How to calculate covalent radius?
How to calculate covalent radius?
In case of homonuclear diatomic molecules of A2 type (e.g. F2, Cl2, Br2, I2 ... etc.) the bond length, d(A-A) is given by
d(A - A) = r(A) + r(A)
d(A - A) = 2 � r(A)
r(A) = d(A-A) / 2
The above equation shows that in the case of homonuclear diatomic molecule of A2 type, the covalent radius of an atom A, r(A) is equal to one half of the inter- nuclear distance, d(A-A). Therefore, the covalent radius of an atom in a homonuclear diatomic molecule can be obtained by dividing the internuclear distance by two.
Example
1. Cl2 molecule
The value of Cl-Cl bond distance as found experimentally is 1.98�. Thus
r(Cl)= d(Cl- Cl) / 2 = 1.98/2 = 0.99�
2. Diamond
The value of d(C-C) distance as found experimentally in a variety of saturated hydrocarbons is 1.54�.
r(C) = d(C - C) / 2 = 1.54 / 2 = 0.77 �
b. Heteronuclear diatomic molecule
In case of heteronuclear diatomic molecule of AB type, bond length
d(A - B) is given by
d(A - B) = r(A) + r(B)
r(A) and r(B) are the covalent radii of A and B atoms.
Example
i) CCl4 molecule
The experimental value of d(C - Cl) is 1.76 �
Thus d(C-Cl) = r(C) + r(Cl)
r(C) = d(C - Cl) - r(Cl)
= 1.76 - r(Cl)
Thus the covalent radius of carbon atom can be calculated by subtracting the covalent radius of Cl atom from d(C-Cl) bond length. The covalent radius of Cl atom can also be obtained, provided that covalent radius of C atom is known.
ii) Sic
The experimental value of d(Si-C) is 1.93 �. Thus,
d(Si - C) = r(Si) + r(C)
r(Si) = d(Si - C) - r(C) = 1.93 - r(C) = 1.93 - 0.77 = 1.16 �
The experimental values of covalent bond length for some common homonuclear diatomic molecules are given below.
Molecule : Bond : Bond length (�)
H2 : H-H : 0.74
F2 : F-F : 1.44
Cl2 : Cl-Cl : 1.98
Br2 : Br-Br : 2.28
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In case of homonuclear diatomic molecules of A2 type (e.g. F2, Cl2, Br2, I2 ... etc.) the bond length, d(A-A) is given by
d(A - A) = r(A) + r(A)
d(A - A) = 2 � r(A)
r(A) = d(A-A) / 2
The above equation shows that in the case of homonuclear diatomic molecule of A2 type, the covalent radius of an atom A, r(A) is equal to one half of the inter- nuclear distance, d(A-A). Therefore, the covalent radius of an atom in a homonuclear diatomic molecule can be obtained by dividing the internuclear distance by two.
Example
1. Cl2 molecule
The value of Cl-Cl bond distance as found experimentally is 1.98�. Thus
r(Cl)= d(Cl- Cl) / 2 = 1.98/2 = 0.99�
2. Diamond
The value of d(C-C) distance as found experimentally in a variety of saturated hydrocarbons is 1.54�.
r(C) = d(C - C) / 2 = 1.54 / 2 = 0.77 �
b. Heteronuclear diatomic molecule
In case of heteronuclear diatomic molecule of AB type, bond length
d(A - B) is given by
d(A - B) = r(A) + r(B)
r(A) and r(B) are the covalent radii of A and B atoms.
Example
i) CCl4 molecule
The experimental value of d(C - Cl) is 1.76 �
Thus d(C-Cl) = r(C) + r(Cl)
r(C) = d(C - Cl) - r(Cl)
= 1.76 - r(Cl)
Thus the covalent radius of carbon atom can be calculated by subtracting the covalent radius of Cl atom from d(C-Cl) bond length. The covalent radius of Cl atom can also be obtained, provided that covalent radius of C atom is known.
ii) Sic
The experimental value of d(Si-C) is 1.93 �. Thus,
d(Si - C) = r(Si) + r(C)
r(Si) = d(Si - C) - r(C) = 1.93 - r(C) = 1.93 - 0.77 = 1.16 �
The experimental values of covalent bond length for some common homonuclear diatomic molecules are given below.
Molecule : Bond : Bond length (�)
H2 : H-H : 0.74
F2 : F-F : 1.44
Cl2 : Cl-Cl : 1.98
Br2 : Br-Br : 2.28
V
