6. Molecular Geometry, Intermolecular Forces and Bonding Theories

Both have four pairs of electrons around the central atom, so both are built on a tetrahedron. But in methane all four pairs are bonds, and in water two are lone pairs. A lone pair is held by only one nucleus, so its cloud is fatter, and it pushes the bonding pairs together. The next section simulates this.

From the NIST CCCBDB, which gives experimental bond angles (for water, 104.48° from rotational spectroscopy). A script reads them, and nothing was typed from memory.

A bond angle is the angle between two bonds, so two are enough to draw it. In BF₃ and NH₃ the third atom is out of the plane of the page, and the angle between any two of the three is the same.

A bonding pair is held between two nuclei, so it is pulled into a narrow region along the bond. A lone pair belongs to the central atom alone, so it spreads out in a fatter cloud close to that nucleus. The wider cloud takes up more angular room, and the bonds are squeezed. The simulation represents this by weighting lone pairs a little more.

One region of electron density. VSEPR counts directions in which electrons sit round the central atom: a double or triple bond is one of them. So CO₂ (two double bonds) has two regions and is linear, and the carbon in ethylene has three and is flat, with angles near 120°.

In the middle plane, not at the poles. There the lone pair has only two close neighbours at 90° instead of three, so it feels less repulsion. Try SF₄ (seesaw), ClF₃ (T-shaped) and XeF₂ (linear), and look for where the lone pairs end up.

It is a model, and a good one: it reproduces the measured angles of NH₃ and H₂O to within about a degree. It treats electron pairs as points repelling with a steep law, with lone pairs weighted more, and finds the lowest-energy arrangement by a short numerical search.

A water molecule has a positive end and a negative end. Near a negative rod the molecules turn their positive ends toward it, and the rod pulls on the near positive ends harder than it pushes on the far negative ends, because the near ends are closer. So a neutral stream of dipoles is attracted by either sign.

No. The lean is drawn in proportion to the measured dipole moment, so a bigger dipole bends more, but the size is for display. Hanging a rod beside a stream is a qualitative demonstration, and the dipoles, in debye, are from the NIST CCCBDB: water 1.86, dichloromethane 1.62, chloroform 1.04, carbon tetrachloride 0.

The unit of dipole moment: the charge separation of one electron and one proton about 21 pm apart, roughly. Water has 1.86 D, hydrogen chloride 1.09 D.

It uses electronegativity difference as the size of each bond dipole, which is only a rough guide, and it leaves out the dipole contributed by lone pairs. Water's two lone pairs, for example, add to the dipole. The pattern is what the model gets right: which molecules are polar and which are not, and the order within a family.

The model says nearly so, because P and H have almost the same electronegativity. But phosphine has a measured dipole of 0.58 D, from its lone pair, whose electrons are off to one side of the molecule. Lone pairs matter.

Yes, 0.53 D, though it contains only oxygen atoms and each bond would have zero dipole. This comes from the formal charges in its resonance structures: the atom in the middle is positive and the ends share a negative charge, and the molecule is bent.

Water, chloroform and dichloromethane bent in the field because their arrows add up. Carbon tetrachloride did not because its four arrows, pointing to the corners of a tetrahedron, cancel exactly.

The Lewis structure pairs up electrons in localized bonds and lone pairs. The molecular orbital picture puts the electrons into orbitals spread over the whole molecule. Oxygen has two electrons in a pair of antibonding orbitals of equal energy, and by Hund's rule they sit in separate orbitals with parallel spins. This is worked out in the molecular orbital section.

2S + 1, where S is the total spin of the electrons. All electrons paired gives S = 0 and multiplicity 1 (a singlet). Two unpaired electrons with parallel spins give S = 1 and multiplicity 3 (a triplet). The NIST database lists O₂ as a triplet, and N₂ as a singlet.

Related. There, a beam of single atoms with one unpaired electron split in a magnetic field. Here, molecules with two unpaired electrons are drawn into a strong field. Both are the magnetic moment of unpaired electron spin.

The four hybrids are not identical: a lone pair takes a little more s character and the bonds a little less p, so they close slightly. The idea of equal sp³ hybrids is the ideal case; the lone-pair squeeze from VSEPR is the correction.

A σ bond is formed by overlap along the line between the nuclei (two hybrids, or an s orbital with a hybrid, meeting head on). A π bond is formed by sideways overlap of p orbitals above and below the line. In the last unit you found the second pair in a double bond adds less to the bond energy than the first (C=C 590 kJ/mol against C–C 330): sideways overlap is weaker.

They are a mathematical way of combining orbitals that gives a good picture of bonds in a molecule with a definite shape. Nothing physical happens in an atom to mix them: it is the molecule's own wave function, rewritten in a convenient basis. Hybrids and the electron-pair picture of Lewis go together, and they work well for geometry. For energies and magnetism, as with oxygen, the next section's molecular orbitals do better.

Atoms in period 3 and below with five or six regions of electron density, like phosphorus in PCl₅ and sulfur in SF₆, are described with sp³d and sp³d² hybrids. As in the Lewis unit, the role of d orbitals in such molecules is debated; the shapes (trigonal bipyramid, octahedron) are what VSEPR already gave you.

The 2s and 2p orbitals of the same atom can mix, which pushes σ2p up. The mixing matters when 2s and 2p are close in energy, as in boron, carbon and nitrogen. By oxygen the gap has grown and the mixing is small, and σ2p drops below π2p. For O₂ the final filling comes out the same either way. The order matters for B₂ and C₂, where it decides whether the π2p pair fills before σ2p.

Eight valence electrons from each atom fill every bonding and antibonding orbital, so bonding and antibonding electrons are equal. A bond order of zero means no net bonding, and neon exists as separate atoms. Helium, dihelium, likewise.

Yes: N₂ (order 3) is 109.8 pm long and takes 945 kJ/mol to break, O₂ (order 2) 120.8 pm and 498, F₂ (order 1) 141.2 pm and 159, from the NIST data. As the bond order falls, the bond lengthens and weakens.

With 8 valence electrons it fills σ2s, σ*2s, and puts all four of its remaining electrons into the pair of π2p orbitals: two π bonds and no σ bond from the p orbitals. A bond order of 2 made entirely of π bonding is unusual, and the measured molecule is diamagnetic, as the filling here predicts.

Even a nonpolar molecule has electrons that move, so at any instant the charge is slightly uneven and the molecule is a tiny, flickering dipole. That induces a matching dipole in a neighbour, and the two attract. All molecules have these forces, and they grow with the number of electrons and the surface area. They are why methane can be liquefied at all.

An N–H, O–H or F–H bond is very polar, because N, O and F are small and highly electronegative, and it leaves the hydrogen almost bare: a small positive charge on a very small atom, with no inner electrons shielding it. That hydrogen can approach a lone pair on a neighbouring N, O or F very closely, and the attraction is far stronger than ordinary dipole–dipole attraction. That is a hydrogen bond.

No: carbon is not electronegative enough to polarize C–H much, and it has no lone pair. Methane has only dispersion forces, and it sits right on the trend of its family, which is how you can tell nothing extra is holding it.

From the Wikipedia article on each compound, which cites the CRC Handbook of Chemistry and Physics and other references, read by a script. Water's is 99.98 °C there.

Two things compete as you cool it. Cooling slows the molecules and brings them closer, which raises the density, as for any liquid. But as the water cools, more hydrogen-bonded rings and open clusters form, which take up more room. Above 4 °C the first effect wins; below, the second. Freezing completes the open network.

Water at 4 °C is the densest, so it sinks, and cooler water (denser until 4 °C only) floats up. As the whole lake approaches 4 °C it stops overturning, then the surface cools below 4 °C, is less dense, and stays on top until it freezes. Ice floats on that. Liquid water below stays near 4 °C, and fish survive winter.

Much weaker than a covalent bond but much stronger than ordinary attractions between molecules. It is why water boils 190 °C above the trend of its family, and why so many properties of water are unusual: its high boiling point, high heat capacity and its expansion on freezing all come from the same network of hydrogen bonds.

From Wikipedia's data page for water, which cites the CRC Handbook: liquid density at temperatures from −30 to 100 °C, and 0.92 g/cm³ for ordinary ice (ice Ih), which the source gives to two figures. A script reads it, and the expansion on freezing, about 8.7 %, is worked out from it.