Inorganic Chemistry
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Inorganic Chemistry

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acid with the softer base. As a standard for comparison the prototype hard acid H+ and soft 
acid [(CH3)Hg]
+ are often used. Thus the equilibrium 
will lie to the left or right according to the degree of hardness of the base B. 
Examples of hard acids are H+, cations of very electropositive metals such as Mg2+, and nonmetal 
fluorides such as BF3. Soft acids include cations of late transition and post-transition metals such as 
Cu+, Pd2+ and Hg2+ (see Topics G4, G6, H3 and H5). The hardness of bases increases with the 
group number of the donor atom (e.g. NH3<H2O<F
\u2212) and decreases down any group (e.g. 
NH3>PH3, and F
Although the hard-soft classification provides a useful systematization of many trends it does not 
by itself provide an explanation of the different behavior. Generally it is considered that hard-hard 
interactions have a greater electrostatic component and soft-soft ones depend more on orbital 
interactions, but many other factors may be involved. Soft acceptor and donor atoms are often large 
and van der Waals\u2019 forces may contribute to the bonding (see Topic C9); some soft bases such as CO 
also show \u3c0-acceptor behavior (see Topic H9). It is also important to remember that hard and soft 
behavior is defined in a competitive situation. When reactions are studied in solution some 
competition with solvation is always present (see Topics E1 and E3). 
The tendency of many molecules to aggregate and form dimers (e.g. Al2Cl6 2), larger oligomers, or 
extended polymeric structures can be regarded as a donor-acceptor interaction. Thus in the reaction 
a chlorine atom bound to one AlCl3 uses nonbonding electrons to complex with the other aluminum 
atom; as in most other examples of this type the bridging atoms are symmetrically disposed with 
identical bonds to each aluminum. Polymerization of AXn molecules is more likely to occur when n 
is small, and when the atom A has vacant orbitals and is large enough to increase its coordination 
number. Many oxides and halides of stoichiometry AB2 and AB3 form structures that may be 
regarded as polymeric, although the distinction between this (polar covalent) description and an ionic 
one is not clear-cut (see Topics B1, D4 and F7). 
Hydrogen bonding (see Topic F2) can also be regarded as a donor-acceptor interaction in which the 
acceptor LUMO is the (unoccupied) antibonding orbital of hydrogen bonded to an electronegative 
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Section C\u2014Structure and bonding in molecules 
Molecular solids and liquids 
The condensation of molecular substances into liquid and solid forms is a manifestation of 
intermolecular forces. The enthalpies of fusion (i.e. melting) and vaporization provide a direct 
measure of the energy required to overcome such forces. 
We speak of molecular solids when molecules retain their identity, with geometries similar to 
those in the gas phase. The structures of molecular solids sometimes resemble those formed by 
close-packing of spheres (see Topic D2), although with highly unsymmetrical and polar molecules 
the directional nature of intermolecular forces may play a role. Molecular liquids are more 
disorganized, but the structural changes between solid and liquid can be subtle and the melting point
of a molecular solid is not in general a good guide to the strength of intermolecular forces. A better 
correlation is found with the normal boiling point, as molecules become isolated in the vapor and 
the influence of intermolecular interactions is lost. 
The enthalpy of vaporization \u394Hvap divided by the normal boiling point in kelvin (Tb) gives the 
standard entropy of vaporization (see Topic B3) 
and according to Trouton\u2019s rule its magnitude is normally around 90 J K\u22121 mol\u22121. Trouton\u2019s rule is 
not quantitatively reliable, and breaks down when molecules have an unusual degree of organization 
in either the liquid or vapor phase (e.g. 
Key Notes 
Molecular solids 
and liquids 
Intermolecular forces cause molecular substances to condense to form solids and liquids. 
Trouton\u2019s rule provides an approximate relationship between the normal boiling point of a 
liquid and the strength of intermolecular forces. 
Polar molecules have forces between permanent dipoles. With nonpolar molecules London 
dispersion (or van der Waals\u2019) forces arise between fluctuating dipoles; their magnitude is 
related to molecular polarizability, which generally increases with size. Molecules may 
also have more specific donor-acceptor interactions including hydrogen bonding. 
The polarity of a molecule arises from charge separation caused by electronegativity 
differences in bonds, although contributions from lone-pairs and the consequences of 
molecular symmetry are also important. High polarity gives strong intermolecular forces, 
and also provides a major contribution to the dielectric constant. 
Related topics Electronegativity and bond type (B1) Solvent types and properties (E1) 
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because of hydrogen bonding); it does, however, express a useful qualitative relationship between 
the boiling point and the strength of intermolecular forces. Figure 1 shows the normal boiling points 
for noble gas elements and some molecular hydrides. 
Intermolecular forces 
Between charged ions (whether simple or complex) the Coulomb attraction is the dominant force, as 
discussed in Topic D6. Even with neutral molecules, intermolecular forces are essentially 
electrostatic in origin. With polar molecules the force between permanent electric dipoles is the 
dominant one (see below). When polarity is absent the force arises from the interaction between 
instantaneous (fluctuating) dipoles, and is known as the London dispersion or van der Waals\u2019 
force. Its strength is related to the polarizability of the molecules concerned. Polarizability 
generally increases with the size of atoms, and the sequence of boiling points He<Ne<Ar<Kr shown 
in Fig. 1 reflects this. The boiling point increases down the group in most series of nonpolar 
molecules, for example, CH4<SiH4<GeH4 (also in Fig. 1), the diatomic halogens F2<Cl2<\u2026, and 
the order CF4<CCl4<CBr4<CI4 found with other molecular halides. (Ionic halides tend to show the 
reverse order, reflecting the decrease in lattice energy expected as the size of ions increases; see 
Topic D6.) 
In addition to forces of a strictly nonbonding nature, molecules may have chemical interactions 
that contribute to the apparent intermolecular forces. Donor and acceptor centers on different parts of 
a molecule can lead to self-association and polymerization, as discussed in Topic C8. Hydrogen 
bonding is one manifestation of this type of interaction (see Topic F2), which is especially important 
in polar hydrides of period 2 elements, NH3, H2O and HF. The extent to which the boiling points of 
these compounds are out of line as a consequence can be seen in Fig. 1. Hydrogen bonding can also 
have an important influence on the structure of 
Fig. 1. Normal boiling points of some molecular hydrides, with noble gas elements for 
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liquids and solids: thus ice has structures in which each water molecule is hydrogen bonded to four 
Molecular polarity 
The polarity of a molecule is measured by its dipole moment µ: imagine charges +q and \u2212q 
separated by a distance d, then, by definition, µ=qd. A practical unit for µ at the molecular