What is the relationship between bond length and bond strength as bond strength increases bond length?

Atoms participate in a chemical bond formation to acquire a completed valence-shell electron configuration similar to that of the noble gas nearest to it in atomic number. Ionic, covalent, and metallic bonds are some of the important types of chemical bonds. Bond energy and bond length determine the strength of a chemical bond.

Types of Chemical Bonds

An ionic bond is formed due to electrostatic attraction between cations and anions. Often, the ions are formed by the transfer of electrons from one participating atom to the other. However, these bonds do not have a defined directionality because the electrostatic force of attraction is distributed uniformly throughout the three-dimensional space.

A covalent bond is a chemical bond formed by the sharing of electron pairs between adjacent atoms. The shared pair of electrons is called the bonding pair. Covalent bonds are directional in nature.

A metallic bond is formed between two metal atoms. Metallic bonding is described by the “Electron Sea model”. Based on the low ionization energies of metals, the model states that metal atoms lose their valence electrons easily and become cations. These valence electrons create a pool of the delocalized electrons surrounding the cations over the entire metal.

Bond Energies and Bond Length

The strength of a covalent bond is measured by the energy required to break it—that is, the energy necessary to separate the bonded atoms. Separating any pair of bonded atoms requires energy. The stronger a bond, the greater the energy required to break it.

The energy required to break a specific covalent bond in one mole of gaseous molecules is called the bond energy or the bond dissociation energy. The bond energy for a diatomic molecule is defined as the standard enthalpy change for the endothermic reaction. Molecules with three or more atoms have two or more bonds. The sum of all bond energies in such a molecule is equal to the standard enthalpy change for the endothermic reaction that breaks all the bonds in the molecule.

The strength of a bond between two atoms increases as the number of electron pairs in the bond increases. Generally, the greater the number of bonds between two atoms, the shorter the bond length and the greater the bond strength. Thus, triple bonds are stronger and shorter than double bonds between the same two atoms; likewise, double bonds are stronger and shorter than single bonds between the same two atoms. When one atom bonds to various atoms in a group, the bond strength typically decreases as we move down the group.

This text is adapted from Openstax, Chemistry 2e, Section 7.1: Ionic Bonding, Openstax, Section 7.2: Covalent Bonding, Section 10.5: The Solid State of Matter, and Section 7.5. Bond Strength: Covalent Bonds.

Page 2

Skip to content

Trial ends in

Get cutting-edge science videos from JoVE sent straight to your inbox every month.

Before we go into the details explaining the bong lengths and bond strengths in organic chemistry, let’s put a small summary for these two properties right from the beginning as it stays relevant for all types of bonds we are going to talk about.

So, remember this: the shorter the bond, the stronger it is.

To understand the principles behind bond strength and bond length pertaining to organic molecules, let’s first discuss the data known for the hydrogen halides:

The bond strength increases from HI to HF, so the HF is the strongest bond while the HI is the weakest.

Why is this the case? First, looking at the periodic table, we can notice a pattern correlating the bond strength and the atomic size.

Remember that the atomic size increases down the periodic table and fluorine, for example, uses an sp3 hybrid orbital made of its second shell orbitals to form a bond with hydrogen:

The other halogens are on the 3rd, 4th, and 5th rows of the periodic table and therefore, they use larger orbital during the hybridization and consequently bond formation. If we put them next to each other, we can use this demonstration of differences in bond length to explain the bond strengths as well:

What we see is as the atoms become larger, the bonds get longer and weaker as well. Longer bonds are a result of larger orbitals which presume a smaller electron density and a poor percent overlap with the s orbital of the hydrogen. This is what happens as we move down the periodic table and therefore, the H-X bonds become weaker as they get longer.

So, keeping this in mind, let’s now see how the length and the strength of C-C and C-H bonds are correlated to the hybridization state of the carbon atom.

Bond Length and Strength in Organic Molecules

Why do you think the bond strength of the C-H bond alkane, alkene, and alkyne follows the pattern shown below?

We have concluded, in the previous part, that the bond strength is inversely correlated to the bond length, and according to this, the data suggest that the C-C bond in alkanes must be the longest as it is the weakest, and the C-C bond in alkynes is the shortest as it appears to be the strongest.

And this, in fact, is true because remember, the bond length decreases going from sp3 to sp hybridization:

To understand this trend of bond lengths depending on the hybridization, let’s quickly recall how the hybridizations occur. For the sp3 hybridization, there is one s and three p orbitals mixed, sp2 requires one s and two p orbitals, while sp is a mix of one s and one p orbitals.

Now, there is something called “s character” which is referred to the % of the s orbital initially involved in the hybridization process. For example, in the sp3 hybridization, there is a total of four orbitals – one s and three p, and out of these only one is (was) an s. Therefore, the s character of an sp3 orbital is ¼ = 25%. With the same principle, sp2 orbitals are 33%, and sp orbitals have 50% s character:

The next question is – how the s character is related to the bond length and strength. Here, you need to remember that for a given energy level, the s orbital is smaller than the p orbital. A smaller orbital, in turn, means stronger interaction between the electrons and the nucleus, shorter and therefore, a stronger covalent bond. This is why the C-C bond in alkynes is the shortest/strongest, and that of alkanes is the longest/weakest as we have seen in the table above.

The C-C vs C-H Bond Strength

The relative size of the s orbital explains also why the C-C σ bond is weaker than the C-H σ bond. And that is because the hydrogen uses a “pure” s orbital (100% s character) which is closer to the nucleus than is the sp3 orbital of carbon. As a result, the nuclei are held closer in an sp3 – s C-H bond than in a sp3 –sp3 C-C bond:

Now there are different types of C-H bonds depending on the hybridization of the carbon to which the hydrogen is attached. As in all the examples we talked about so far, the C-H bond strength here depends on the length and thus on the hybridization of the carbon to which the hydrogen is bonded.

The higher the s character in the hybrid orbital connecting the two atoms, the shorter and stronger is the C-H bond:

To summarize the information in the table, remember the bond strength order C(sp)-H > C(sp2)-H > C(sp3)-H. The reverse would be true about the bond lengths.

All these values mentioned in the tables are called bond dissociation energies – that is the energy required to break the given bond. Specifically, we are talking about the homolytic cleavage when each atom gets one electron upon breaking the bond. The bond dissociation energies of most common bonds in organic chemistry as well as the mechanism of homolytic cleavage (radical reactions) will be covered in a later article which you can find here.

The Strength of Sigma and Pi Bonds

There is one important thing we should address when comparing the strength of a single bond with a double or a triple bond. Remember, that a multiple bond consists of one σ and one or two π bonds. Now, if we compare the single bond strength with the double bond, we have 88 kcal/mol :152 kcal/mol. This is not a 1:2 ratio which indicates that σ bonds are stronger than π bonds otherwise the double bond would have been 176 kcal/mol strong (2 x 88).

Using the difference of values of C(sp2)- C(sp2) double bond and C(sp2)- C(sp2) σ bond, we can determine the bond energy of a given π bond.

1.

For each set. determine the hybridization of the relevant atoms and indicate the shorter and stronger bond:

The shorter and stronger bond is shown in red.