# Potential Energy Diagrams For Formation Of Bonds

### Potential Energy Diagram For The Formation Of A Covalent Bond

Explanation for the graph:

Consider the formation of a H2 molecule. The potential energy of one H atom in the presence of the other is plotted in the figure.

As the atoms approach one another, the electrons concentrate between the nuclei, and attraction occurs. Hence, the potential energy, U, decreases. At very short distances, the electrons would be ‘squeezed out’. As a result, the two positively charged nuclei will experience a repulsive force due to the other. This results in the curve rising as r decreases further.

At ro, the energy between the atoms is the lowest. This is point of greatest stability for the molecule. Hence, ro, known as the equilibrium spacing of atoms, gives the average separation of the atoms in the molecule. Electrostatic force at equilibriunm separation is 0.

The depth of the well gives the dissociation (or binding) energy of the molecule. This is how much energy that must be put into the system to separate the atoms into infinity, where the potential energy is zero.

An approximation to the potential energy in the vicinity of the equilibrium spacing is

$$U = \, – \frac{A}{r^{m}} + \frac{B}{r^{n}}$$

,where
A and B are constants associated with the attractive and repulsive parts of the potential energy respectively
m and n are small integers. (For ionic and some covalent bonds, the attractive term is often written with m=1)
r is the separation distance.

### Potential Energy Diagram For The Formation Of An Ionic Bond

The point of greatest stability is ro, which gives the equilibrium spacing of the atoms. However, as the atoms approach each other from a large distance, the force is initially repulsive rather than attractive. The atoms require some additional energy, known as activation energy, to be injected into the system in order to overcome the potential barrier between them. Only then will bonds start to form.

Note: The activation energy often reflects a need to break other bonds, before the one under discussion can be made. For example, oxygen (O2) and hydrogen (H2) molecules must be broken into their atoms (O and H) before they can combine to form water (H2O) molecules. The activation energy represents the amount of energy input to break up the O2 and H2 moleculoes. When the atoms combine, there will be a release of energy, much larger than what was put in initially. Oftern, this release of energy provides for the activation energy for further reaction.

### Potential Energy Diagram For The Formation Of a Van Der Waals’ Bond

The potential energy of a Van der Waals’ bond has the same general shape as that of a covalent bond. However, the binding energy would be much smaller.

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