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# Bond Parameters

## Introduction to Bond Parameters

There are certain parameters by which a particular covalent bond is characterized. These are:

• Bond Length
• Bond Angle
• Bond Enthalpy
• Bond Order

In this article we will be discussing these parameters and how these parameters effect covalent bonding.

## Bond Length

In two bonded atoms in a molecule the average of distance between the centres of the bonding atoms is called Bond Length.

Therefore, it represents internuclear separating distance of the atoms which are bonded in a molecule as shown in Fig. No. 1 Fig. No. 1 Bond Length in a Molecule

Using various methods like electron diffraction techniques, X-ray diffraction and spectroscopic, we can calculate bond length. Each atom in bonding pair has its significance in bond length as it depends on both of atoms radii. When formation of covalent bond takes place, the contribution from each atom is called the covalent radius. The bond length in a molecule is expressed as

R= r1+r2

where R is the total bond length and r1 and r2 are the covalent radii of atoms 1 and 2 respectively. Thus, the bond length may be considered as approximate addition of the covalent radii of two bonded atoms. For example, the O-H bond length in ethanol is the sum of the covalent radii of H and O, that is,  37 + 74 = 111 pm. It is usually expressed in picometers (pm) or Angstrom units (Å).

1 pm = 10-12 m and 1 Å = 10-10m

The covalent radius is the distance between a core of atom which is in contact with the core of another atom in bonded state. In atoms bonded by covalent bonds, covalent radius is defined as half ofthe distance between the atoms. While the total size of the atom including its valence shell in a nonbonded situation is called Van Der Waals Radius. It is half of the distance between nuclei of two non-bonded atom. Covalent and Vander Waals radius of a molecule are shown in Figure below: Fig. No. 2 Covalent and van der Waals Radii

We can make the following conclusions from the above figure.

The Internuclear distance between two atoms of the same molecule is 198 pm so that

rcovalent =198/2 = 99

The Internuclear distance between two nearest neighboring atoms which are not bonded is 360 pm so that

rvander Waals = 360/2 = 180 pm

The covalent radii of some elements are given in graph below: Fig. No. 3 Covalent radii of some elements

It is clear from the graph that single covalent radii decrease from left to right across a period and increase down a group just as atomic radii do. The covalent radii of atoms taking part in a multiple bond is smaller than for an atom of the same element involved in single bond.

The average bond lengths of all the three types of bonds that is, single bonds, double bonds and triple bonds are given in Figure No. 4 and the bond lengths of some molecules are given in Figure No. 5 Fig. No. 4 Average Bond lengths of some common bond (Angstrom) Fig. No. 5 Bond Length in some common Molecules(nanometers)

## Factors affecting Bond Length

Factors upon which the Bond Length depends are:

• Bond Multiplicity
• Size of the atom

### Bond Multiplicity

With increase in bond multiplicity Bond length of a bond decreases. Thus, C ≡ C bond length is short when compared with C=C bond which even shorter than C-C bond,

that is, C ≡ C<C=C<C-C.

Similarly, N ≡ N<N=N< N-N and O=O < O-O.

### Size of the atom

As the size of the atoms increases, bond length also increases as bond length is directly proportional to size of an atom. It is also clear from the table that the bond length for a given family increases with increase in atomic number. For Example,

C-C< Si-Si< Ge-Ge

This is expected because the addition of new shells increases the distance between valence electrons and nucleus thereby increasing the size of the atom.

## Bond Angle

Bond angle may be defined as:

the average angle between the orbitals containing bonding electron pairs around the central atom in a molecule.

Units of Bond angle is degree/minute/second. Bond angle tells us about the way in which orbitals are distributed around the central atom in a molecule and therefore, determining geometry of a molecule. A lone pair of electrons at the central atom always tries to repel the shared pair (bonded pair) of electrons, because of which the bonds are displaced slightly inside resulting in a decrease of bond angle. The H-C-H bond angle in methane is 109.5°, the H-O-H bond angle in H2O is 104.5° and H-N-H bond angle in ammonia is 107 °. Fig. No.6 Bond Angle in Methane, Ammonia and Water

## Bond Enthalpy

We know that energy is released at the time of bond formation between the atoms. This means that the bonded atoms possess quite less energy when compared with individual separated atoms and this increased energy is required break the bond. This is called bond dissociation enthalpy and is measure bond strength. Bond dissociation enthalpy may be defined as:

the amount of energy required to break one mole of ends of a particular type between the atoms in the gaseous state.
It is generally expressed in terms of kJ mol-1. For example, the bond dissociation enthalpy of H-H bond in hydrogen molecules is 435.8 kJ mol-1.
H2 (g) → H (g) + H (g) aH = 435.8 kJ mol-1

Similarly, the bond dissociation enthalpy of Cl-Cl in Cl2 is 242.5 kJ mol-1 , I-I (iodine) in l2 is 151 kJ mol-1 and H-I in HI is 298.3 kJ mol-1 etc. Similarly, for molecules containing double bond like O2 and triple bond like N2, bond dissociation enthalpies are:
O2 (g) → O (g) + O (g)     ∆aH = 498.0 kJ mol-1
N2 (g) → N(g) +   N(g)     ∆aH = 946.0 kJ mol-1

So we conclude, strong bond will be formed in the molecule if it has higher bond dissociation enthalpy. The bond dissociation enthalpy of some simple bondsis given in figure no. 7 below: Fig. No. 7 Average Bond Enthalpies

Bond dissociation enthalpy depends upon two factors:

Size of the bonded atoms: Small size of the bonded atoms results in formation of stronger is the bond signifying larger value of bond dissociation enthalpy. For example, the bond dissociation enthalpy of H-H bond (435.8 kJ mol-1) is higher than the bond dissociation enthalpy of Cl-Cl bond (243.5 kJ mol-1)

Bond length: If the bond length is short, value of bond enthalpy will be large. For example, C-C bond length (154 pm) is higher when compared with C=C bond length (134 pm). Consequently, the bond dissociation enthalpy of C-C bond (433 kJ mol-1) is smaller when compared with C=C bond (619 kJ mol-1).

### Average Bond Enthalpy: Bond dissociation enthalpy of polyatomic molecules

In polyatomic molecules the average of the bond dissociation is called Average Bond Enthalpy or Just Bond enthalpy.

Let’s take case of water molecule, the average bond enthalpy required to break the two O-H bonds is different.

H2O (g) →  H (g) + OH (g)      ∆aH1° = 502 kJ mol-1°

OH (g)  →  H (g) + O (g)         ∆ aH2° = 427 kJ mol-1°

The different values of aH° concludes that the second O-H bond undergoes some changes because of the changed chemical environment. This is the reason for difference in the energy of same O-H bond in different molecules such as CH3OH (methanol), C2H5OH (ethanol), water, etc. Therefore, for polyatomic molecules, average bond enthalpy is used. It is obtained as the average of different bond dissociation enthalpies in a molecule. For Example, in water

Average Bond Enthalpy = 502+427/2 = 464.5 kJ mol-1

Thus bond enthalpy is the average or mean enthalpy needed to break bonds of a given type in one mole of the gaseous molecules. Obviously, for diatomic molecules, the bond dissociation enthalpy is same as enthalpy.

## Bond Order

Number of bonds between two atoms in a molecule is called Bond Order. For Example, bond order in H2 in which one electron pair is shared is one, in Owhere two electron pairs shared is two and in N2 in which three electron pairs are shared is three.

H-H             Bond order = 1

O=O            Bond order = 2

N≡N            Bond order = 3

C≡O             Bond order = 3

It may be noted that isoelectronic species have same bond order. For Example,

F2, O22- (18 electrons) have bond order 1

N2, CO and NO+ (14 electron) have bond order = 3

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