Tetrahedral angle

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... 

Section 3 7 Three conformations of cyclohexane have approximately tetrahedral angles at carbon the chair the boat and the skew boat The chair is by far the most stable it is free of torsional strain but the boat and skew boat are not When a cyclohexane ring is present m a compound it almost always adopts a chair conformation... 

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 picture presented so far of the polyethylene chain being of a linear zig-zag geometry is an idealised one. The conformation of a molecular chain is in fact random provided that the bond tetrahedral angle remains fixed. This is best illustrated by considering a piece of wire with one bend at an angle of 109° 28 as shown in Fig. A.5a. 

Halide complexes are also well known but complexes with nitrogen-containing ligands are rare. An exception is the blue phthalocyanine complex formed by reaction of Be metal with phthalonitrile, 1,2-C6H4(CN)2, and this affords an unusual example of planar 4-coordinate Be (Fig. 5.5). The complex readily picks up two molecules of H2O to form an extremely stable dihydrate, perhaps by dislodging 2 adjacent Be-N bonds and forming 2 Be-O bonds at the preferred tetrahedral angle above and below the plane of the macrocycle. 

Like the carbon atom in methane and the nitrogen atom in methylamine, the oxygen atom in methanol (methyl alcohol) and many other organic molecules can also be described as sp3-hybridized. The C-O-H bond angle in methanol is 108.5°, very close to the 109.5° tetrahedral angle. Two of the four sp3 hybrid... 

Sulfur is most commonly encountered in biological molecules either in compounds called thiols, which have a sulfur atom bonded to one hydrogen and one carbon, or in sulfides, which have a sulfur atom bonded to two carbons. Produced by some bacteria, methanethiol (CH3SH) is the simplest example of a thiol, and dimethyl sulfide [(ChP S l is the simplest example of a sulfide. Both can be described by approximate sp3 hybridization around sulfur, although both have significant deviation from the 109.5° tetrahedral angle. 

Figure 4.7 The strain-free chair conformation of cyclohexane. All C-C-C bond angles are 111.5°, close to the ideal 109.5C tetrahedral angle, and all neighboring C-H bonds are staggered.

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

Petroleum contains hydrocarbons other than the open-chain alkanes considered to this point. These include cycloalkanes in which 3 to 30 CH2 groups are bonded into closed rings. The structures of the two most common hydrocarbons of this type are shown in Figure 22.5 (p. 585). Cyclopentane and cyclohexane, where the bond angles are close to the ideal tetrahedral angle of 109.5°, are stable liquids with boiling points of 49°C and 81°C, respectively. 

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)...

The Angles between Bonds.—The above calculation of tetrahedral angles between bonds when the quantization is changed sets an upper limit on bond angles in doubtful cases, when the criterion is only approximately satisfied. For we can now state that the bond angles in H20 and NH3... 

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