The Tetrahedral Angle

5-3 THE TETRAHEDRAL ANGLE The H—C—H bond angle in CH4 is 109°28. We can calculate the tetrahedral angle by simple trigonometry, First, we place the CH4 

Four equivalent valence orbitals centered on carbon can be constructed by scrambling together the 2s, Ip, Ipy, and Ip, orbitals. These equivalent orbitals are called sp hybrids, and their construction is shown schematically in Fig. 5-7- Each hybrid orbital has one-fourth s character and three-fourths p character. 

The four orbitals are directed toward the comers of a regular tetrahedron, and thus are ideally suited for forming four localized bonding orbitals with the four hydrogen Ir orbitals. The valence-bond structure for CH4 is shown in Fig. 5-8. 

The normalized wave functions for the four equivalent hybrid orbitals are listed below (coordinate system as shown in Fig- 5-7)  

Show how these orbitals are obtained by following the procedure used to solve Problem 4-1. 

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The situation becomes more complex in the case of a three-dimensional foam. Since the septa should all be identical, again three should meet at 120° angles to form borders or lines, and four lines should meet at a point, at the tetrahedral angle of 109°28. This was observed to be the case by Matzke [179] in his extensive statistical study of the geometric features of actual foams. 

The tetrahedral geometry of methane is often explained with the valence shell electron pair repulsion (VSEPR) model The VSEPR model rests on the idea that an electron pair either a bonded pair or an unshared pair associated with a particular atom will be as far away from the atom s other electron pairs as possible Thus a tetrahedral geomehy permits the four bonds of methane to be maximally separated and is charac terized by H—C—H angles of 109 5° a value referred to as the tetrahedral angle... 

The H—O—H angle m water (105°) and the H—N—H angles m ammonia (107°) are slightly smaller than the tetrahedral angle These bond angle contractions are easily accommodated by VSEPR by reasoning that electron pairs m bonds take up less space than an unshared pair The electron pair m a covalent bond feels the attractive force of... 

At one time all cycloalkanes were believed to be planar It was expected that cyclopentane would be the least strained cycloalkane because the angles of a regular pentagon (108°) are closest to the tetrahedral angle of 109 5° Heats of combustion established that this is not so With the exception of cyclopropane the rings of all cycloalkanes are nonplanar... 

Phenol IS planar with a C—O—H angle of 109° almost the same as the tetrahedral angle and not much different from the 108 5° C—O—H angle of methanol... 

All bonds between equal atoms are given zero values. Because of their symmetry, methane and ethane molecules are nonpolar. The principle of bond moments thus requires that the CH3 group moment equal one H—C moment. Hence the substitution of any aliphatic H by CH3 does not alter the dipole moment, and all saturated hydrocarbons have zero moments as long as the tetrahedral angles are maintained. 

The angle formed between successive bonds along the chain backbone—0 in Fig. 1.5a-is not free to assume all values, but is fixed at a definite angle depending on the nature of the bond. For the tetrahedral angle associated with carbon-carbon single bonds, d = 109.5°. 

J. A.F. Plateau, who first studied their properties. It is the Plateau borders, rather than the thin Hquid films, which are apparent in the polyhedral foam shown toward the top of Figure 1. Lines formed by the Plateau borders of intersecting films themselves intersect at a vertex here mechanical constraints imply that the only stable vertex is the one made from four borders. The angle between intersecting borders is the tetrahedral angle,... 

The cyclopropane ring is necessarily planar, and the question of conformation does not arise. The C—C bond lengths are slightly shorter than normal at 1.5 A, and the H—C—H angle of 115° is opened somewhat from the tetrahedral angle. These structural... 

In all the groups along the chain, the bond angle is fixed. It is determined by considering a carbon atom at the centre of a regular tetrahedron and the four covalent bonds are in the directions of the four comers of the tetrahedron. This sets the bond angle at 109° 28 as shown in Fig. A.4 and this is called the tetrahedral angle. 

The three simplest alkanes. The bond angles in methane, ethane, and propane are all close to 109.5°, the tetrahedral angle. 

Fig. 8. Calculated solid echo 2H NMR powder spectra for jumps between two sites related by the tetrahedral angle for ij =0, i.e. true absorption spectrum and Tj = 200 ps. xc is the correlation time of motion. R is the reduction factor, giving the total normalized intensity of the spectra for x, = 200 ps. (For x, = 0 all the spectra have total intensity 1)...

For octacovalence a different equation is needed. From symmetry considerations we see that the OC—M—CO bond angle for M(CO)3 with three double bonds is the tetrahedral angle 109.47°. The upper curve in Fig. 1 has been drawn as a straight line passing through the points for n = 1 and n = 2 ... 

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