The Ammonia Molecule

Using the usual self-explanatory notation for the seven valence AOs, we call s, x, y, z the 2s and 2p orbitals on N, and h, h2, h3 the Is orbitals on the H atoms (Hi on the positive x axis). 

Leaving out s for the moment, the AOs belonging to C3v symmetry are (Magnasco, 2009a)  

Hzhz bzhz = 0 Hxhx Hhxhx— = 0 Hyhy H-hyky e 

The three lowest roots of the secular equations give the Hiickel energy of the 3 32le2le2 valence electron configuration of NH3 as a function of angle y  

Taking the first y-derivatives of the As, the stationarity condition for the energy is  

This is what we expect in absence of hybridization, the resulting N—H bonds being strongly bent outwards, and so very far from the principle of maximum overlap. 

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Ammonia as a base. The ammonia molecule has a powerful affinity for protons and hence. 

In general, we know bond lengths to within an uncertainty of 0.00.5 A — 0.5 pm. Bond angles are reliably known only to one or twx) degrees, and there arc many instances of more serious angle enxirs. Tn addition to experimental uncertainties and inaccuracies due to the model (lack of coincidence between model and molecule), some models present special problems unique to their geometry. For example, some force fields calculate the ammonia molecule. Nlln to be planar when there is abundant ex p er i m en ta I evidence th at N H is a 11 i g o n a I pyramid. 

The condensation of amidrazone with isonitrosoacetophenone occurs via formation of the hydrazone 136. The elimination of the ammonia molecule from intermediate 136 yields 3-methyl-6-phenyl-l,2,4-triazine 4-oxide 137 (71LA12). 

Notice that in each case the oxygen or nitrogen atom is surrounded by eight valence electrons. In each species, a single electron pair is shared between two bonded atoms. These bonds are called single bonds. There is one single bond in the OH- ion, two in the H20 molecule, three in NH3, and four in NH4+. There are three unshared pairs in the hydroxide ion, two in the water molecule, one in the ammonia molecule, and none in the ammonium ion. 

Ammonia and acetic acid in waste water give rise serious pollution problems which bring about eutrophication of rivers, lakes, etc [1, 2]. These have been treated by the conventional method of biological techniques, adsorption, and thermal incineration. A band of researchers have suggested that the ammonia molecules could be transferred to N2 using a photocatalytic redox mechanism as shown follows 4NH3 + 3O2 2N2 + 6H2O. However, it has been... 

The hydronium ion has the same number of electrons and atoms as the ammonia molecule, so it is reasonable for these two species to have the same shape. 

The strong base is a soluble hydroxide that ionizes completely in water, so the concentration of OH matches the 0.25 M concentration of the base. For the weak base, in contrast, the equilibrium concentration of OH is substantially smaller than the 0.25 M concentration of the base. At any instant, only 0.8% of the ammonia molecules have accepted protons from water molecules, producing a much less basic solution in which OH is a minor species. The equilibrium concentration of unproton-ated ammonia is nearly equal to the Initial concentration. Figure 17-7 summarizes these differences. 

The titration reaction is lSIH3(a ij) -I-H3 0 (a q) NH4 (a q) + H2 0(/) At the stoichiometric point, all the ammonia molecules have been converted to ammonium ions, so the major species present are NH and H2 O. The pH of the solution is thus determined by the acid-base equilibrium of... 

Even though both ligands form Ni — N bonds of similar strength, ethylenediamine binds to Ni many orders of magnitude more strongly than does NH3. Why is this Think about complexation at the molecular level. One of the Ni — N bonds in either complex can be broken fairly easily. When this happens to [Ni (NH3)g, the ammonia molecule drifts away and is replaced by another ligand, t q)ically a water molecule from the solvent ... 

Chemists were convinced that all the chlorine atoms had to be bonded to the cobalt in some way, and since ammonia is a gas at room temperature they could not understand why the ammonia molecules did not evaporate away. One of the first proposed explanations was the chain theory, in which the ammonia... 

Because the breadth of chemical behavior can be bewildering in its complexity, chemists search for general ways to organize chemical reactivity patterns. Two familiar patterns are Br< )nsted acid-base (proton transfer) and oxidation-reduction (electron transfer) reactions. A related pattern of reactivity can be viewed as the donation of a pair of electrons to form a new bond. One example is the reaction between gaseous ammonia and trimethyl boron, in which the ammonia molecule uses its nonbonding pair of electrons to form a bond between nitrogen and boron ... 

However, it was Maxwell in 1848 who showed that molecules have a distribution of velocities and that they do not travel in a direct line. One experimental method used to show this was that ammonia molecules are not detected in the time expected, as derived from their calculated velocity, but arrive much later. This arises l om the fact that the ammonia molecules tnterdiffuse among the air moixules by intermolecular collisions. The molecular velocity calculated for N-ls molecules from the work done by Joule in 1843 was 5.0 xl02 meters/sec. at room temperature. This implied that the odor of ammonia ought to be detected in 4 millisec at a distance of 2.0 meters from the source. Since Maxwell observed that it took several minutes, it was fuUy obvious that the molecules did not travel in a direct path. 

Analysis by Clausius in 1849 showed that the ammonia molecules travel only some 0.001 cm. between collisions with air molecules at atmospheric pressure, in time intervals of about lO b sec. between collisions. This meemt... 

The addition of ammonium salts will change this equilibrium to the left, i.e. the concentration of the ammonia molecules will be increased and the concentration of the hydroxyl anions will be reduced. Due to this reason the hydrolysis of the ester groups in pectin, expressed in reaction (3), will be retarded because of the reduced OH content in the solution, and reaction (4) will be favoured. 

Examples of tunneling in physical phenomena occur in the spontaneous emission of an alpha particle by a nucleus, oxidation-reduction reactions, electrode reactions, and the umbrella inversion of the ammonia molecule. For these cases, the potential is not as simple as the one used here, but must be selected to approximate as closely as possible the actual potential. However, the basic qualitative results of the treatment here serve to explain the general concept of tunneling. 

The double arrow in the chemical equation above indicates that the reaction is reversible. This means that while some hydrochloric acid molecules are breaking down into hydrogen and chlorine ions, some ions are also combining to produce hydrochloric acid. The same ongoing, continuous process also occurs to the ammonia molecules. Some ammonia molecules accept a hydrogen ion to become an ammonium ion while some ammonium ions give up a hydrogen ion to become an ammonia molecule. 

Hie possibility that a particle with energy Jess than the barrier height can penetrate is a quantum-mechanical phenomenon known as the tunnel effect. A number of examples are known in physics and chemistry. The problem illustrated here with a rectangular barrier was used by Eyring to estimate the rates of chemical reactions. ft forms the basis of what is known as the absolute reaction-rate theory. Another, more recent example is the inversion of the ammonia molecule, which was exploited in the ammonia maser - the fbiemnner of the laser (see Section 9.4,1). 

To illustrate the application of Eq. (37), consider the ammonia molecule with the system of 12 Cartesian displacement coordinates given by Eq. (19) as the basis. The reducible representation for the identity operation then corresponds to the unit matrix of order 12, whose character is obviously equal to 12. The symmetry operation A = Cj of Eq. (18) is represented by the matrix of Eq. (20) whore character is equal to zero. Hie same result is of course obtained for die operation , as it belongs to the same class. For the class 3av the character is equal to two, as exemplified by the matrices given by Eqs. (21) and (22) for the operations C and Z), respectively. The representation of the operation F is analogous to D (problem 12). 

Many molecules have more than one well-defined structure - or even none. If there is more than one equilibrium structure the passage from one to another can take place because of the tunnel effect , although it may be impossible from a purely classical point of view. The best known example is certainly the ammonia molecule, NH3. 

The presence of the potential barrier in the ammonia molecule results in splitting of the vibrational energy levels, as shown in Fig. 5. The separation between die two components of the first level is equal to 23.87 GHz 0.79 cm-1). The corresponding absorption line is easily observable in the microwave spectrum of ammonia. In fact, this transition was utilized in the MASER,f the forerunner of die LASER. 

As a second example of molecular symmetry, consider the ammonia molecule. It has three symmetrically equivalent hydrogen atoms, but it is not... 

Fig, 3 Cartesian displacement coordinates for the ammonia molecule, The Z(CO a is perpendicular to the plane of the paper (which is not a plane of symmetry)... 

The group developed above to describe the symmetry of the ammonia molecule consisted only of the permutation operations. However, if the triangular pyramid corresponding to this structure is flattened, it becomes planer in me limit. The RF3 molecule shown in Fig. lb is an example of this symmetry. In this case it becomes possible to invert the coordinate perpendicular to the plane of the molecule, the z axis. Obviously, the operation of reflection in the (horizontal) plane of the molecule, <7h> is identical. It is easy, then, to identify the irreducible representations A and A" as symmetric or antisymmetric, respectively, under the coordinate inversion. The group composed of the identity and the inversion of the z axis is then <5 = s> whose character table is of the form of Table 7. 

Rg. 5 (a) Potential function rad energy levels as functions of die normal coordinate Q(Ai) (b) Structure of the ammonia molecule in its two equivalent inverted configurations. 

Ammonia reacts with boron trichloride to form a molecule called an adduct or Lewis acid base complex in which the lone pair on the ammonia molecule is shared with the boron atom to form a covalent bond and completing an octet on boron (Figure 1.16) ... 

We see that it is a consequence of the Pauli principle and bond formation that the electrons in most molecules are found as pairs of opposite spin—both bonding pairs and nonbonding pairs. The Pauli principle therefore provides the quantum mechanical basis for Lewis s rule of two. It also provides an explanation for why the four pairs of electrons of an octet have a tetrahedral arrangement, as was first proposed by Lewis, and why therefore the water molecule has an angular geometry and the ammonia molecule a triangular pyramidal geometry. The Pauli principle therefore provides the physical basis for the VSEPR model. 

Figure 4.12 Representation of the bonding and nonbonding electron pair domains in the ammonia molecule, an AX3E molecule.

Figure8. (a) Pump-probe spectra of (NH3)2NH+ through the A (v= 0,1,2 corresponding to 214, 211, 208 nm, respectively) states the data reveal the influence of the vibrational level probed in the experiments, (b) Pump-probe spectrum of (NH3hH+ and (NH3)sH+ with pump pulses at 208 nm and probe pulses at 312 nm A (v = 2) of the ammonia molecule. The role of cluster size is evident. The delay time is the interval between the pump and probe laser, (a) Taken with permission from ref. 65 (b) Taken with permission from ref. 68.

In the CH4 molecule, the bond angle is the expected value, 109° 28. There are eight electrons around the carbon atom (four valence shell electrons from C and one from each H atom), which results in a regular tetrahedral structure. In the ammonia molecule, the nitrogen atom has eight electrons around it (five from the N atom and one from each H atom), but one pair of electrons is an unshared pair. 

To provide further illustrations of the use of symmetry elements and operations, the ammonia molecule, NH3, will be considered (Figure 5.6). Figure 5.6 shows that the NH3 molecule has a C3 axis through the nitrogen atom and three mirror planes containing that C3 axis. The identity operation, E, and the C32 operation complete the list of symmetry operations for the NH3 molecule. It should be apparent that... 

Up to this point, we have dealt with the subject of acid-base chemistry in terms of proton transfer. If we seek to learn what it is that makes NH3 a base that can accept a proton, we find that it is because there is an unshared pair of electrons on the nitrogen atom where the proton can attach. Conversely, it is the fact that the hydrogen ion seeks a center of negative charge that makes it leave an acid such as HC1 and attach to the ammonia molecule. In other words, it is the presence of an unshared pair of electrons on the base that results in proton transfer. Sometimes known as the electronic theory of acids and bases, this shows that the essential characteristics of acids and bases do not always depend on the transfer of a proton. This approach to acid-base chemistry was first developed by G. N. Lewis in the 1920s. 

R. S. Berry. Known as the Berry pseudorotation, the mechanism involves the trigonal bipyramid (D)fl) passing through a square based pyramid (C4v) as shown in Figure 14.8. This behavior is somewhat similar to the inversion of the ammonia molecule (C3 ) as it passes through a planar (D)fl) structure. 

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