Question

Why is the latent heat of fusion of a substance always less than its latent heat of vaporization?

Answer 1

Hint: We know already that the latent heat of vaporization of water is more than the latent heat of fusion of ice because the kinetic energy of boiling is much larger on boiling. Since the energy required to separate the atoms from liquid to gas is much greater than just bringing the atoms a little far that is from solid to liquid.

Complete step by step solution:
We have studied that in solids, the molecules are compact due to which there is less degree of freedom. In the case of a liquid, the molecules are closely packed not as closely as in a solid, Hence a higher degree of freedom and the intermolecular forces are weaker than that of a solid. In the case of gases, the molecules are sufficiently far apart that there are little to no attractive forces. Because of this a gas can easily be compressed and take the shape of the container.
Now as you heat a solid turning it into a liquid, you increase the kinetic energy of its molecules, moving them further apart until the forces of attraction are reduced to allow it to flow freely. Keep in mind the forces of attraction still exist. Now as you heat a liquid, turning it into a gas, the kinetic energy of the molecules is increased to a point where there are no forces of attraction between the molecules.
The energy required to completely separate the molecules, moving from liquid to gas, is much greater than if you were just to reduce their separation, solid to liquid. Hence the reason why the latent heat of vaporization is greater than the latent heat of fusion.

Note:
As we all know that the latent heat is a hidden type of heat. While changing the phase the temperature is constant and hence the special heat in that particular case tends to infinity. The molecules in this case just gain enough energy to change their phase.