Чамберс К., Холлидей А.К. Современная неорганическая химия, 1975

66 ENERGETICS

K =

Here, the reaction proceeds effectively to completion; (HC1) is very large relative to (H2) and (C12) and hence Kc (and Kp) are also large. In these circumstances the reverse arrow is usually omitted.

The equilibrium constant at constant temperature is directly related to the maximum energy, called the free energy AG. which is obtainable from a reaction, the relationship being

Here G is the free energy and AG the change in free energy during the reaction, R the gas constant and T the absolute temperature.

At 298 K, under standard conditions (G = G^) log10Kp - - 0.000733AG^

where AG^ is the change in free energy under standard conditions. The above equation enables us to calculate the equilibrium constant for any value of AG or vice versa, and we readily see that for a reaction to 'go to completion', i.e. for K to be large, AG needs

to be large and negative.

When AG = 0, the equilibrium constant K is unity. A large positive value of AG indicates that the reaction will not 'go', being energetically unfavourable under the specific conditions to which AG refers.

FREE ENERGY AND ENTROPY

Free energy is related to two other energy quantities, the enthalpy (the heat of reaction measured at constant pressure) and the entropy. S. an energy term most simply visualised as a measure of the disorder of the system, the relationship for a reaction taking place under standard conditions being

where AG^ is the change in free energy, A/T9" the change in enthalpy, AS^the change in entropy (all measured under standard conditions). and T is the absolute temperature.

If overall disorder increases during a reaction, AS is positive: where overall disorder decreases. AS is negative.

ENERGETICS 67

SPONTANEOUS REACTIONS

We have seen above that for a reaction to "go to completion' AG must be negative. Enthalpies of reaction often amount to several hundred kJ mol""l but values of entropy changes are rarely greater

40 kJ mol"1, then TAS is important and can result in a negative value for AG even when AH is positive—i.e. for an endothermic reaction. In the endothermic dissolution of ammonium nitrate in water, quoted in the introduction on p. 62, it is the entropy contri bution which produces the spontaneous reaction since the TAS^ is greater than AH^ and produces a negative value for AG^. Also in the introduction the mixing of two gases was mentioned. In this case the enthalpy of 'reaction' is very small but clearly disorder is increased by the mixing of the two gases. Thus AS is positive and the terms —TAS and AG are negative.

THE EXTRACTION OF METALS

From the above discussion, we might expect that endothermic reactions for which the enthalpy change is large cannot take place. However, a further consideration of the equation

Most metals react exothermically with oxygen to form an oxide. Figure 3.4 shows how the value of AG for this process varies with temperature for a number of metals (and for carbon), and it can be seen that in all cases AG becomes less negative as the temperature is increased. However, the decomposition of these metal oxides into the metal and oxygen is an endothermic process, and Figure 3.4 shows that this process does not become even energetically feasible for the majority of metals until very high temperatures are reached.

Let us now consider the reduction of a metal oxide by carbon which is itself oxidised to carbon monoxide. The reaction will become energetically feasible when the free energy change for the combined process is negative (see also Figure 3.3). Free energies.

68

Temperature, K

Figure 3.4. AG/T values for the reactions

2Zn + O2 -> 2ZnO

2Fe + O2 -> 2FeO

2Mg + O2 -* 2MgO

2C + O2 -H. 2CO

fAl + O2 -> fAl2 Oj

ENERGETICS 69

like enthalpies, are additive, and the minimum temperature for energetic feasibility can readily be found.

As an example, consider the reduction of zinc oxide to zinc by the reaction :

ZnO + C -* Zn + CO

Reference to Figure 3.4 shows that the reduction is not feasible at 800 K, but is feasible at 1300 K. However, we must remember that energetic feasibility does not necessarily mean a reaction will 4go' ; kinetic stability must also be considered. Several metals are indeed extracted by reduction with carbon, but in some cases the reduction is brought about by carbon monoxide formed when air, or airoxygen mixtures, are blown into the furnace. Carbon monoxide is the most effective reducing agent below about 980 K, and carbon is most effective above this temperature.

Since AG^ -

and AG^= - RTlnK,

1

0 g - = -

Hence an alternative to Figure 3.4 is to plot Iog10 K against 1/T {Figure 3.5); the slope of each line is equal to —A//-e/'2.303jR. A discontinuity in the line for a given metal-metal oxide system corresponds to a change in phase (solid, liquid, gas) of the metal or its oxide (usually the metal). The change in slope is related to the enthalpy change involved in the change. Thus for magnesiummagnesium oxide,

2Mg(l) + O2(g) -» 2MgO(s) : A/f f = - 1220 kJ mol ~]

2Mg(g) + O2(g) -> 2MgO(s) : AHf = -1280 kJ moP[

and hence

2Mg(l) -> 2Mg(g) : A/T9- - 260 kJ mol "l

which is twice the enthalpy of vaporisation of one mole of magnesium.

When studying the AG^ — T diagrams we saw that the extraction of a metal from its compound by a reducing agent becomes energetically feasible when the free energy change for the combined process is negative (see also Figure 3.3).

70 ENERGETICS

50r

g 45

0»

O

40

35

30

25

20 -b.p of zinc-

15-

10

temperature at which reduction becomes energetically feasible it is necessary to determine the temperature at which the equilibrium constant for the reduction indicates a displacement of the reaction in favour of the metal.

Consider the reduction of zinc oxide, by carbon monoxide. The equations are:

ENERGETICS 73

The heats of formation of the gaseous atoms, 4, are not very different; clearly, it is the change in the bond dissociation energy of HX, which falls steadily from HF to HI, which is mainly res ponsible for the changes in the heats of formation, 6. We shall see later that it is the very high H—F bond energy and thus the less easy dissociation of H—F into ions in water which makes HF in water a weak acid in comparison to other hydrogen halides.

COVALENT COMPOUNDS. OTHER SYSTEMS

We have just seen that a knowledge of bond energies enables enthalpies of reaction to be calculated. This is certainly true for simple diatomic systems. When polyatomic molecules are considered, however, the position can be more complicated and there are a number of different dissociation energies for even a twoelement polyatomic molecule. Consider, for example, ammonia. There are three N—H bond dissociation energies (p. 47) and the bond dissociation energy is different for each N—H bond and depends on the environment of the atoms concerned. The same conditions apply to any polyatomic molecule. However, average values, called average thermochemical bond energies (or average standard bond enthalpies) have been determined from a wide variety of compounds, and tables can be found in most data books. In spite of the known limitations of these bond energies, they are useful in estimating enthalpies of reactions, as indicated on p. 63, and the likely stabilities of covalent compounds. However, special care is needed when small positive or negative values for enthalpies are obtained (often as the difference between two larger values), since the predictions may then be unreliable because of the lack of precision in the original data.

IONIC COMPOUNDS: LATTICE ENERGY

Let us consider the formation of sodium chloride from its elements. An energy (enthalpy) diagram (called a Born-Haber cycle) for the reaction of sodium and chlorine is given in Figure 3.7. (As in the energy diagram for the formation of hydrogen chloride, an upward arrow represents an endothermic process and a downward arrow an exothermic process.)

The enthalpy changes evolved are:

A/I! the enthalpy of atomisation (or sublimation)of sodium.

where A is a constant for a particularcrystal type. z+ and z~ are the charges on the ions, r^ and r~ are the ionic radii (see p. 29) and B is a small constant of repulsion. The important quantities which determine the magnitude of the lattice energy are, therefore, ionic charges z. and the ionic radii r. Since z increases and r decreases across a period it is not surprising to find that a Group II halide has a much higher lattice energy than the corresponding Group I halide. Calculated lattice energies for the alkali metal halides are in good agreement with values determined from Born-Haber cycle measurements; for example for sodium chloride, the cycle gives - 787 and the calculation - 772 kJmol ~1 .

For other compounds, the agreement is not always so good. The assumption that the lattice is always wholly ionic is not always true; there may be some degree of covalent bonding or (where the ions are very large and easily distorted) some appreciable van der Waals forces between the ions (p. 47).

IONIC COMPOUNDS: STOICKIOMETRY

To date there is no evidence that sodium forms any chloride other than NaCl; indeed the electronic theory of valency predicts that Na+ and Cl~, with their noble gas configurations, are likely to be the most stable ionic species. However, since some noble gas atoms can lose electrons to form cations (p. 354) we cannot rely fully on this theory. We therefore need to examine the evidence provided by energetic data. Let us consider the formation of a number of possible ionic compounds; and first, the formation of "sodium dichloride", NaCl2. The energy diagram for the formation of this hypothetical compound follows the pattern of that for NaCl but an additional endothermic step is added for the second ionisation energy of sodium. The lattice energy is calculated on the assumption that the compound is ionic and that Na2+ is comparable in size with Mg2 + . The data are summarised below (standard enthalpies in kJ):