agreement is mostly much better. Table 2 AH/72 (kcd)
-AH
(kcal)
'/sb
020 NzN N4N N2O N40 C2C C4C C6C C2N Cz 0 C40
We now recall Herzberg's ( 1 ) condition for chemical stability. A molecule will be unstable (or metastable) if it can change into something else with a net increase in the number of bonds. I t is, of course, not -AH but - AG that determines the direction of change. The difference TAS, a t 300'K and 1 atm, is about 8 kcal when a mole of a diatomic molecule dissociates into free atoms. I t is about 5 kcal when a polyatomic molecule dissociates into two molecules, whether diatomic or polyatomic. Thesc values of TAS are too small to matter in a reaction involving a net change in the number of bonds. But when there is no net change in the number of bonds, i t may well be sufficient to ensure complete dissociation. This is a sufficient explanation of the instability of Hez, of Bez, and of Ne2. Surprisingly, it does not seem to have occurred previously in print. Examples of Chemical Instability
We shall now discuss the chemical stability or instability of some of the molecules in Table 1. The molecules Oz, N2, and CO are stable. The molecule Cz with two bonds is unstable with respect to diamond and to graphite, each of which has four bonds per pair of C atoms. An analogous statement holds for BN. The molecule Bz with one bond per pair of atoms is unstable with respect to a hexagonal layer lattice with three bonds per pair of atoms. The actual crystal, described as "complicated," is presumably more stable than this hypothetical layer lattice. The molecules CN and NO. We are a t last ready to compare and contrast the behavior of NO with that of CN. The dimerization processes are: [C~NI+[CJN]-[N~CZC~NI
ro
1
The former process involves an increase in the number of bonds from five to seven with -AH = 112 kcal and consequently goes to completion. In the latter process, the number of bonds remains unaltered a t five and consequently dimerization occurs hardly a t all. A recent analysis (4) of the experimental facts indicates
that for this dimerization -AH is only 2.6 kcal whereas -TAS = 4.3 kcal a t 300°K and 1atm. The postulated structures for CN and (CN)%imply that in the dimerization there occurs promotion of an s electron in each CN group. This probably accounts for the small value of -AH as compared with an average value 144 kcal for two bonds. The dimerization of NOn. The extent of the dimerization of NO2 to N204has been accurately measured and leads to the values (5) AH = 12.9 kcal and TAS = 6.3 kcal a t 300°K and 1 atm. Our discussion consequently leads unambiguously to the conclusion that in the process: there is no change in the net number of bonds. The question of why NOn does not dimerize more completely is now replaced by the question of whether we can assign reasonable structures to NO and to N20r so that on dimerization the net number of bonds remains unchanged. The answer is:
with seven bonds on each side. The molecule NO? resembles COz but has an extra antibonding electron which by electrostatic repulsion causes the molecule to be bent. The formula shown for N2O4 appears to imply two kinds of NO groups, but there will, of course, be a delocalization of the electron pairs forming the second bonds, and this may well explain why -AH is as large as 12.9 kcal by contrast with only 2.6 kcal in the dimerization of NO. Other Discussionr
The above discussion differs from previous discussions, including a recent one by Linnett (6),in that electron spin has not been mentioned. I n fact, ele* tron spin plays no part whatever except that it allows two electrons to occupy each orbital. Fluorine. The reader will doubtless have noticed that nothing has been said about fluorine. This m o b cule is known to be peculiar in all respects. In particular, its enthalpy of dissociation has an anomalously small value. Summary
Provided the number of bonds in a molecule composed of the elements Be to 0 is defined in a systematic and regular manner, the energy per bond lies in the range (72 20) kcal. A conceivable chemical change, in particular dimerization, will occur only if there is a net increase in the number of bonds. There is no mystery in the experimental facts that NO and NO1 dimerize only slightly, whereas CN dimerizes completely.
*
Acknowledgment
The author is grateful to Professor H. C. LonguetHiggins and Dr. J. E. Prue for constructive comments. Literature Cited (1) HERZBERQ,G., "The Structure of Molecula4" (Editw: Volume 43, Number 9, September 1966
/
475
DEBYE,P.), Blaekie a d Son, Ltd., Londou, 1932, p. 174. (2) L m m , G. N., J. Am. Chem. Soe., 38, 762 (1!116). (3) COTTRELL, T. L., "The St,rength of Chemical Bonds," 2nd ed., Butterworths Scientific Publications, 1954. (4) GUGGENHEIM, E. A., MOT. P h v ~ . 10,401 , (1966).
476
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journal of Chemical Education
(5)
GIIUUUE, W. F., AND KEMP,J . U., J. C h ~ m Pl!!,s., . 6 , 40
(1938). 6) LINNETT, J. W., "The Elect,ronic Structrtrr 01 1\Iulccules," hIethuen and Compa~~y, Lt,d., London, 1964.
