# London Dispersion Forces

Many times, molecules deviate from ideal gas behaviour when it is in the vapour state. It usually leads to the condensation of gases to the liquid or solid states. The strong interactions between the liquid and solid states are what allows them to remain even at a high temperature. But non-polar molecules have the same characteristics, which implies that we cannot contribute the electrostatic attraction to the intermolecular interactions between them. These interactions are what we call as dispersion forces.

In the year 1930, a scientist once explained that noble gas atoms have the ability to attract another atom by some forces. The scientist that explained this theory was Fritz London. His approach was entirely based on the theory of second-order perturbation. Now let us look at the London forces definition.

### London Forces Definition

Let us answer the main question, that is what are dispersion forces. We define the London dispersion force as when two atoms or molecules are closer to each other than the weak intermolecular force between two atoms or molecules is called London dispersion forces. When the temperature is decreased, the London dispersion forces are the main reasons why the non-polar atoms or molecules condense to solids or liquids.  Even though it is weak, the dispersion forces are usually dominant.

Some common types of intermolecular forces are Hydrogen bonding, dipole-dipole, ion-ion, and London dispersion forces. We will now look at various intermolecular force's strengths.

London dispersion bond is weaker than the dipole-dipole bond, which is more fragile than H-bonding, which is, in turn, weaker than the Ion-ion bond. So, we can see that the dispersion bond is the weakest intermolecular force and Ion-ion force is the most potent force. Now that we have answered the question of what are dispersion forces, and understood the London forces definition, we will now look at some London dispersion forces examples.

### London Dispersion Forces Examples

We know that dipole in an atom is caused when there is an unequal distribution of electrons near the nucleus. When an induced dipole comes in contact with an atom or molecule, electrostatic attraction occurs due to the distortion between the atoms or molecules.

This image shows the London dispersion forces acting on a Helium atom.

Let us look at some London dispersion forces examples. Let’s consider two molecules of Chlorine.  We know that there exist strong London dispersion forces between the chlorine molecules. We also know that there exists a covalent bond between the two molecules. Therefore, due to the unequal distribution of electrons, it gives rise to the London dispersion force between two chlorine molecules.

To get a grasp of what are dispersion forces, we will look at another example. We will look at the effects of attraction of dispersion forces between two neon atoms.

This image shows the London dispersion forces acting on two Neon atoms.

### London Dispersion Forces Formula

Polarizability is the tendency of molecules to form induced dipoles. Induced dipole moment can be expressed in terms of its strength (μ).

μ = ⍺ * E

Where E is the electric field, α is the polarizability, and μ is the Induced dipole moment.

The London dispersion force formula is given as follows.

$V_{11} = \frac{3\alpha_{2} I}{4r^{6}}$

The above formula is for a single molecule. For two identical molecules, we will use the following equation.

$V_{12} = \frac{3\alpha_{1}\alpha_{2}I_{1}I_{2}}{2I_{1} + I_{2}r^{6}}$

Where r is the distance between two molecules, I is the Ionization energy, and Α is the polarizability.

### Solved Problems

Question 1) Consider two elements, Cl₂ and Br₂. Why do both turn solid when cooled? When the temperature reaches 25℃, why does Br₂ turn into liquid, while Cl₂ becomes a gas?

Answer 1) Molecules are turned into solids because of the dispersion forces acting on them. The kinetic energy of the molecules decreases when the elements are cooled, and at the same time, the dispersion forces are more than the kinetic energy. These forces are responsible for turning these elements into a solid-state.

The reason why this phenomenon occurs is that, at 25℃, the forces between the Br₂ molecules are enough to change their state and make them into a liquid state. But when it comes to the Cl₂ molecules, the London dispersion forces are weak.

Question 2) Using London dispersion forces arrange n-pentane, propane, n-butane, 2-methylpropane, in terms of their boiling points.

Answer 2) We know that the four elements are non-polar and alkanes. Therefore, the only intermolecular forces important here are the dispersion forces. As the molecular mass of the compound increases the forces between them gets more robust. Consequently, we can easily say that propane having the smallest molecular mass, will have the lowest boiling point. Similarly, since n-pentane has the largest molecular mass, the boiling point will be the highest. When we compare the two butane isomers, n-butane has a larger surface area; as it has an extended shape, therefore, its boiling point will be more than 2-methylpropane.