The H2O Molecule

As the second example of a triatomic molecule, we shall consider the bonding in the water molecule. Water in its ground state has an angular configuration in which the H — O—H angle is about 105°. 

The ion will have its four lone pairs distributed in the four 

Ideally one can, therefore, consider the H—O—H angle as derived from the tetrahedral angle of 109° 28. This angle is smaller in the HgO molecule (about 105°), owing to the expansion of the electron cloud by the two protons. This idea is consistent with the fact that the F—O — F angle in OFg is only 102°, since we expect F to draw much more electron density than H . The result is that the pure sp hybridization is disturbed even more. The 2p character in the F—O bond is larger and the angle is closer to 90°. 

Notice that the four hybrid orbitals all are orthogonal to each other. They are also normalized to 1 the coefficients of are needed for that purpose. The four hybrid orbitals are called sp hybrids. 

Using two of the sp hybrids to form bonds with the two hydrogen atoms, e.g., and ip2, we have a set of LCAO—MO s, 

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Given the bond distances and intemuclear angle in Problem 9, what is the moment of inertia of the H2O molecule about its principal axis through the oxygen atom (the y-axis in File 4-5) ... 

Run a MOPAC calculation using the PM3 Hamiltonian to determine the normal vibrational modes of the H2O molecule. 

To illustrate, again consider the H2O molecule in the coordinate system described above. The 3N = 9 mass weighted Cartesian displacement coordinates (Xl, Yl, Zl, Xq, Yq, Zq, Xr, Yr, Zr) can be symmetry adapted by applying the following four projection operators ... 

The H2O molecule, therefore, has three normal vibrations, which are illustrated in Figure 4.15 in which the vectors attached to the nuclei indicate the directions and relative magnitudes of the motions. Using the C2 character table the wave functions ij/ for each can easily be assigned to symmetry species. The characters of the three vibrations under the operations C2 and (t (xz) are respectively + 1 and +1 for Vj, - - 1 and + 1 for V2, and —1 and —1 for V3. Therefore... 

If we compare the vectors representing a translation of, say, the H2O molecule along the z-axis, as illustrated in Figure 4.14(a), with the dipole moment vector, which is also along the z-axis and shown in Figure 4.18(a), it is clear that they have the same symmetry species [i.e. T(piJ = T T )] and, in general. 

The H2O molecule has no 2 or bi vibrations but selection mles for, say, CH2F2, which has vibrations of all symmetry species, could be applied in an analogous way. 

Figure 4 shows the measured angle of 105° between the hydrogens and the direction of the dipole moment. The measured dipole moment of water is 1.844 debye (a debye unit is 3.336 x 10 ° C m). The dipole moment of water is responsible for its distinctive properties in the Hquid state. The O—H bond length within the H2O molecule is 0.96 x 10 ° m. Dipole—dipole interaction between two water molecules forms a hydrogen bond, which is electrostatic in nature. The lower part of Figure 4 (not to the same scale) shows the measured H-bond distance of 2.76 x 10 ° m or 0.276 nm. 

Fig. 6. Hydrated sodium ion,, in aqueous solution (4).The H2O molecules form ion—dipole bonds to the central metal ion. The waters are in...

Tin(II) chlorides are similarly complex (Fig. 10.5). In the gas phase, SnCh forms bent molecules, but the crystalline material (mp 246°, bp 623°) has a layer structure with chains of comer-shared trigonal pyramidal SnClsl groups. The dihydrate also has a 3-coordinated structure with only I of the H2O molecules directly bonded to the Sn (Fig. I0.5c) the neutral aquo complexes are arranged in double layers with the second H2O molecules interleaved between them to form a two-dimensional H-bonded network... 

Addition of the appropriate amount of water to anhydrous H3PO4, or crystallization from a concentrated aqueous solution of syrupy phosphoric acid, yields the hemihydrale 2H3PO4.H2O as a congruently melting compound (mp 29.3 "). The crystal structure shows the presence of 2 similar H3P()4 molecules which, together with the H2O molecule, are linked into... 

Water is a volatile, mobile liquid with many curious properties, most of which can be ascribed to extensive H bonding (p. 52). In the gas phase the H2O molecule has a bond angle of 104.5° (close to tetrahedral) and an interatomic distance of 95.7 pm. The dipole moment is 1.84 D. Some properties of liquid water are summarized in Table 14.8 together with those of heavy water... 

The coordination chemistry of the large, electropositive Ln ions is complicated, especially in solution, by ill-defined stereochemistries and uncertain coordination numbers. This is well illustrated by the aquo ions themselves.These are known for all the lanthanides, providing the solutions are moderately acidic to prevent hydrolysis, with hydration numbers probably about 8 or 9 but with reported values depending on the methods used to measure them. It is likely that the primary hydration number decreases as the cationic radius falls across the series. However, confusion arises because the polarization of the H2O molecules attached directly to the cation facilitates hydrogen bonding to other H2O molecules. As this tendency will be the greater, the smaller the cation, it is quite reasonable that the secondary hydration number increases across the series. 

In this chapter we will illustrate some of the methods described in the previous sections. It is of course impossible to cover all types of bonding and geometries, but for highlighting the features we will look at the H2O molecule. This is small enough that we can employ the full spectrum of methods and basis sets. 

The initiating radical is derived from the monomer by addition of the H2O molecule with a reduction of Co " to Co ". (reaction Scheme [29])... 

The hydrogen evolution reaction (h.e.r.) is of particular importance in corrosion for a number of reasons. Firstly, the reduction of the HjO ion in acid solutions or the H2O molecule in neutral and alkaline solution is a common cathodic reaction for the corrosion of metals in acid, neutral and alkaline solutions the fact that iron will corrode in neutral water free from dissolved... 

In Fig. 37 two areas have been shaded. The area in the upper left corner, where protons in occupied levels are unstable, we have already discussed. In the lower right-hand corner the shaded area is one where vacant proton levels cannot remain vacant to any great extent. In aqueous solution any solute particle that has a vacant proton level lower than that of the hydroxyl ion will capture a proton from the solvent molecule, since the occupied level of the latter has the same energy as the vacant level of a hydroxyl ion. Consequently any proton level that would lie in this shaded area will be vacant only on the rare occasions when the thermal agitation has raised the proton to the vacant level of a hydroxyl ion. On the other hand, there are plenty of occupied proton levels that lie below the occupied level of the H2O molecule. For example, the occupied level of the NH3 molecule in aqueous solution lies a long way below that of H20. 

Even recent textbooks mention only the traditional view that if water were not dissociated at all, hydrolysis would not occur. From Fig. 30, however, it is quite clear that in the proton transfer (150) we are concerned with the gap between the occupied proton level of the (NJIi)+ ion and the vacant level of the H2O molecule near the top of the diagram. The existence of the vacant proton level of the (OII) ion, near the bottom of the diagram, is irrelevant. 

We have discussed the triply charged ion Fe+++ in aqueous solution. Let us consider now the water molecules that are in contact with such an ion, and let Fig. 50a depict one such H2O molecule. The protons in the H2O molecule will be repelled by the large positive charge of the Fe+++ ion—will be so strongly repelled that it is possible that, sooner or later, the thermal agitation will be sufficient to transfer a proton to a... 

The Urea Molecule. In Fig. 40 the vacant level of the CON2H4 molecule lies 0.085 electron-volt below the vacant level of the H2O molecule. If, when dissolved in formic acid, the vacant level of CON2H4 lies in a similar position relative to the vacant level of the H2O molecule in this solvent, it is clear that the tendency for protons to be transferred from the solvent, according to... 

In Sec. 128 it was found that the vacant proton level of indicator 2 lies at 0.192 electron-volt below the occupied level of (HaO)+ in dilute aqueous solution. Using the successive increments listed in the last column of Table 39, we find, counting upward, that the value for indicator 5 is —0.052, referred to the same zero of energy. Proceeding by the same stepwise method to No. 6 we find for the energy of the vacant proton level the positive value +0.038. This still refers to the occupied level of the (II30)+ ion in dilute aqueous solution. It means that work equal to 0.038 electron-volt would be required to transfer a proton from the (H30)+ ion in very dilute solution to the vacant level of No. 6 in the concentrated acid solution in which the measurements were made. A further amount of work would be required to transfer the proton from the occupied level of No. 6 to the vacant proton level of one of the H2O molecules in the same concentrated solution. This is the situation because, as mentioned above, the changing environment has raised the proton level of the (HaO)+ ion relative to that of each of the indicator molecules. 

The rotation of the ammonium ion in salts at ordinary temperatures provides justification for the customary treatment of the ion as spherically symmetrical in the theoretical discussion of the structure of ionic crystals. Further, the rotation of molecules such as NHj and H20 about symmetry axes accounts for the fact that these molecules occupy positions in crystals with symmetry elements not compatible with those of the non-rotating molecule. Thus in Ni(NH3)6CU the NHj molecules lie on four-fold axes, and in alum the H2O molecules on three-fold axes. The rotation of the molecules,... 

Al(III) is an example of an aquatic ion that forms a series of hydrated and protonated species. These include AlOrf Al(OH)J, Al(OH)3, and other forms in addition to AP. (For simplicity, we omit the H2O molecules that complete the structures of these complexes.) Most of these species are amphoteric (able to act as an acid or a base). Thus the speciation of Al(III) and many other aquatic ions is sensitive to pH. In this case, an aggregate variable springs from the conservation of mass condition. In the case of dissolved aluminum, the total dissolved aluminum is given by... 

The H2O molecules are cooled in a supersonic expansion to a rotational temperature of 10K before photodissociation. The evidence for pathway competition is an odd-even intensity alteration in the OH product state distribution for rotational quantum numbers V = 33 45. This intensity alternation is attributed to quantum mechanical interference due to the N-dependent phase shifts that arise as the population passes through the two different conical intersections. 

The gaseous state has been defined as "a state of matter in which the substance expands readily to fill any containing vessel" (1). What this means is that any collection of molecules in the gaseous state is firee to move in all directions and that the gaseous molecules will fill any container in which they are confined. For the H2O molecule in a gaseous state (which has 3... 

The preservative powers of salt stem from its chemistry and its interaction with water. The H2O molecule is a tetrahedral structure. It does not look like a tetrahedron because two of the positions are occupied not by atoms but by electron pairs. Another molecule with a tetrahedral structure is carbon tetrachloride. The difference between the structures of the two molecules is that carbon tetrachloride has no unbonded electron pairs (Figure 8.1). 

We had earlier vindicated treating one of the OH bonds in the H2O molecule as a spectator bond in studying the abstraction reaction. Another key assumption that needed to be checked was the centrifugal sudden (CS) approximation which was invoked to reduce the number of rotational basis functions used in the computations.28 Under the CS approximation and using only the K = 0 rotational basis functions, there was a total of 220 million basis functions for J = 15 alone. Relaxing the CS approximation, for example, with K = 0,1 and J = 15 led to 650 million basis functions. To approach the fully coupled-channel (CC) results, i.e. without... 

There are two main ways of representing the H2O molecule the point-charge model and molecular orbital representation. 

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