Bond Length: Explanation and Factors

Bond length is defined as the distance between two nuclei of atoms in a covalent bond. It can also be defined as the internuclear distance when there is a maximum possible orbital overlap. This distance is not actually constant, since the atoms are constantly vibrating. Therefore it is the average inter-nuclear distance that is considered as bond length.

Similar to the trend of atomic radius, bond length decreases across a period as the atomic number increases, and increases down a group as the number of shells increases. Bond length is experimentally determined and it can be measured by techniques such as microwave spectroscopy, neutron diffraction, and X-ray diffraction.

Bond length is measured in units of picometres (pm) or Ångstrom (A°). Normally, bond lengths lie in the region of 1-2 A°. As an example, the C-C bond length is normally about 1.54 A° or 154 pm. In comparison, the shortest bond length, H-H, is only 0.74 A°.

Lengths of some bonds

Covalent Radius

Another important thing to consider is the covalent radius. One-half of the bond length between two nuclei, of similar atoms, joined together by a single covalent bond is called the covalent radius of that atom. 

image for bond length

The covalent radii can be used to predict the bond length of heteronuclear molecules, although the predicted length is often longer than the actual length. The reason being the factor of electronegativity. 

Covalent radii

Effect of Hybridization on Bond length

Another factor that influences the bond length is the hybridization of bonded atoms. sp3 bonded atoms will have a longer bond length because of more p character, as compared to sp2 or sp hybridized atoms. This also implies that bonds are shortened when there is more s-character, owing to the fact that, the s-orbital is closer to the nucleus than the p-orbital(s).

In case of multiple bonds, the bond length is shortened further by virtue of proper π-orbital overlapping for double and triple bonds. In this way, bond order also plays a role in the determination of bond length. 

Bond lengths may even vary depending on the overall molecule. For example, the C-H bond length is different in methane and chloromethane. Hence bond length is also dependent on the steric nature of substituents.

Explanation of Bond length

To understand the concept of bond length, let us take the example of a simple hydrogen molecule. When two hydrogen atoms interact, there are certain types of associated potential energy terms, namely the favorable proton-electron attraction (negative), and the unfavorable electron-electron and proton-proton repulsions (positive). 

A balance is found between these energy terms to lower the overall energy of the system in terms of stability. As the atoms approach each other to a certain distance, the net energy of the system is lowered. A bond is formed at the internuclear distance where there is lowest possible energy. This distance is known as the bond length; and the energy as bond energy.

Graphical Representation

Graph of bond length

Another aspect to be looked at is the way the energy of the system is lowered. When the atoms are being brought together, the electron of each atom begins to be influenced by the other’s nucleus, in addition to its own. The attractive forces come into play, and the electrons occupy the region between the two nuclei as the energy of the system is lowered.

However, repulsive forces between the two electrons exist and are accommodated by the spin-pairing of the electrons, which is an important feature of covalent bonding. Spinning electric charges create magnetic fields. The direction of these magnetic fields must be opposite if the electrons are to be brought together, and so spin-pairing takes place.

The third interaction is the proton-proton repulsion between the two nuclei. This is specifically the reason why the atoms cannot be brought any closer than the bond length, and an optimum distance has to be maintained between the two atoms. That optimum distance being the bond length itself.

Concepts Berg

What is bond order?

Bond order refers to the number of covalent bonds present between two atoms. It can be predicted with the help of molecular orbital theory. The higher the bond order, the shorter and stronger the bond.

What is bond length?

The average distance between the nuclei of two atoms in a covalent bond is known as bond length. It is measured in units of nanometres (nm), picometres (pm), or Ångstrom (A°). It is determined experimentally. An example is that of the C-H bond at 107pm.

Which is the shortest bond?

The shortest bond is H-H with a bond length of 74 pm.

Why are shorter bonds stronger?

In case of multiple bonds, shorter bonds correspond to better orbital overlap which in turn results in stronger bonds.

What is meant by bond angle?

Bond angle refers to the geometrical angle between two adjacent bonds. VSEPR theory can be used to predict bond angles from molecular geometries.

Which bond is longer, single or double?

Single bond is the longer one, as there is only the head-on overlap (σ bond). In case of a double bond (π), sidewise orbital overlap has to occur in addition to the head-on overlap. The atoms are brought closer for proper sidewise orbital overlap and the bond length is reduced in the process.

What are the bond lengths in CH4 and CH3+?

CH4 is sp3 hybridized, which means that it has 25% s-character and 75% p-character. The C-H bond length is 1.11 A°. 

In comparison, CH3+ is sp2 hybridized. It has 33.33% s-character and 66.66% p-character. More s-character implies that the nucleus has a better hold on the valence electrons and the valence electrons are closer to the nucleus, with reference to the s-orbital. This corresponds to a shorter bond length.

Which bond is longer, C-N or C-O?

As oxygen is more electronegative than nitrogen, the covalent radius of oxygen is smaller as compared to nitrogen. This suggests the C-O bond (1.42 A°) to be shorter than the C-N bond (1.47 A°) if other factors such as bond order are kept constant.

The same would be the case for other bonds involving a comparison of bound oxygen and nitrogen, including the O-H and N-H bonds.

Which has a greater bond length, Li2+ or Li2?

According to MOT, both Li2+ and Li2 have a bond order of 0.5. With that information alone, their bond lengths should be the same.

Which of the following has the longest bond length, C=O, N=O, C=C, or C=N?

We can predict the bond lengths with the help of covalent radii of all the relevant atoms. C has a covalent radius of 0.77 , O has 0.75 , and N has 0.74 A°. Adding these radii and taking into account the factors of electronegativity and bond order, we can determine that C=C will be the longest bond from the given options.

Are all the bond lengths the same in SF6?

Yes, all the bond lengths are 1.56 A° in SF6.

Does bond length follows this order F2 < Cl2 < Br2 < I2?

Yes, fluorine is the smallest molecule of the halogens and has the shortest bond length. This is followed by chlorine, bromine, and then iodine in order of increasing bond lengths.

Which bond length is greater, N-N or P-P?

P-P bond length is greater because phosphorus has a larger atomic radius than nitrogen.

Reference Books

  • General Chemistry Principles and Structure | Third edition, by James E. Brandy (St. John’s University, Jamaica, New York) and Gerard E. Humiston (Widener University, West Chester, Pennsylvania) – [SI version, Prepared by Henry Heikkinen (University of Maryland, USA)]
  • Chemistry | Fifth edition, by Steven S. Zumdahl and Susan A. Zumdahl (University of Illinois, Urbana Champaign, IL, USA)

Reference links

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