Thermal stabilities of ionic solids

Key point: Lattice enthalpies may be used to explain the chemical properties of many ionic solids, including their thermal decomposition.

The particular aspect we consider here is the temperature needed to bring about thermal decomposition of carbonates (although the arguments can easily be extended to many inorganic solids):

MCO(s)→MO(s) CO₂(g)

Magnesium carbonate, for instance, decomposes when heated to about 300°C, whereas calcium carbonate decomposes only if the temperature is raised to over 800°C. The decom position temperatures of thermally unstable compounds (such as carbonates) increase with cation radius (Table 3.11). In general, large cations stabilize large anions (and vice versa).

The stabilizing influence of a large cation on an unstable anion can be explained in terms of trends in lattice enthalpies. First, we note that the decomposition temperatures of solid inorganic compounds can be discussed in terms of their Gibbs energies of decomposition into specified products. The standard Gibbs energy for the decomposition of a solid, ∆G=∆H - T∆S, becomes negative when the second term on the right exceeds the first, which is when the temperature exceeds

In many cases it is sufficient to consider only trends in the reaction enthalpy, as the reaction entropy is essentially independent of M because it is dominated by the formation of gaseous CO₂. The standard enthalpy of decomposition of the solid is then given by

where ∆_decomp  is the standard enthalpy of decomposition of CO₃^-2 in the gas phase (Fig. 3.49)

Because ∆_decomp  is large and positive, the overall reaction enthalpy is positive (decomposition is endothermic), but it is less strongly positive if the lattice enthalpy of the oxide is markedly greater than that of the carbonate because then ∆H_L (MCO₃,s) – ∆H_L (MO, s) is negative. It follows that the decomposition temperature will be low for oxides that have relatively high lattice enthalpies compared with their parent carbonates. The compounds for which this is true are composed of small, highly charged cations, such as Mg⁺², which explains why a small cation increases the lattice enthalpy of an oxide more than that of a carbonate.

Figure 3.50 illustrates why a small cation has a more significant influence on the change in the lattice enthalpy as the cation size is varied. The change in separation is relatively small when the parent compound has a large cation initially. As the illustration shows in an exaggerated way, when the cation is very big, the change in size of the anion barely affects the scale of the lattice. Therefore, with a given unstable polyatomic anion, the lattice enthalpy difference is more significant and favourable to decomposition when the cation is small than when it is large.

The difference in lattice enthalpy between MO and MCO₃ is magnified by a larger charge on the cation as ∆H_L ∝ |z_A z_B|d.

As a result, thermal decomposition of a carbonate will occur at lower temperatures if it contains a higher charged cation. One consequence of this dependence on cation charge is that alkaline earth carbonates (M⁺²) decompose at lower temperatures than the corresponding alkali metal carbonates (M⁺).

The use of a large cation to stabilize a large anion that is otherwise susceptible to decom position, forming a smaller anionic species, is widely used by inorganic chemists to prepare compounds that are otherwise thermodynamically unstable. For example, the interhalogen anions, such as ICl^-₄, are obtained by the oxidation of I^- ions by Cl₂ but are susceptible to decomposition to iodine monochloride and Cl:

To disfavour the decomposition, a large cation is used to reduce the lattice enthalpy difference between MICl4 and MCl/MI. The larger alkali metal cations such as K⁺, Rb⁺, and Cs can be used in some cases, but it is even better to use a really bulky alkylammonium ion, such as N^tBu₄⁺ (with ^tBu C(CH₃)₃).

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مواضيع ذات صلة

The Fermi level

Densities of states

Band formation by orbital overlap

The conductivities of inorganic solids

Nonstoichiometry

Intrinsic point defects

Solubility

The Born–Mayer equation

Structure maps

The radius ratio

Ionic radii

Characteristic structures of ionic solids