atomic packing factor for nacl

Themes > Science > Chemistry > Inorganic Chemistry > More Information about Chemical Bonding > Ionic Bonds

Because ionic compounds are aggregates of many ions, rather than discrete molecules, bond length and bond energy as decribed for molecular compounds have little meaning for ionic compounds.

In a crystal, each ion is attracted and repelled by many other ions. The geometry of the arrangement of ions, the interionic distances, and the charges on the ions all influence the strength of ionic bonding.

The thermodynamic quantity that expresses the sum of all these effects and is used to measure the strength of ionic bonding is the lattice energy - the energy liberated when gaseous ions combine to give one mole of a crystalline ionic compound.

For sodium chloride: the thermochemical equation that represents the lattice energy is;

Na+(g) + Cl-(g) ® NaCl(s)     D H = -769 kJ

Atomic Packing

The way atoms or ions are arranged in the solid-state controls the properties of the materials. The packing arrangement of atoms depends on the relative radii of the atoms involved and also on the character of bonding between atoms.

The density of packing in a crystal is most conveniently determined by the atomic packing factor, which is defined as the ratio;

volume of the atoms per unit cell / volume of the unit cell

A space lattice can be considered as an infinite array of points in space, so arranged that it divides space into equal volumes with no space excluded. Every point, which is called a lattice point, has identical surroundings with every other point. The smallest volume that contains the full pattern of repetition is called a unit cell.

Knowing the type of unit cell for a particular crystalline solid and the corresponding atomic radii, it is possible to calculate the true density of the crystalline solid.

For example; consider a unit cell of a cubic crystal with side a and n number of atoms in the pattern. The weight of the unit cell is equal to the weight of atoms per unit cell. The weight of atoms per unit cell is found from;

nM / NA

where M = the atomic weight

NA = the Avogadro number

n = the number of atoms per unit cell

Since the volume of the unit cell will be a3, the density of the crystal, r , will be the weight of the unit cell divided by its volume a3;


= nM / a3 NA

or generally;


= nM / V NA

where V = cell volume

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Wed, 06/03/2009 - 14:31