introduction-to-inorganic-chemistry

11 Interpretation of main-group valencies in terms of a simple model of main-group atoms

11.1 Basic theory

The valencies of main-group elements can be interpreted on the basis of a very simple model of atoms and bonding, as was done originally by Lewis (1916). Such a model is as follows:

1.Atoms consist of a nucleus, shells of inner or “core” electrons, and a shell of outer or “valence” electrons. Except for hydrogen and helium, the number of valence electrons is given by the group number, N.

2.Except for hydrogen and helium, the number of electrons in a complete shell is eight. This is the number possessed by inert gas atoms (except He), and constitutes a stable arrangement. This arrangement is called an “octet”.

3.For hydrogen and helium, the number of valence electrons is one (H) or two (He), and the number in a complete shell, two.

4.Atoms combine in ways that enable them to achieve an even number of electrons, especially a complete shell. (Very few main-group molecules have an odd number of electrons; exceptions are NO, NO2, and ClO2.)

5.One way atoms achieve complete shells is by the transfer of electrons from those with a smaller number of outer electrons to those with a larger number to form ions, e.g.

This explains why the positive electrovalencies of main-group elements are given by +N and the negative electrovalencies by −(8 − N). (Here dots and crosses are used to indicate electrons from different atoms. Electrons are indistinguishable, however, and Lewis formulae are often drawn just with dots. I will use dots and crosses to start with, to help you to see where electrons have come from.)

6.Another mode of combination is by the sharing of electrons between atoms, e.g.

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Each shared pair of electrons corresponds to a covalent bond - one pair to a single bond, two to a double bond, three to a triple bond. (Shared pairs are called “bond” pairs, unshared pairs “lone” pairs.) This mechanism explains why the principal covalencies of main-group elements are given by N up to Group 4M and 8 − N thereafter.

7.Combinations between the ionic and covalent extremes correspond to unequal sharing of the bonding electron pairs, e.g.:

Note that the bonding electrons are closer to the more electronegative atom.

8.In combination with atoms of more electronegative elements, some atoms can increase the number of electrons around them above the number for a closed shell, e.g.:

This explains why, for elements beyond Group 4M, valencies can rise above 8 − N, in twos, up to a maximum of N. When an element has such a valency, it is said to be “hypervalent”.

9.Hydrogen is a special case, having one electron in a shell of total capacity two. Stable arrangements can be achieved by the loss of an electron (to give H+), gain of an electron (to give H–), or sharing an electron pair as in H–H. The formation of H– was predicted by Lewis and verified by examining the electrical properties of fused lithium hydride. The latter is obtained as a white powder, m.p. 680 ºC, by heating lithium in hydrogen. In the molten state, it conducts electricity, and lithium is deposited at the cathode and hydrogen at the anode, in quantities in accordance with Faraday’s Laws. (In the electrolysis of aqueous acids, of course, hydrogen appears at the cathode.)

Lewis’s theory explains the relations between ordinary valency, electrovalency, and covalency found in Chapter 8 (e.g. V = E = C = 1 for hydrogen).

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Exercise

Write a Lewis structure for each of the following species:

(i) H2O; (ii) NH3; (iii) BF3; (iv) N2; (v) ClF3; (vi) H2SO4.

(Click here for answers http://bit.ly/fK1fpQ or see Appendix 1)

11.2 Refinement of model in the light of the quantum theory of atoms

(i)The valence shell of 8 actually comprises two shells: an s shell of 2 and a p shell of 6 (for details, click here http://bit.ly/eekMTf or see Appendix 4). The valency of N – 2 for heavier members of Groups 3M and 4M corresponds to the non-participation of the s electrons in the bonding, as if they formed part of the core. This is called the “inert-pair” effect.

(ii)Calculations show that, in molecules formed by main-group elements, only s and p orbitals of the valence shell are used (not d). This sets an upper limit of 8 to the number of electrons in the valence shell. The reason why molecules like SF6 can form is that the polarity of the bonds reduces the number of electrons in the valence shell of the central atom to 8. The 12 electrons in the Lewis structure reside in a somewhat larger shell than the valence shell, located partly on the fluorine atoms. This is called the “Lewis shell”.

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For there to be ≤8 electrons in the valence shell of the sulfur atom in SF6, the polarity of the molecule must be Sx+(Fx/6−)6 with x ≥ 2. (For an explanation, click here http://bit.ly/fM3PNf or see Appendix 5.) Quantum-mechanical calculations give x 3. This corresponds to the semipolar bond structure:

S3+(-----F0.5−)6

0.5

Note that the valency of the sulfur atom is still 6, but is made up of a covalency of 3 and an electrovalency of +3. The corresponding Lewis structure is

with a space between the bonding pair and the sulfur atom to indicate polarity.

(iii)Modern theory pictures molecules like benzene and diborane as having pairs of electrons delocalized over several atoms. Lewis structures for such molecules can be drawn with fractional electron pairs, as in the example below. The fractions indicate that each pair of electrons spends a fraction of time between one pair of nuclei and a fraction between another pair.

Refinements (ii) and (iii) both apply to species like SO42−. A simple bond formula for this can be drawn with 1½ bonds. A Lewis structure can therefore be drawn with 1½ bonding pairs:

. .

[S( :: O :)4]2− : = ½

. .

I have again put a space between the bonding electrons and the sulfur atom to indicate polarity. In this case, to keep within an octet, the polarity must be Sx+(Oy−)4 with 4y − x = 2 and x ≥ 2. Quantummechanical calculations give x 2. This suggests the structure

S2+(= =O−)4

1

with each sulfur-oxygen bond having an ionic component of ½ (S½+O–) and a covalent component of 1 (⅔ of a fully covalent 1½ bond), totalling 1½.

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Exercises

(i)Calculate the lowest charge the phosphorus atom can carry in PF5.

(ii)Write a Lewis structure for CH3NO2, and calculate the lowest charge the nitrogen atom in this molecule can have.

(iii)Repeat this for the [NO3]− ion, with fractional pairs.

(Click here for answers http://bit.ly/fFbGDB or see Appendix 1)

11.3 The dative bond

Ammonia gas (NH3) reacts with boron trifluoride gas (BF3) to give a colourless molecular solid, H3NBF3. This can be explained by adding a further postulate to 1−9 above:

10.A bond can be formed between an atom with a lone pair and an atom with an incomplete shell, e.g.

The boron atom now has an octet, and there is a new kind of bond between the nitrogen atom and the boron. This is similar to a covalent bond, but instead of one electron being supplied by each atom, both electrons come from the same atom, in this case the nitrogen.

The bond just described has been variously written and variously named. One way of writing it is

N→B

whence the name “dative” bond (Latin, dare, give). Another way of formulating it is to imagine first the transfer of one electron to give N+ and B− and then the formation of an ordinary covalent bond:

+N B−

From this, it is sometimes called a “semipolar double bond” - a combination of a single ionic bond and a single covalent bond.

In practice, there can be little doubt that a dative bond is generally weaker than a double bond. In Me3NBF3, the N−B distance is about 1.6 Å, as compared with about 1.4 for a double bond and 1.6 for a single bond. The donation of the electron pair is evidently only partial - enough to form about half an ionic bond and half a covalent bond to give a bond order of about one. The symbol +X Y− for a donor bond thus needs to be used with care. For most purposes, the symbol X→Y is preferable, since it does not imply a particular bond order.

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The dative bond has proved a mixed blessing to the concept of valency. On the one hand, it enables formulae to be drawn for a great many species that could not satisfactorily be formulated without it. An example is carbon monoxide, which when formulated as C=O does not do justice to the fact that the bond length is 1.13 Å, as compared with 1.22 Å for C=O in aldehydes and ketones. When written as a Lewis structure, however,

the possibility of the formation of a donor bond becomes evident, to complete the octet of the carbon atom:

The shorter distance is now accommodated. Many other examples will be given in the chapter on coordination compounds (Chap. 13).

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On the other hand, the dative bond is of indefinite order. The degree of donation is evidently dependent on the relative electronegativities of the donor and the acceptor, and this can vary widely. In the case of an ordinary covalent bond, this does not matter, since loss of covalency through unequal sharing of the bonding pair is compensated for by gain in electrovalency. In the case of the dative bond, however, it is not, and in the limit of unequal sharing there is no bond at all:

This means that dative bonds do not form everywhere where they might be predicted to on paper, so that dative bonding tends to be something that is invoked to explain the formulae of molecules once they are known, rather than a means of predicting the formulae of molecules yet to be made. Thus, for example, we can write down on paper a molecule of the formula

but no substance of this composition has ever been made. Presumably, the neon atom is too electronegative to part with its electrons.

Exercise

Write a Lewis structure for (i) CH3NC; (ii) [NNN]−

(Click here for answers http://bit.ly/ia1vYO or see Appendix 1)

X=O or X→O?

Donor bonds allow atoms to preserve their octet where my treatment uses polar double bonds. For example:

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Here R = CH3, F, O−, etc. Lewis gave a dot formula of this type for [SO4]2−. The Oxford chemist N.V. Sidgwick extended this to other molecules. Most modern textbooks follow Sidgwick, at least for nitrogen compounds. However, quantum-mechanical calculations suggest that polar double bonds are a better approximation for most molecules (or even polar triple bonds as in CO if the symmetry allows it). Exceptions are molecules of the type R3NO with weakly electronegative R groups (e.g. CH3). For these a donor bond is better. [Note that the N−O bond in (CH3)3NO is much longer (1.40 Å) than that in F3NO (1.16 Å).]

Ammonium

The Lewis structure for the [NH4]+ ion can be derived by regarding it either (i) as a derivative of N+ (with four valence electrons, forming covalent bonds to four hydrogen atoms), or (ii) as a derivative of NH3 and H+ (the lone pair on the nitrogen atom forming a dative bond with H+). The result is the same:

11.4 Isoelectronic principle

Systems are said to be “isoelectronic” (Greek isos, equal) if they have the same number of nuclei and the same number of electrons. Thus, Na+ and F– are isoelectronic with Ne, and the following constitutes an isoelectronic series:

O2–, F–, Ne, Na+, Mg2+, Al3+

The isoelectronic principle states that, for small variations in nuclear charge at least, the arrangement of electrons in isoelectronic species is approximately same.

A simple example of this is provided by the OH– ion. This is isoelectronic with the HF molecule, O– having the same number of electrons as F. Now the bond formula for the HF molecule is

H–F

According to the isoelectronic principle, therefore, the bond formula of OH– can be written

H–O–

with F replaced by O–.

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This principle is particularly helpful in thinking about species containing dative bonds. Such species are often isoelectronic with, and close in nuclear charge to, stable species containing ordinary covalent bonds. Thus,

is isoelectronic with CF4, N+ having the same number of electrons as C and O– as F. Similarly

is isoelectronic with N2, C– and O+ having the same number of electrons as N. It is also isoelectronic with the cyanide ion and the acetylide ion

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Thus, it seems that, if the parent species is stable enough, species that are isoelectronic with it will also be stable, provided that the nuclear charges do not differ too much. The last point is illustrated by the series N2, CO, BF, BeNe, the third and fourth members of which do not exist as stable substances.

Exercise

Write down the formulae of as many species as you know to exist that are isoelectronic with CO2.

(Click here for answers http://bit.ly/i0h05f or see Appendix 1)

11.5 Transition elements

Lewis’s model can explain some of the valencies of transition elements. If their atoms have N valence electrons (N = group number), this accounts for the highest valencies up to group 8T. If a complete shell contains 18 electrons, this explains the formulae of many “nonclassical” compounds, considered in Chapter 13. A valence shell of 18 electrons corresponds to the filling of d, s, and p orbitals (3d, 4s, and 4p for first-row transition elements; 4d, 5s, and 5p for second-row; 5d, 6s, and 6p for third-row).

However, this leaves many valencies unaccounted for. To explain how these arise, Lewis suggested that transition-element atoms can have variable cores. Consider, for example, titanium. This has a valency of four, equal to the group number. Its atom therefore has four valence electrons. However, titanium also has a valency of three. In this valency, its compounds have similar structures to those of scandium, whose atom has three valence electrons. In trivalent compounds, therefore, a titanium atom behaves as if it has only three valence electrons, i.e. as if the fourth electron has become part of the core. In other words, the core of a titanium atom can be [Ar] or [Ar3d1] (the configurations of Ti4+ and Ti3+ respectively) depending on how the atom is bound. Lewis structures can accordingly be drawn for transition-element compounds by specifying the charge on the core (in this case Ti4+ or Ti3+).

The valencies of inner transition elements may also be understood in terms of variable cores and ≤N valence electrons (on my group numbering).

11.6 Shapes of molecules

Lewis structures can be used to explain and predict the shapes of molecules. The basic assumption is that, if the core of an atom is effectively spherical (as for most atoms it is), groups of electrons in the Lewis shell (single bond pairs, double-bond quartets, fractional bond pairs, etc.) get as far apart as possible. Thus, two groups take up a linear arrangement, three a trigonal-planar one, four tetrahedral, five trigonalbipyramidal, six octahedral, and so on.

For main-group atoms, lone pairs are included. For example, in an H2O molecule, there are two bond pairs and two lone pairs round the oxygen atom. These take up a tetrahedral arrangement, making the molecule angular, as observed. For transition-metal atoms, lone pairs are excluded (Chap. 13).

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