The N2 molecule

Nitrogen is the most abundant uncombined element in the earth s surface. It is one of the four essential elements (C, H, O, N) that support all forms of life. It constitutes, on the average, about 15% by weight in proteins. The industrial fixation of nitrogen in the production of agricultural fertilizers and other chemical products is now carried out on a vast scale. 

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Nitrogen molecules, a major constituent of air, are excited by electron collisions and the excitation energy is transferred to the O 2 molecules, or the N2 molecules may be dissociated and O atoms fonned via the reactions... 

Consider an N2 molecule, in the ground vibrational level of the ground electronic state, which is bombarded by 100 eV electrons. This leads to ionization of the N2 molecule to... 

Let us consider systems which consist of a mixture of spherical atoms and rigid rotators, i.e., linear N2 molecules and spherical Ar atoms. We denote the position (in D dimensions) and momentum of the (point) particles i with mass m (modeling an Ar atom) by r, and p, and the center-of-mass position and momentum of the linear molecule / with mass M and moment of inertia I (modeling the N2 molecule) by R/ and P/, the normalized director of the linear molecule by n/, and the angular momentum by L/. 

We could explain the results of this experiment die way we did before die final distribution is clearly much more probable than the initial distribution. There is, however, another useful way of looking at this process. The system has gone from a highly ordered state (all the H2 molecules on the left, all the N2 molecules on the right) to a more disordered, or random, state in which the molecules are distributed evenly between the two bulbs. The same situation holds when marbles rather than molecules are mixed (Figure 17.3). In general, nature tends to move spontaneously from more ordered to more random states. 

Of the eight nonmetals listed in Table 21.1, nitrogen is by far the least reactive. Its inertness is due to the strength of the triple bond holding the N2 molecule together (B.E. N=N = 941 kj/mol). This same factor explains why virtually all chemical explosives are compounds of nitrogen (e.g., nitroglycerin, trinitrotoluene, ammonium nitrate,... 

Le Duff Y. Raman band shape of the N2 molecule dissolved in liquids, J. Chem. Phys. 59, 1984-7 (1973). 

Now consider the alkynes, hydrocarbons with carbon-carbon triple bonds. The Lewis structure of the linear molecule ethyne (acetylene) is H—O C- H. To describe the bonding in a linear molecule, we need a hybridization scheme that produces two equivalent orbitals at 180° from each other this is sp hybridization. Each C atom has one electron in each of its two sp hybrid orbitals and one electron in each of its two perpendicular unhybridized 2p-orbitals (43). The electrons in the sp hybrid orbitals on the two carbon atoms pair and form a carbon—carbon tr-bond. The electrons in the remaining sp hybrid orbitals pair with hydrogen Ls-elec-trons to form two carbon—hydrogen o-bonds. The electrons in the two perpendicular sets of 2/z-orbitals pair with a side-by-side overlap, forming two ir-honds at 90° to each other. As in the N2 molecule, the electron density in the o-bonds forms a cylinder about the C—C bond axis. The resulting bonding pattern is shown in Fig. 3.23. 

It seems probable also that, to within one or two percent, doublebond and triple-bond radii for various atoms should bear constant ratios to single-bond radii. We have chosen 0.79 for the triple-bond factor, which gives agreement with the observed distance in the N2 molecule, and 0.90 for the double-bond factor. The radii given in Table VI are obtained with these factors. 

The principle underlying surface area measurements is simple physisorb an inert gas such as argon or nitrogen and determine how many molecules are needed to form a complete monolayer. As, for example, the N2 molecule occupies 0.162 nm at 77 K, the total surface area follows directly. Although this sounds straightforward, in practice molecules may adsorb beyond the monolayer to form multilayers. In addition, the molecules may condense in small pores. In fact, the narrower the pores, the easier N2 will condense in them. This phenomenon of capillary pore condensation, as described by the Kelvin equation, can be used to determine the types of pores and their size distribution inside a system. But first we need to know more about adsorption isotherms of physisorbed species. Thus, we will derive the isotherm of Brunauer Emmett and Teller, usually called BET isotherm. 

It is easily seen that He does not form a stable molecule because both the bonding and the antibonding orbital are occupied by two electrons, which gives a net repulsive interaction. The N2 molecule is much more stable than O2, since in the latter the two additional electrons are located in antibonding orbitals. 

Sabatier s Principle is illustrated in Fig. 6.40 where the ammonia rate is plotted for similar conditions versus the type of transition metals supported on graphite. The theory outlined so far readily explains the observed trends metals to the left of the periodic table are perfectly capable of dissociating N2 but the resulting N atoms will be bound very strongly and are therefore less reactive. The metals to the right are unable to dissociate the N2 molecule. This leads to an optimum for metals such as Fe, Ru, and Os. This type of plot is common in catalysis and is usually referred to as a volcano plot. 

For solid nitrogen five modifications are known that differ in the packing of the N2 molecules. Two of them are stable at normal pressure (transition temperature 35.6 K) the others exists only under high pressure. At pressures around 100 GPa a phase transition with a marked hysteresis takes place, resulting in a non-molecular modification. It presumably corresponds to the a-arsenic type. Electrical conductivity sets in at 140 GPa. 

Figure 6.7 shows the calculated electron density distributions for the H2 and N2 molecules in their equilibrium geometry together with the standard deformation densities. There is clearly a buildup of electron density in the bonding region in both molecules. In the N2 molecule there is also an increase in the electron density in the lone pair region and a de-... 

It is interesting to note that both CO and CN are isoelectronic with the N2 molecule. That is, they have the same number and arrangement of electrons as the N2 molecule. However, as we will see later, these species are quite different from N2 in their chemical behavior. The properties of many homonudear and heteronudear molecules and ions are presented in Table 3.1. 

Decomposition of 1,2,3,4-benzotetrazine 1-oxides 282 involves opening of the tetrazine ring to afford ortho-azidonitroso derivatives, followed by their cyclization with the evolution of the N2 molecule to give benzofurazans 283 (Equation 56) <2002EJO3435>. 

The N2 molecule exhibits the expected s-rich hybridization in nN and p-rich hybridization in onn. In other respects its Lewis structure appears quite ordinary, exhibiting the expected similarities to the isoelectronic CO molecule. The a spin set of the cation is also unexceptional. 

Since the first step of all of these reactions is dinitrogen coordination to either the surface of the catalyst or transition metal center of the complex, let us briefly discuss the nature and importance of the M-N2 interaction, and the possible coordination modes ofN2 to transition metal centers. These issues were the subjects of many discussions in the literature [10, 11] and it is commonly agreed that the interaction of the N2 molecule with transition metal centers facilitates the activation of the N=N triple bond the stronger the M-N2 interaction, the easier to break the N=N triple bond. 

Because the N2 molecule in the complex is still expected to have partial multiple bond character, the d-type functions could be needed. Therefore, d-type function have been added to nitrogen atoms (using a Gaussian exponent of 0.8) of the dinitrogen molecule. Our preliminary test of the effect of phosphorus atom d-type functions on the calculated Zr-PH3 bond lengths of model complexes A1 and A7 showed that the influence of d-type functions on the P atom is insignificant. Therefore, here we will not include d-type of functions for P-atoms. 

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