Electrons in Molecules: Ions in Structures and Solutions

James Richard Fromm

An electron can be transferred from one neutral (uncharged) atom to another. When this happens, the atom from which the electron is transferred becomes a positive ion or cation and the atom to which the electron is transferred becomes a negative ion or anion because an electron has one negative charge. Electrons can also be transferred from one ion to another or between an ion and a neutral atom.

The transfer of an electron to or from an atom involves energy. The energy required to remove one electron from an atom or ion is characteristic of the ion atom and is its ionization potential. The energy obtained when an electron is acquired by an atom or ion is its electron affinity. The electron transfer can take place with a gain of energy only when the electron affinity of the receiving species is greater than the ionization potential of the donating species, which is rarely the case, or if the ions once formed associate themselves into a new configuration of lower energy. Most electron transfer reactions occur when the ions once formed associate themselves into structured lattices called ionic crystals. The association of ions into ion pairs is less common, although it occurs when ionic salts are dissolved in some organic solvents. Most ions exist as individual solvated ions when in solution, as discussed in earlier sections. We now consider the energies and geometries involved in ionic structures.

Energy Considerations in Ionic Structures

The energy required to produce any cation from an atom, the ionization energy of the atom, is always larger, and usually much larger, than the energy which is released when an electron is added to any atom, the electron affinity. This is true even if an electron is being removed from an atom which loses it easily, like sodium, and is being added to an atom which readily acquires it, such as chlorine. The ionization energy of sodium is +502.838 kJ/mole while the electron affinity of chlorine is only -354.809 kJ/mole. The reaction

Na(g) + Cl(g) rarrow.gif (63 bytes) Na+(g) + Cl-(g)

would require about 150 kJ/mole to proceed while the reaction

Na(c) + 0.5Cl2(g) rarrow.gif (63 bytes) Na+(g) + Cl-(g)

would require three times as much. Electron affinity alone cannot provide sufficient energy to form ions or ionic structures; the energy must come from the assembly of isolated ions into stable multi-ion structures.

Ions with the same type of charge repel each other, but ions of opposite charge attract each other. The simplest possible ionic structure which might be stable is the gas-phase ion pair, which consists of one cation and one anion held together by electrostatic attraction. It is relatively simple to calculate how much energy would be gained by this association using the Coulomb law of electrostatic attraction. Since the attractive force is F = Q1Q2/4(pi)(epsilon)0r2, it follows that the energy of two singly-charged ions separated by vacuum at a distance r will differ from the energy of the two isolated ions by the product of that force times distance r because energy is the product of force and distance:

E = Fr = -e2/4(pi)(epsilon)r

The energy of the two associated ions will be less than the energy of the two isolated ions by this amount if the ions are of opposite charge. For sodium ion the ionic radius is 95 pm and for chloride ion it is 181 pm so the distance of separation of the centers of the two ions is 276 pm. The energy for one ion pair, multiplied by the Avogadro number NA, gives the molar energy of [Na+Cl-](g) relative to the molar energy of the isolated ions as:

E = (1.602... x 10-19)2(6.022...x 10+23/4(pi)(8.854...x 10-12)(276 x 10-12)

This is -504.69 kJ/mole, so the standard molar enthalpy of formation of the ion pair estimated using the Coulomb law is -128.46 kJ/mole. Even for a single sodium ion and chloride ion in the gas phase, it is the lower energy available through association of ions of opposite charge that drives the formation of ionic compounds.

The ionic radii used in the calculation above were the radii of sodium and chloride ions found in ionic crystals. They are, however, very similar to the radii of these ions under other conditions. The actual distance between the ions in Na+Cl-(g) has been measured and found to be 236.1 pm.

Association of ions of opposite charge is not normally into ion pairs, although some stable ion pairs are found in the gas phase and in some nonaqueous solvents. It is far more common to find ions either as solvated ions in aqueous solution or in the form of the solid ionic crystals, which are large ordered three-dimensional arrays of ions.

When ions go into solution from the gas phase, they can enter a lower-energy state because the molecules of the solvent orient themselves around the individual ions in response to the charge. The process of ionic solvation in aqueous solutions is highly exothermic. For sodium chloride, a typical strong electrolyte salt, the heat of solvation is a large -783.507 kJ/mole. This is the sum of the heat of solvation of one mole of sodium ions and one mole of chloride ions and corresponds to the reaction

Na+(g) + Cl-(g) rarrow.gif (63 bytes) Na+(aq) + Cl-(aq).

The diagram shown in the Figure below is the Born-Haber cycle for sodium chloride and its ions. The Born-Haber thermochemical cycle is named after the two German physical chemists, Max Born and Fritz Haber, who first used it in 1919. The figure shows not only the enthalpies involved in the formation of solvated, in this case aquated, ions but also those involved in the formation of ionic crystals. The enthalpy change in the formation of an ionic lattice from the gaseous isolated ions is -787.381 kJ/mole. That enthalpy change, which in this example corresponds to the reaction

Na+(g) + Cl-(g) rarrow.gif (63 bytes) NaCl(c),

is called the lattice energy of the ionic crystal. Although the lattice energy is not directly measurable, the appropriate Born-Haber cycle permits its calculation from measured heats. For all known ionic crystals, the lattice energy has a large negative value. The lattice energy of an ionic crystal is responsible for the formation and stability of ionic crystal structures.

Energy Considerations in Solvated Ions

The use of the Born-Haber cycle for solvated ions rather than ionic crystals permits the calculation of the heat of solvation of ions. The heat of solvation of ions in aqueous solution is normally large and negative, like the lattice energy of ionic crystals. When ionic crystals are placed in water, some dissolve easily and some do not; some dissolve with considerable evolution of heat, some (like sodium chloride) with no obvious evolution of heat, and a smaller number of ionic salts have an endothermic reaction when they dissolve in water so that the solution is cooled by their dissolution. The reason salts behave in this way is that the energy difference between the lattice energy, which is large and negative, and the heat of solvation, which is generally also large and negative, can be either positive or negative.

Copyright 1997 James R. Fromm