JEE Chemistry Chemical Bonding and Molecular Structure Notes Set 07

VSEPR Theory

The shape of a molecule is decided by the number of electron pairs (bonding and non-bonding) in the valence shell of the central atom. These pairs repel each other and so arrange themselves as far apart as possible. A double or triple bond counts as a single super pair for this purpose, and when resonance structures exist the rules apply to any one of them.
Lone pairs are held by one nucleus only and spread out more, so the repulsion order is: lone pair-lone pair > lone pair-bond pair > bond pair-bond pair. This is why lone pairs squeeze bond angles below the ideal values.
With no lone pair: 2 pairs give linear (\( \ce{BeCl2} \)), 3 trigonal planar (\( \ce{BF3} \)), 4 tetrahedral (\( \ce{CH4} \)), 5 trigonal bipyramidal (\( \ce{PCl5} \)), 6 octahedral (\( \ce{SF6} \)) and 7 pentagonal bipyramidal (\( \ce{IF7} \)).

Shapes with Lone Pairs

4 pairs: 1 lone pair gives pyramidal (\( \ce{NH3} \), \( \ce{XeO3} \), \( \ce{ClO3-} \)), 2 lone pairs give bent (\( \ce{H2O} \)).
5 pairs: 1 lone pair gives see-saw (\( \ce{SF4} \), \( \ce{XeO2F2} \)), 2 lone pairs give T-shape (\( \ce{ClF3} \)), 3 lone pairs give linear (\( \ce{XeF2} \), \( \ce{I3-} \), \( \ce{ICl2-} \)). In the trigonal bipyramid the lone pairs, and also double bonds, go to the roomier equatorial positions, while the more electronegative atoms prefer the axial positions.
6 pairs: 1 lone pair gives square pyramidal (\( \ce{BrF5} \), \( \ce{IF5} \), \( \ce{XeOF4} \)), 2 lone pairs give square planar (\( \ce{XeF4} \), \( \ce{ICl4-} \)); the two lone pairs sit trans to each other. 7 pairs: \( \ce{XeF6} \) is a distorted octahedron and \( \ce{XeF5-} \) is pentagonal planar with two lone pairs above and below the plane.
SO2 and O3 are bent (3 pairs, one lone pair), \( \ce{NO2^-} \) is bent with bond order 1.5, and \( \ce{NO2^+} \) is linear.

Hybridisation and the Steric Number

Hybridisation is the mixing of atomic orbitals of the same atom, with similar energy, to give the same number of equivalent hybrid orbitals directed to minimise repulsion. It is the orbitals, not the electrons, that mix, so filled orbitals may take part. Hybrid orbitals overlap better than pure ones and give stronger bonds.
Steric number = number of atoms bonded to the central atom + number of lone pairs on it. Steric number 2: sp (linear); 3: \( sp^2 \) (trigonal planar); 4: \( sp^3 \) (tetrahedral); 5: \( sp^3d \) (trigonal bipyramidal); 6: \( sp^3d^2 \) (octahedral); 7: \( sp^3d^3 \) (pentagonal bipyramidal). The rule does not apply to odd-electron species or to molecules with 3-centre bonds such as \( \ce{B2H6} \).
s-character is 50% in sp, 33% in \( sp^2 \) and 25% in \( sp^3 \); more s-character means shorter and stronger bonds and a wider angle.

sp, sp2 and sp3 Examples

sp: \( \ce{BeCl2} \), \( \ce{HgCl2} \), HCN, \( \ce{CO2} \), \( \ce{C2H2} \), \( \ce{N3-} \), \( \ce{NO2^+} \), \( \ce{N2O} \). In ethyne the two pi bonds lie in perpendicular planes, and in \( \ce{CO2} \) the two pi bonds are also perpendicular. In allene \( \ce{H2C=C=CH2} \) the two CH2 groups lie in perpendicular planes.
\( sp^2 \): \( \ce{BF3} \), \( \ce{BCl3} \), \( \ce{SO3} \), \( \ce{NO3-} \), \( \ce{CO3^2-} \), benzene, graphite, \( \ce{O3} \) and \( \ce{NO2^-} \) (central atom with one lone pair, bent). In \( \ce{SO3} \) the three S-O bonds are equivalent. In solid \( \ce{N2O5} \) exists as \( \ce{NO2^+} \) (sp) and \( \ce{NO3^-} \) (\( sp^2 \)).
\( sp^3 \): \( \ce{CH4} \), \( \ce{NH3} \), \( \ce{H2O} \), \( \ce{NH4^+} \), \( \ce{BF4^-} \), diamond, \( \ce{SiO2} \) (a covalent network solid), silicates built from \( \ce{SiO4^4-} \) tetrahedra, \( \ce{NH2^-} \), hydrazine, \( \ce{H2O2} \), \( \ce{SOCl2} \) (pyramidal), \( \ce{XeO4} \) and white \( \ce{P4} \) (each P bonded to three others with a lone pair).

sp3d, sp3d2 and sp3d3

\( sp^3d \): \( \ce{PCl5} \) is trigonal bipyramidal with axial bonds longer and weaker than equatorial ones. In the solid, \( \ce{PCl5} \) is ionic, \( \ce{[PCl4]^+[PCl6]^-} \), and \( \ce{PBr5} \) is \( \ce{[PBr4]^+Br^-} \). \( \ce{PF5} \) stays covalent; fast pseudo-rotation makes all F look equivalent in NMR. \( \ce{PCl3F2} \) has the three Cl equatorial and two F axial, so it is non-polar, while \( \ce{PCl2F3} \) is polar. \( \ce{SF4} \) is see-saw, \( \ce{ClF3} \) T-shaped and planar, and \( \ce{XeF2} \) and \( \ce{I3^-} \) are linear.
\( sp^3d^2 \): \( \ce{SF6} \) (crowded and very unreactive), \( \ce{[SiF6]^2-} \), \( \ce{[AlF6]^3-} \), \( \ce{[XeO6]^4-} \) (perxenate), \( \ce{BrF5} \), \( \ce{XeOF4} \), \( \ce{XeF4} \). \( \ce{ICl3} \) does not exist as a monomer; it is the planar dimer \( \ce{I2Cl6} \) with bridging chlorines, and the liquid self-ionises to \( \ce{ICl2^+} \) and \( \ce{ICl4^-} \).
\( sp^3d^3 \): \( \ce{IF7} \) is a pentagonal bipyramid with angles of 72 and 90 degrees. \( \ce{XeF6} \) is a distorted octahedron in the gas phase and in the solid it is ionic, \( \ce{[XeF5]^+F^-} \).

Comparing Bond Lengths

1. Down a group the atoms are bigger, so bond length increases: HF < HCl < HBr < HI and F-F < Cl-Cl < Br-Br < I-I.
2. For the same pair of atoms, single > double > triple bond length (C-C > C=C > C triple bond C). Across a period with similar size, bond length falls as the electronegativity difference grows, so the H-X bond shortens from C to F.
3. A higher bond order and a smaller size both give a shorter bond.

Comparing Bond Angles

Check the factors in this order. (1) Hybridisation of the central atom: sp (180) > \( sp^2 \) (120) > \( sp^3 \) (109.5) > \( sp^3d^2 \) (90). (2) Number of lone pairs on the central atom: more lone pairs, smaller angle, as in \( \ce{CH4} \) (109.5) > \( \ce{NH3} \) (107) > \( \ce{H2O} \) (104.5).
(3) Central atom: when the central atom is more electronegative, the bond pairs sit closer to it and repel more, so the angle is larger: \( \ce{NH3} \) 107 > \( \ce{PH3} \) 93 > \( \ce{AsH3} \) 92 > \( \ce{SbH3} \) 91. Heavier hydrides of period 3 and below use almost pure p orbitals on the central atom (Drago's observation).
(4) Terminal atoms: larger terminal atoms spread apart more, so the angle rises from \( \ce{PF3} \) (98) to \( \ce{PCl3} \) (100), \( \ce{PBr3} \) (101) and \( \ce{PI3} \) (102). Likewise \( \ce{Cl2O} \) (111) has a wider angle than \( \ce{OF2} \) (103).
Bent's rule: more electronegative substituents prefer hybrid orbitals with less s-character, so in \( \ce{CH2F2} \) the F-C-F angle is below 109.5 while the H-C-H angle is above it. In carbonyl halides the C=O double bond takes up more room, so the X-C-X angle follows \( \ce{COF2} \) < \( \ce{COCl2} \) < \( \ce{COBr2} \) < \( \ce{CO2} \) (180).

Worked Examples

1. Shape of \( \ce{XeF2} \): steric number 5 with 3 lone pairs in the equatorial plane, so the molecule is linear. Shape of \( \ce{ClO3^-} \): 3 bonds and 1 lone pair on Cl, so trigonal pyramidal.
2. Shape and hybridisation of \( \ce{ICl4^-} \): I has 7 + 1 = 8 electrons, 4 used in bonds, giving 2 lone pairs and 6 pairs in all, so \( sp^3d^2 \) and square planar.
3. Why \( \ce{PCl3F2} \) is non-polar: the three Cl atoms are in the equatorial plane, where their bond dipoles cancel, and the two F atoms are axial and cancel each other.

Phosphorus Oxides as Multicentre Examples

\( \ce{P4O6} \) has a \( \ce{P4} \) tetrahedron with an O bridging each of the six edges, so it has no P-P bonds and every P-O bond (about 165 pm) is a single bond. \( \ce{P4O10} \) has the same cage with an extra terminal O on each P; the terminal P=O bonds (143 pm) are shorter than the bridging P-O bonds (160 pm) because of p-pi to d-pi back bonding, the P-O-P angle is about 127 degrees, there are four such pi bonds, and no P-P bonds.