Chemistry Reference
In-Depth Information
The covalent radius of nonmetallic element is calculated according to the homonu-
clear or heteronuclear nature of the molecules. Thus, in the case of homonuclear mol-
ecules (Cl
2
, Br
2
, graphite) in solid state, this radius is equal to half the experimentally
measured distance between the nuclei of two neighboring atoms. For heteronuclear
molecules the distance between the two covalent bound atoms is experimentally
determined. From that value, the value of the known radius is subtracted in order to
obtain the unknown radius. For example, the length of the covalent Cl-Cl bond is
1.998 Å, therefore the covalent radius of the chlorine atom is 0.994 Å. If the covalent
C-Cl bond is 1.766 Å, the value of the known covalent radius of the chlorine atom is
subtracted and so the covalent radius of C is obtained, that is 0.722 Å.
Besides the covalent radius, there is also the Van der Waals radius, which is char-
acteristic for atoms in covalent compounds. This radius represents the shortest dis-
tance between the atoms that are not chemically bound, that is, the distance at which
they can approach without the electronic clouds repelling each other.
The ionic radius is difficult to measure because it varies depending on features
such as the environment surrounding the ion and the number of ions bound to a partic-
ular ion. However, there are different methods that can be used to measure this radius.
The most used are those of Landé and of Pauling. The ionic radius of an element is
the contribution of each ion to the distance between the nuclei of two neighboring
ions or the distance between the nucleus of a cation and its neighboring anion is the
sum of the radii of the two ions. The radius of the positive ions is always smaller than
the radius of the atoms of origin because the change to the cation state is made by
the removal of one or more electrons from the outer layer, which increases the effec-
tive nuclear charge. It follows that the anion radius is always larger than that of the
corresponding atoms because electron addition decreases the electric nuclear charge.
Also, the ionic radii change with the oxidation state of the ion, with the increase
of the oxidation state leading to a decrease in ionic radius.
Figures 2.8
, 2.9, and 2.10
compare the atomic radius, ionic radius, and the covalent radius for periods 1 and
2, and period 3 and period 4 elements, respectively (Brezeanu et al. 1990; Whitten
et al.
1988; Housecroft and Constable 1997). It can be seen from these figures that
covalent radii follow the same general trend as the ionic radii: they have even smaller
values than the ionic radii for metals and higher values for the nonmetals.
The d-block elements have similar properties from this point of view, and because
they are found together in natural minerals, they are difficult to separate.
In the case of lanthanides and actinides, the ionic radii decrease greatly and the
differences between the atomic radii and ionic radii are significant. They are much
bigger than those of other elements. If other elements display 10-20% decreases, in
lanthanides and actinides the ionic radii would decrease by 50-60%. Also, among
lanthanide elements and actinide elements, respectively, the differences between
the atomic and the ionic radii are quite small. They are practically equal in most
instances (
Figures 2.11
and 2.12).
2.3.4 i
onizAtion
e
nergies
The ease with which an atom forms positive ions by electron transfer is dependent on
its ionization energy (IE). The
ionization energy
, or the
ionization potential
, is the
