introduction-to-inorganic-chemistry

5 On the nature of the limiting types of binary compound

In this chapter, I shall discuss the limiting types of binary compound. I shall do this on the assumption that matter is composed of atoms, but without any reference to the structure of the atom as we now understand it. This something that I shall bring in later.

5.1 Nonmetallic compounds

5.1.1 Volatile

The nature of compounds of this type can be arrived at by the following kind of argument:

(i)Gases are readily compressed, whereas liquids and solids are not. This suggests that, in gases, atoms are joined together in relatively small clusters, which are dispersed throughout the volume occupied by the gas.

(ii)Gases exert a pressure on the surface of a container. This suggests that the clusters of atoms are in continual, random motion, their bombardment of the walls creating the pressure we observe.

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(iii)If the temperature of a gas is lowered at constant volume, its pressure drops (according approximately to the gas law, P1V1/T1 = P2V2/T2). This suggests that the lowering of the temperature has the effect of slowing down the motion of the clusters.

(iv)If the temperature of a gas is lowered far enough, the gas liquefies. If is cooled further, it solidifies.

This suggests that there are forces between the clusters that are capable of holding the clusters together once their motion has been slowed down.

(v)The distinction between volatile and involatile substances must therefore lie in the relative strengths of the forces between the clusters. In the case of volatile substances, the forces must be relatively weak.

(vi)This conclusion is supported by the following observations:

(a)The latent heats of vaporization of volatile substances are relatively low. For example:

(The values of ∆H are for the vaporization of the liquid at the boiling point.)

(b)Coloured volatile substances generally have the same colour in the liquid and the solid as they have in the gas, suggesting that the interactions between the clusters in the condensed state is relatively slight. For example, chlorine retains its yellow colour in the liquid and the solid: by contrast, sodium is purple in the vapour and becomes metallic in the condensed state.

(c)Structure determinations show that, for volatile substances, the clusters that are present in the gaseous state are still present in the solid state, with relatively long distances between them. For example, electron diffraction of gaseous chlorine reveals the presence of diatomic clusters with an interatomic distance of 2.0 Å, while X-ray diffraction of solid chlorine reveals the presence of the same clusters, packed together in an orderly way, with the chlorine-chlorine distances between the clusters of 3.3 Å at their shortest.

(vii)The presence of clusters in a volatile liquid, held together but moving about, is supported by the phenomenon of Brownian motion. When pollen grains are suspended in water and viewed with a microscope, they are seen to be undergoing a continual jerky motion, as if they are continually being bombarded by the clusters that make up the water.

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In the above discussion “cluster” has been used to keep the argument fresh, and to avoid anticipating the conclusion. We can now substitute the technical word “molecule”, from the Latin molecula, meaning “a little mass”. The weak forces between molecules are called van der Waals’ forces, after the Dutch physicist who invoked them to explain the deviation of real gases from the behaviour predicted by the gas laws.

On the constitution of molecules

The formulae of the following molecules

H2, Cl2, HCl

can be accounted for by supposing that hydrogen and chlorine atoms are capable of uniting with one other atom, almost as if each atom had a single hook on it, and could engage the hook of another atom to form a single connection (“bond”) between them:

H–H, Cl–Cl, H–Cl

Similarly, the formulae of the following molecules

CH4, CH3Cl, CH2Cl2, CHCl3, CCl4

suggest that the carbon atom is capable of forming four such bonds:

The formulae of a great many compounds can be rationalized in this kind of way, as is done routinely in organic chemistry. The number of bonds formed by an atom is called its valency. This is discussed further in Chapter 8.

There is a good deal of evidence that the bonds around an atom are in definite directions in space. Thus, for example, compounds made up of molecules of the type Cwxyz, where w, x, y, and z are different atoms or groups of atoms, can be resolved into optically active isomers, familiar from organic chemistry. These are isomers whose crystals are the mirror image of each other, and which rotate plane polarized light in opposite directions. Formation of such isomers would not be possible if the molecules were planar (there would be only one isomer), but is consistent with their being tetrahedral in shape:

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The molecule shown now differs from its mirror image [draw this and show that it is different]. This arrangement of four atoms around a carbon atom has been confirmed by numerous electron diffraction studies of carbon compounds in the gas phase and X-ray diffraction of carbon compounds in the solid state.

5.1.2 Involatile nonmetallic compounds

Some nonmetallic compounds are involatile because their molecules are very large (e.g. higher paraffins). Although the van der Waals interactions between atoms in different molecules are small (they are the same as the interactions between atoms of small molecules), there are so many atoms that the total interaction between molecules is large. Compounds of this type nevertheless dissolve in volatile solvents (e.g. higher paraffins in lower ones), because each molecule can interact with as many solvent molecules as it can get round it. These interactions add up to overcome the large interaction between molecules of the compound. Very large molecules are called “macromolecules”.

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Other involatile nonmetallic compounds are different in being insoluble in volatile solvents (e.g. diamond, silicon carbide, and silica). The nature of these compounds can be inferred as follows:

(i)From the above discussion of volatile compounds, the molecules of these compounds in the vapour phase must interact very strongly in the liquid and solid phases.

(ii)In many volatile compounds, carbon atoms are known to bond to four other atoms in directions defined by a tetrahedron (see above). Now if carbon atoms were to bond to each other in this kind of way, instead of a small molecule being produced, a continuous three-dimensional network would be formed, each atom being held in the network by very strong bonds - the same kind of bonds that hold the atoms of each molecule together in volatile compounds. In two dimensions this may be drawn:

Such a structure would satisfy (i) and suggests itself for diamond.

(iii)A determination of the structure of diamond by X-ray crystallography shows that it indeed has this

structure, with carbon-carbon bond lengths of 1.54 Å, as compared with 1.53 Å in C2H6. (For a picture, click here http://bit.ly/hhA4OJ or see Appendix 2.)

(iv)In a similar way, we can “guess” the structures of silicon carbide and silica. Silicon also forms volatile compounds in which the silicon atom is surrounded by a tetrahedron of other atoms (e.g.

simple molecules like SiH4 and SiCl4, and resolvable ones of the type Siwxyz). Silicon carbide could thus have a similar structure to that of diamond:

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Further, since oxygen forms compounds in which its atom has two neighbours, silica could have a structure of the diamond type, only with an oxygen atom between every pair of silicon atoms:

That silicon carbide and silica indeed have structures of this kind has been shown by X-ray crystallography. (Both compounds are polymorphic, but in each case, the different forms have the same arrangement of nearest neighbours, and differ only in the relative orientation of more distant neighbours.)

Compounds of this type thus consist of giant assemblies of atoms tightly held together. Such assemblies of atoms are called “frameworks” and such compounds “nonmolecular”.

Liquefaction of compounds of this type involves the breaking of some of the bonds, for only in this way can atoms move positions. Clearly, however, the system will resist whole-scale breaking of bonds, and fluidity will rely on a process whereby the breaking of one bond is compensated for by the remaking of another bond somewhere else. Consequently, the fluidity of such compounds in the liquid state is low: that is, their viscosity is high.

Vaporization of compounds of this type does require a break-up of the network of bonds, and the vapour effectively consists of fragments of the solid. In the case of diamond, these are C2 molecules; for silica, they are SiO2 molecules. Silicon carbide decomposes.

Note

It is important to be able to work out the overall composition of a compound from diagrams of the kind given in the discussion above. This can be done by picking out the central atom in the diagram, counting the number of nearest neighbours to it (x), and then working out the share that the central atom has of these neighbours. This is done by counting the number of other atoms of the same type that the central atom has to share each neighbour with (y), from which the share the central atom has of each neighbour is 1/y. The composition is then ABz, where A represents the central atom, B its neighbour, and z = x/y. The method can readily be extended to cases where there is more than one kind of neighbour.

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Exercise

(i)Verify the compositions of silicon carbide and silica from the above diagrams.

(ii)Work out the composition of a compound having the following structure:

(Click here for answers http://bit.ly/h2WMuP or see Appendix 1)

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5.2 Salt-like compounds

These are composed of ions. The evidence for this is relatively simple:

(i)A solution of salt in water conducts electricity: a solution of sugar does not. Something must be carrying the charge.

(ii)In dilute solution, the elevation of the boiling point of water or the depression of the freezing point is approximately twice as great for a certain number of moles of salt as it is for the same number of moles of sugar. Thus, instead of behaving like a solution containing NaCl molecules, it behaves as if twice as many particles are present. Between them these particles must be the carriers of the charge, and since salt itself is neutral, they must be either

Nax+ and Clx– or Nax– and Clx+.

(iii)When an electric current is passed through molten salt, chlorine is formed where a conventional current enters the melt (the positive electrode or anode) and sodium where it leaves (the negative electrode or cathode). The sodium particles must therefore be Nax+ because they release conventional (positive) electricity to the wire leading from the cathode. The chloride particles must accordingly be Clx–. Faraday called Nax+ and Clx– “ions” from the Greek ion meaning “goer”, “cations” being goers to the cathode and “anions” to the anode.

(iv)The value of x can be found by dividing the quantity of electricity required to deposit one mole of

sodium, or produce the equivalent amount of hydrogen (½ mol of H2), F, by the Avogadro constant, L:

x = F/L

This value was called the “electron” before the particle that bears this name was discovered. If we give it the symbol e, the sodium and chloride ions can be written

Nae+ and Cle–

However, the e is always dropped, the charge (q) being replaced by the “charge number”, z = q/e. The electron itself is written e–, and its positive counterpart, the positron, e+.

(v)The idea that salt contains ions is further supported by the structure of the solid, as determined by X-ray diffraction. Instead of there being discrete molecules in the solid as there are in the case of chlorine, each sodium atom is surrounded by chlorine atoms, and each chlorine atom by sodium atoms, just as one would expect if they were oppositely charged ions. (For a picture, click here http://bit.ly/fDtj3g or see Appendix 2.)

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(vi)Further support is provided by calculations of the energy of the solid based upon the idea that it is made up of fairly hard charged spheres. Good agreement with experiment is obtained. (Details are given in some textbooks.)

(vii)Mass spectrometric analysis of sodium chloride vapour shows that, at temperatures a little above

the boiling point, the vapour contains NaCl, Na2Cl2, and Na3Cl3 molecules, the proportion of Na2Cl2 and Na3Cl3 decreasing with increase of temperature. For NaCl, spectroscopic measurements give the sodium-chlorine distance (r) as 2.36 Å and the dipole moment (µ) as 3.00×10–29 coulomb meter. If µ is conceived of as arising from a positive and negative charge of magnitude xe a distance r apart, we can write

µ=xer

From this and e = 1.60 × 10–19 coulomb, we obtain x = 0.8. This corresponds to a charge distribution of Na0.8+Cl0.8–, which is reasonably close to that expected for an ion pair, Na+Cl–. Further, electron diffraction studies of Li2Cl2, which is formed in higher concentrations than Na2Cl2, indicate that it has the rhombus-shaped structure that we would expect it were made up of ions:

The picture of sodium chloride that we arrive at is as follows:

(i)In the solid, the compound is made up of ions, held together in a giant assembly by the attraction of opposite charges, each cation being immediately surrounded by anions, and each anion by cations.

(ii)In the liquid, the ions have enough kinetic energy to move about. Even so, the arrangement of the ions at any instant differs little from that in the solid, each cation being surrounded by a majority of anions and vice versa.

(iii)In the vapour, there are molecules, the molecules being small aggregates of ions. These readily condense into the liquid and solid since the electrostatic energy of the system is significantly higher when each ion has several neighbours of opposite charge than when it has a few.

(iv)At very high temperatures, the molecules dissociate into atoms, as when sodium chloride is introduced into a flame.

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Exercise

(i)Obtain an expression for the electrostatic energy of a Na+Cl– molecule in terms of the cation-anion distance, r.

(Hint: click here http://bit.ly/flCfG7 or see Appendix 1)

(ii)From this obtain an expression for the electrostatic energy that one mole of Na+ and Cl– ions would have if they were all in the form of widely separated Na+Cl– molecules.

(Hint: click here http://bit.ly/dSyEo0 or see Appendix 1)

(iii)Repeat (i) and (ii) for (Na+Cl–)2 molecules, assuming that they are square.

(Hint: click here http://bit.ly/dIEVnL or see Appendix 1)

(iv)Compare your results with the corresponding expression for the solid,

E = –1.748Le2/4πε0r

(This is derived in some textbooks.)

(v)Evaluate the electrostatic energy in the three cases using Le2/4πε0 = 1389 kJ Å mol–1 and the observed values of r:

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

5.3 Metallic compounds

The nature of these is more difficult to determine. However, we can get so far along the following line:

(i)Metals conduct electricity without electrolysis taking place. The carriers of electricity cannot therefore be ions. They must either be some kind of charged entity that can travel through a conductor without affecting it or else a component of the atoms making up the conductor, which, by a process of successive displacement from one atom to another, can effectively be transferred from one end of the conductor to the other.

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