CHEMISTRY [Periodic Properties]

 Periodic Properties

Modern periodic law state that the physical and chemical properties of elements are periodic functions of atomic number, i. e. , after certain interval of atomic number, properties of elements are repeated. The elements having same electron configuration of outer shells are found in the same group. As most of the properties of an element are dependent on its outermost electronic configuration ; So the elements of a particular group having similar electronic configuration show similarity in properties.

         The periodic in the properties of elements is due to the periodicity in the number of valence electronic of elements. If elements having similar valence electrons are grouped together, their properties are also similar. Thus, the periodic repetition or periodicity must be due to the repetition of similar electronic configuration of outermost shells after certain intervals. There are so many properties which are periodic in nature given below :

(i) Atomic and ionic radii 

(ii) Ionisation potential 

(iii) Electron affinity 

(iv) Electronegativity

(v) Atomic volume, density, melting point boiling point and oxidation number etc.

Atomic Radii

Generally, the distance of the outermost orbit in the configuration from the center of the nucleus is known as atomic radius. The mathematical expression for radius is given as : 

r = n²h²/4πmZ^*e²

  = 0.529 . n²/Z^*

r  ∞  n² /Z^*

  where, n= Outermost orbit, Z^* = Effective nuclear change.

But according to wave mechanics, there is no certainty regarding exact position occupied by electrons at any time. An electron may be very close to the nucleus at any time, while at other times it may be for away from the nucleus. Hence, inspite of the uncertainty some operational definitions of atomic radii have been arrived at. So there are four operational concepts an atomic radii, which depend upon the environment of an atom. These are :

(i) Van der Waals radius

(ii) Covalent radius

(iii) Metallic radius 

(iv) Ionic radius.

(i) Van der Waals Radius :  Non-metals for aggregates of molecules in solid state, In this state molecules are held together by weak attractive forces which are called Van der Waals forces. These forces are not present in gaseous state. It is defined as : "Half if distance between the nuclei of two adjacent atoms belonging to two neighboring molecules of an elements in the solid state is known as Van der Waals radius of the atom." 

Van der Waals radius is non-bonded distance of close approach. It is greater than covalent radius. It is half of its Van der Waals distance. It is the distance between two non-bonded atoms of two adjacent molecules in solid state. The values of these radii are obtained from X-ray studies of various elements in solid state. In Cl2 solid, the distance between two non-bonded neighboring Cl atoms is 3.6Å which is Van der Waals distance. 

therefor,           Van der Waals radius of Cl = 3.6/2

                                                                                   = 1.8Å

The Van der Waals radius of chlorine atoms is given in.

Van der Waals radii of some elements are given in table1.

Table 1 : Van der Waals Radii (Å)

Group

15                            16                      17                        18

N= 1.5                   O= 1.40               H= 1.2                He= 1.20

P= 1.9                    S= 1.85               F= 1.36               Ne= 1.60

As= 2.0                  Se= 2.0               Cl= 1.8                Ar= 1.21

Sb= 2.2                  Te= 2.20             Br= 1.95              Kr= 2.0

                                                            I= 2.15               Xe= 2.20

  (ii) Covalent Radius: It is defined as : "One-half of the distance between the nucleus of two covalently bonded atoms of the same elements in a molecule."  

It may be noted that Van de Waals radius is non-bonded distance of closer approach and covalent radius is the bonded distance of closer approach. It is effective radius of an atom in the direction of its covalent bond. 

The distance between nuclei of two hydrogen atoms hydrogen molecule of found by spectroscopy to be .074Å will be the covalent radius of H-atom.

Covalent = Distance between the nucleus of two atoms of same                              element by single covalent bond/2

The distance between two Cl atoms bonded by single covalent bond is 1.98Å, here, covalent radius of Cl atom is 0.99Å. The covalent radius of Cl atom is given in .

The value of covalent radius is less than Van der Waals radius due to overlap radius of electron cloud. In study of chemistry covalent radius is generally used. Covalent radius is nearly same as atomic radius.

The Van der Waals radii and covalent radii of some elements are given in .

Table2 : Van der Waals and Covalent Radii (Å) 

Elements    H          N       O         F           Cl       Br         I           S

Van der     1.2        1.5      1.4     1.35      1.80     1.95      2.15      1.85

Waals radius

Covalent    0.37     0.75   0.73     0.72     0.99    1.14      1.33      1.04

radius

from the above table it is clear Van der Waals radius is greater than the covalent radius. So covalent radius is shorter in comparison to Van der Waals radius. This is due to the fact that in formation of chemical bonds atoms come very closer to each other, so distance between nuclei decreases.

The covalent and Van der Waals radii in chlorine atom is given in .

The covalent radius is additive, i. e., the sum of covalent radii of two atoms is equal to the internuclear distance of the molecules formed by those atoms. For example, covalent radius of HCl is 1.36Å.

r_H  +  r_Cl     =   r_HCl

0.37 + 0.99 = 1.36Å

Hence, it is additive.

(iii) Metallic Radius or Crystal Radius

Metallic radius is used for metal atoms which are supposed to be closely packed in the metallic crystal. It is defined as : "One half of the distance between the nuclei of two adjacent metal atoms in the metallic close packed crystal lattice." 

In solid sodium, the distance between the nearest two sodium atoms is 3.72Å. The half of this distance, i. e. , 3.72/2= 1.86Å is the crystal or metallic radius of Na. The metallic radius of sodium is given in.

The metallic are larger than covalent radii. This is because the average bond order of an individual metal-metal bond is considerably less than one; hence, the individual bond is weaker. However, metallic radii are smaller than the Van der Waals radii. This is due to the fact that bonding forces in the metallic crystal lattice are much more stronger than the Van der Waals forces and depend upon co-ordination number (C.N), e. g. ,

                                 Metallic radius of Na = 1.86Å.

                                 Covalent radius of Na = 1.54Å.

Metallic radii decrease from left to right in a period.

Element                       Li                   Be                   B                         C

 Metallic radii(Å)      1.55              1.12              0.98                  0.91

periodicity of atomic radii : As we know that,

                                      r = 0.529 . n²/Z^{* ,}

where n is outermost orbit and Z^* is effective nuclear charge.

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